Combine a focused search and matching function with a massive worldwide database of users and you have Be2.com, a great forum for gay singles to find love. This is a no-nonsense site, which allows you to make your sexual orientation clear from the moment you sign up. The result is a platform which makes be2.com a gay dating site well worth using. There are some innovative features to help you get in touch with the perfect partner. There is a definite focus on finding long-lasting love and the site is designed to make it simple to navigate and maximize your chances of success. There is also a great money-back guarantee if you don't meet a requisite number of people.
Getting in touch with other members is made simple. You can use standard mail message and instant chat options. There is also a 'flirt' tool at your disposal. Meanwhile, if the whole process is a little intimidating, Be2 also provides pre-made questions to simplify things. If you want to find out a bit more about a member, just submit 5 questions to a potential match via the useful "Just Ask" feature. The result will give you a good overall picture of your compatibility. If you really want to make your profile stand out, then be2.com gives you the opportunity to add a video profile. The most outstanding feature is the personality test. More of that to come. The result though is that you will only be matched with members who are a genuinely good fit.
As any Be2 gay review will tell you, the sign-up process is the crux of the system. The very first thing you will be asked is your gender and the gender you are looking to be matched with. As a result, you are guaranteed to be matched only with gay singles. The rest of the search and matching process merely narrows down the field. You will be asked for standard personal information, such as date of birth, physical appearance, religion and attitudes to smoking, drinking, etc. However, what makes Be2.com stand out is the personality questionnaire, which is based on a psychological and scientific model. Like Zoosk, this is a site which goes beyond the standard personal questions to explore your personality. The questions take around 10 minutes to answer and ask you to rate personality traits and how you behave in a relationship. The whole model was revised in 2013 and the result is an effective system. All that is left is to upload a photo and you are free to begin your search!
Be2 really is a joy to use. The site itself was re-designed in 2013 and is now a streamlined, no-nonsense platform. The focus is on simplicity, making the platform as easy as possible to use. For a start, it is very pleasing on the eye, with a gentle mauve on cream color scheme. Direct from your personal dashboard, you have direct access to your profile, potential matches and your inbox, via tabs at the top of the page. Meanwhile, the sidebar shows you exactly who has just joined the site and gives you access to your favorites lists.
Interestingly, there are several ways to find a suitable match. Firstly, you can conduct a standard search. The quick search allows you to find someone using variables such as age and height. The advanced search widens these search terms remarkably and as a result you can look for someone based on location, ethnicity, religion and attitudes towards smoking and drinking. There are other methods to find someone too. It is well worth running a "Compatibility Report" on someone who grabs your interest. Based on your respective answers to questionnaires and quizzes, you will find out the chances of being a successful match. Meanwhile, boosting b2.com's gay dating credentials, the "Just Ask" feature is a great way to ask more detailed questions of a potential match in relation to your own identity and to work out their compatibility for yourself.
Free members can create a profile and browse the site. However, if you want meaningful functionality and real results, then you will need to become a paid member. This will allow you to contact members freely, send and receive text messages and see who has viewed your profile. Membership for 3 months costs $66.60 per month, a 6-month package will set you back $33.30 monthly and a 12-month deal costs the equivalent of $16.60 each month. However, if you are a paid member and have not got in touch with at least 10 members during your plan, then be2 offers a full refund!
This is not a dedicated gay dating site, like Compatible Partners. Nonetheless, as any Be2 gay dating review will tell you, this is a great gay dating platform. Similar to Match, this is an extensive dating site and there are more than 30million users in 37 countries. As a result, there should be plenty of gay singles out there. The search process is geared up for it. Be2 is aimed at generating serious relationships. If this is what you're after, then it might be the site for you.
Quite simply, this is a well-organized, comprehensive dating site which is a great platform for gay singles. With numerous useful features, a simple-to-use design and a massive database of users, it is well worth checking out.


Find articles about deploying and managing Office 365 Groups.
How Office 365 Groups, Planner, and Teams provide project management capabilities for organizations.
How to review and configure your Office 365 settings to control the creation of Groups within your tenant.
Deleted Office 365 Groups can now be restored for up to 30 days, including data stored in Groups-based applications such as Planner and Teams.
Microsoft is rolling out a new feature to automatically create Office 365 Groups based on managers and their direct reports. Here's how to prepare for the change.
Microsoft has announced that Site Mailboxes are being removed from SharePoint Online, and will no longer be able to be created from March 2017. Office 365 Group to provide collaboration in Office 365.
Get-O365GroupReport.ps1 v1.01 has been released with improvements and bug fixes for reporting on Office 365 Groups.
Get-O365GroupReports.ps1 is a PowerShell script for reporting on new, modified, and deleted Office 365 Groups (also known as Unified Groups).


Recently during my daily web searching and browsing for all things related to plus size fashion, I came across a new fresh face. A new plus model to the scene, from Puerto Rico named Ana Garcia. She caught my attention because she is a beautiful curvy Latina and you don't see many plus size Latina models. Also she was a runner up in the Torrid model search in Puerto Rico. I contacted Ana and she was kind enough to do a interview for the blog. Read the interview and get to know Ana along with me.
Why or how did you get into the plus model industry?
One of my future goals in Puerto Rico is to prove that being a Plus Size Model can be a beautiful thing, but in the meantime I have to start at the bottom and make my way up. First of all I have to work on my portfolio then I will knock on doors of people in the industry. Furthermore, I will never give up my dream.
How long have you been a plus model?
I consider myself as an aspiring plus size model and I've still got a lot to learn about this industry. I'm starting to work on my portfolio and the desire I have to learn and to grow is amazing. Everything about this industry puts a smile on my face every time.
What are you goals for plus modeling?
You were recently a contestant at the Torrid plus model search in Puerto Rico. Can you tell us briefly about your experience?
The experience was so amazing! Everyone in the staff was very nice. The organization, the details and the effort they put on making the girls feel so good about themselves is priceless. All of the girls chosen and not chosen were supportive and nice to each other. I would recommend this contest to any girl in a heartbeat.
Since the Torrid plus model search, have you done any other campaigns or runway shows?
My second runway show is going to be in The Curvy Revolution 2011. Here in Puerto Rico plus size modeling is not that common, but I have faith that it will change. There are so many beautiful, intelligent and talented plus size girls that are trying to get their voice heard and I know in my heart people are going to listen.
Where do you shop for trendy and stylish plus size clothes?
My style is a little laid back and casual. Here in Puerto Rico there are a few plus size stores like Torrid "Love this store". Recently, a plus size store close to my job opened called Plump Couture, I went there the other day the store and the clothes were gorgeous. But, sometimes I shop at the Mainstream stores that have plus size sections like Old Navy and Forever 21.
What is your favorite thing about being a plus size model?
My favorite thing is being able to give girls and women a positive and real image. We all are different some have bigger hips, bigger breasts while some are taller or petite, but we have to love and appreciate what we have. Sometimes we want to lose a little bit of weight or tone our bodies because with a healthy lifestyle you can enjoy who you are and you can be who you really are. Just live day by day and be grateful with what you have.
Where can we find you (Facebook, twitter or website)?
If you interested in learning more about Ana go to her facebook page. She will also be walking the runway next month at The Curvy Revolution in Las Vegas. I will also be there so I hope to meet Ana and get some shots of her on the runway. Thanks for reading and hope you enjoy the interview.
**Pictures provided by model her self, please do not use with out her permission.
Prada, one of the world's most expensive fashion brands, is making little effort to show that its goods are free of forced labour, according to a new report. An assessment of the quality replica handbags and transparency of efforts by 20 major apparel companies to safeguard against forced labour from their supply chains, undertaken by KnowTheChain, an accountability initiative, gave Prada a score of nine out of 100. The Italian luxury brand, which charges hundreds of pounds for its bags and clothing, was one of three companies that scored less than 25 out of 100. The other two were China's top shoe firm, Belle International Holdings, and prada replica Shenzhou International Group Holdings, another Chinese company. Companies were ranked by KnowTheChain on a range of indicators including auditing processes, worker recruitment and labour rights, using information provided by the brands and data available on public platforms.


1. Download and install the Android Studio.
We can create an <a> anchor hyperlink which will share a specific URL on Facebook.
For example, the following URL which share my About page on Facebook.
If you have the infinite redirect loop problem in Internet Explorer 8. Add the following header in PHP.
We can find out the Request for permissions URL of a Facebook application as we discussed previously.
The following URL is the request for permissions page of a Facebook application.
The [FB_APP_URL] is the App Namespace which is set in the Facebook application settings.
Update 2012-01-14: For OAuth 2.0 implementation, please refer to the new post.


How could it be otherwise, this week began the best dressed in the Oscars 2013 and in it a name we love by Jared: Jessica Chastain. The redheaded actress chose a Giorgio Armani with which was spectacular and with which I chose as my favorite . Will the winner or will fall behind other famous?
Naomi Watts was the one who won your votes to choose it as the best dressed of the Oscars 2013 with a new design of Giorgio Armani Privé with an asymmetrical neckline and opting for a metallic finish. To my surprise won a little red carpet level.
My second personal bet, Emmanuelle Riva has to be because he chose Lanvin and how it looked deserves any compliment, allthough the eighth penalty with your votes. To see this time if it goes any position.
The fourth name I prefer Oscar Charlize Theron and Dior dress with peplum included in pure white.
Along with Oscar saw several parties left us if anything it looks best on the red carpet at the awards. In the Vanity Fair Oscars Party had to choose. These highlighted Kate Bosworth in Giambattista Valli with a romantic short.
Miranda Kerr succeeds and where it goes is not surprising that at this event was one of the best dressed with this design long reminding Hollywood divas. Valentino design to fight for first place in the list.
We continue with the party of Vanity Fair with Lily Collins pretty good hand of Zuhair Murad with a stunning back.
This firm also saw Kate Beckinsale this time dodging inches long and successful sporting sandals together the impact of her embroidery.
Questioned for better and for worse, Nicole Richie boasted great guy with a Roberto Cavalli in the Elton John party . Good or bad in this black and white design?
Better Emma Roberts in this design by Oscar de la Renta with minimal tail?
Or Naomi Campbell with a long, tight dress in midnight blue velvet? The bearing is made of felt.
Just as Sharon Stone who chooses a design in black with embroidery and so perfect.


Scripps MD Anderson Cancer Center is a leader in caring for people with laryngeal and hypopharyngeal cancers, commonly known as throat cancers. Our oncology specialists treat these cancers with advanced therapies designed to eliminate disease and prevent recurrence, including minimally invasive surgery that uses small incisions, potentially resulting in shorter hospital stays and a faster recovery.
Laryngeal and hypopharyngeal cancers are cancers that start in the throat. Laryngeal cancer develops in the section of the throat called the larynx, also known as the voice box. The larynx contains the vocal cords and is used for speaking, breathing and swallowing. Hypopharyngeal cancer develops in the lower section of the throat (pharynx), below and behind the larynx.
Depending on the cancer type, location and stage, Scripps surgeons may perform several types of surgical treatments for laryngeal and hypopharyngeal cancer. Whenever possible, Scripps surgeons use minimally invasive robotic surgical techniques, which can mean smaller incisions, faster recovery time and less bleeding and scarring. Should you need reconstructive surgery after your treatment, count on our plastic surgeons for the expertise that has restored function and brought comfort and confidence to many patients.
Vocal cord stripping, for early-stage cancers, is when the surgeon removes superficial layers of tissue from the vocal cords.
Endoscopic laser surgery, for early-stage cancers, is when the surgeon uses an endoscope to locate a tumor and then removes it with a high-energy laser.
Cordectomy is when the surgeon removes all or part of the vocal cords. If the vocal cords are completely removed, normal speech is no longer possible.
Laryngectomy removes part or all of the larynx. The amount removed depends on the size and location of the cancer.
Supraglottic laryngectomy removes only the supraglottis, which is the upper part of the larynx above the vocal cords, and preserves normal speaking.
Hemilaryngectomy removes half of the larynx (voice box) and can partially preserve a patient's voice.
Total laryngectomy is when all of the larynx is removed. This surgery includes a tracheostomy (also known as tracheotomy), which places a permanent incision through the front of the neck to the windpipe (trachea) to help a patient breathe.
Partial or total pharyngectomy is when the surgeon removes all or part of the lower throat (pharynx) and may remove the larynx. This surgery may require a reconstructive procedure to help patients swallow.
Lymph node removal surgery, also known as neck dissection, is performed if cancer has spread from the larynx and hypopharynx to lymph nodes of the neck.
Thyroidectomy may be needed if cancer spreads to the thyroid. It may be performed to remove all or part of the thyroid gland. The patient may need hormone replacement therapy after this surgery.
3-D conformal radiation therapy allows the radiation oncologist to visualize a patient's anatomy in 3-D. The specialized software for 3-D conformal radiation therapy matches radiation doses to the size and shape of a tumor and thereby minimizes exposure to nearby tissues and organs.
Chemotherapy may be given to help shrink a large tumor before surgery, to treat cancer that cannot be removed with surgery or to treat cancer that has spread to other areas.
Chemoradiation, which combines chemotherapy and radiation, has been shown to shrink laryngeal and hypopharyngeal tumors more than either treatment alone. In addition, chemoradiation may be used instead of surgery to preserve the larynx.
As leaders in throat cancer care, we know what it takes to fight a winning battle. That's why we equip our patients with the support and resources necessary to achieve their best possible outcome. From connecting you with support groups and services to empowering you with the latest resources and research, Scripps helps you along every step of your cancer journey.


text:
Nine-year-old receives charming letter from NASA after job application
6 Aug, 2017 04:11 AM 3 minutes to read
Jack was one of the first applicants to apply, writing an adorable letter explaining why he was qualified for the job. Photo / NASA
By Matthew Wright
A courageous boy from New Jersey received a letter of support from NASA after he applied for the role of planetary protection officer.
Jack Davis, 9, applied for NASA's new position that was listed this week in hopes of finding help to protect the Earth against aliens, the Daily Mail reported.
In official terms, the position involves the assistance with the "avoidance of organic-constituent and biological contamination in human and robotic space exploration".
It adds that "space flight missions may intentionally or unintentionally carry Earth organisms and organic constituents to the planets or other solar system bodies".
Jack was one of the first applicants to apply, writing an adorable letter explaining why he was qualified for the job.
"My name is Jack Davis and I would like to apply for the planetary protection officer job," he said in the letter.
Jack Davis, 9, applied for NASA's planetary protection officer new position that was listed this week in hopes of finding help to protect the Earth against aliens. Photo / NASA
"I may be nine but think I would be fit for the job.
"One of the reasons is my sister says I am an alien also I have seen almost all the space and alien movies I can see.
"I have also seen the show Marvel Agents of Shield and hope to see the movie Men in Black.
"I am great at video games.
"I am young, so I can learn to think like an Alien."
The youngster signs off the letter giving himself the title "Guardian of the Galaxy".
Jack received this sweet letter back from NASA saying it hopes to see him there one day. Photo / NASA
The fourth grader would soon hear back from eminent Dr James L Green, the director of NASA's planetary science division.
He said: "I hear you are a 'Guardian of the Galaxy' and that you're interested in being a NASA Planetary Protection Officer. That's great!
"Our Planetary Protection Officer position is really cool and is very important work. It's about protecting Earth from tiny microbes when we bring back samples from the Moon, asteroids and Mars. It's also about protecting other planets and moons from our germs as we responsibly explore the Solar System.
"We are always looking for bright future scientists and engineers to help us, so I hope you will study hard and do well in school. We hope to see you here at NASA one of these days!"
In addition, Jack got a call from ASA's planetary research director, Jonathan Rall, at the NASA DC headquarters.
NASA has stated that while the job role "may not be in real-life what the title conjures up", it plays an important role in "promoting the responsible exploration of our solar system by preventing microbial contamination of other planets and our own".
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redpajama_set_name: RedPajamaCommonCrawl


After trying a new wash day routine last week Sunday, my hair throughout the week was quite moisturised. The first couple of days, my hair wasn't feeling its usual dryness but by the end of the week it wasn't as 'squidgy' as it usually is. It pretty much stayed at the same level throughout the week so it's something to work on. This week I avoided puffs and tried to give my hairline even more of a break. I prepped my hair in 4-5 flat twists every evening.
Next Post Protective Style 2: My First Twists!
I just wanted to ask how long you've been growing out your hair for and what product do you use when doing a twist out.
I love your style, I want to steal those looks;P lol. Your very pretty too.
Me too! That's why I love them. From morning til even bedtime, the lipstick stays put!
Oh and what lipstick do you use?
U look stunning,how do u do flat twists??


Our technologies aren't just breaking the norms. They're becoming them.
Worldwide, Westport and its affiliates have filed over 950 patent applications, relating to over 225 inventions.
And we held about 400 issued patents worldwide, including more than 90 issued U.S. patents.
Westport's extensive intellectual property (IP) portfolio gives Westport and its partners a competitive advantage. Our expertise includes: injectors (combined gaseous fuel/pilot fuel injectors and monofuel injectors), combustion chamber geometry and control strategies, engine fuel systems, cryogenic storage and delivery (cryogenic tanks and cryogenic pumps), compressors, vehicle integration, and other related technologies.
This chart shows only a portion of our full IP portfolio*—natural gas injection, engine, and combustion technology—and illustrates our strength and leadership in this market.
Based on the patent search results of publicly available data within the International Patent Classification F02, meeting the search term criteria: one of ("engine" or "combustion" or "injector" or "injection valve") and ("natural gas" or "methane" or "gaseous fuel") and in the claims, not ("fuel cell" or "turbine"). This chart includes issued or granted patents from: Argentina, Australia, Austria, Belgium, Brazil, Bulgaria, Canada, Ceuta and Melilla, China, Czech Republic, Denmark, European Patent Office Grants, Finland, France, Georgia, Germany, Greece, Hong Kong, Hungary, India, Ireland, Italy, Japan, Latvia, Malaysia, Mexico, Moldova, Monaco, Netherlands, OAPI grants, Philippines, Poland, Portugal, Romania, Russian Federation, Serbia, Singapore, Slovakia, Slovenia, South Africa, South Korea, Spain, Sweden, Switzerland, Taiwan, Tajikistan, Turkey, UK, Ukraine, USA, USSR, Yugoslavia, and pending published patent applications from: Canada, China, the European Patent Office, USA, and the World Intellectual Property Office.
Contact us to get more information about our IP licensing opportunities.


The gorgeous HOTEL was an old school house tucked up a steep Park City road, tastefully remodeled into a 12 room boutique luxury hotel. White walls, gorgeous finishes, tall ceilings, old wood floors, gorgeous chandeliers...such a gorgeous setting. The stay included your breakfast menu every morning along with anything you need. Since the hotel has limited rooms, they had the whole hotel to themselves. Can you imagine your closest friends and family all walking down to have breakfast together each morning?
Erin and Mike had hoped for snow for their wedding weekend but instead, they had a beautiful brisk day with the sun shining- a perfect day for everyone to venture out and enjoy the town. They were told to meet back at the Hotel at 4pm sharp to witness, what they thought was a "Suprise Engagement" for Erin.
Erin and Mike had kept this secret wedding from both their parents but early that afternoon Erin and Mike told Erin's parents the good news that way her mom could help her get ready. Erin had a few wedding dresses in the closet to choose from...what a dream right? She also had a few wedding shoes and some Ugg slippers to wear. I was squeeling inside over the beautiful details. She also gave her mom a peek at the wedding ring to which her mom's jaw hit the floor. The hair and makeup artist arrived and they all got ready. When it was time, Erin came down the stairs, her dad took her hand while the secret was told. Everyone turned around to see Erin in a beautiful wedding dress, everyone was floored, Mike's mom cried and the surprise was on them!!! The day couldn't have been any better.
I cannot thank Erin and Mike enough for treating me to this much-needed getaway weekend! Being a part of something this secretive and exciting was SO fun!!
Decor - A unique mix of new and old - Pottery Barn/Restoration Hardware silver candle holders, Pottery Barn candles and Pottery Barn napkins. The tall set of silver square candle stick holders were purchased from my favorite antique store in Chelan, WA. Waterford crystal toasting glasses, sourced from etsy and ebay. Silver chargers and Wexford glassware were found from endless weekends searching local thrift stores, Mike's favorite weekend activity. I loved how each charger was from a different pattern/design and I proudly polished them all. Finally simple preserved boxwood garlands purchased from BHLDN, tied it all together. We paired these items with the hotels while dishware and silver flatware. In my mind it was such a beautiful mix, and pulled off an environment for a simply elegant dinner. No bright in colors, overdone florals or centerpieces you can't see around. Rather an event that felt like we were at home with our closest family and friends, sharing stories over good food and wine.
Location Selection - While living in the area, we were walking around looking at houses, and literally stumbled upon the school house. The moment we walked in, we just knew, and I said to Mike "If we ever get married it will be HERE, it's literally perfect."
Jewelry - From my personal collection, all estate pieces purchased from Goldsmith Lucerne in Chelan, WA.
Mike's suit - JCrew, shoes - Macys, belt Nordstrom, watch - burberry from Nordstroms (let me know if you need specific brands on shoes and belt, can get those for you if so.
I have lost track of how many sessions I have done with this gorgeous family. Ever since the twins were "one" I think. Well, every session we out-do and one-up the last. I LOVE this silly family of 5. Take a look from our recent mini session here in Boise.


The '90s are alive and well in this classic reboot of the first-person-shooter game System Shock. Night Dive Studios founder Stephen Kick capitalized on grunge-era nostalgia to raise more than $1,000,000 on Kickstarter in less than a month, shattering the original goal. The game won't be ready until December, so occupy yourself with The Oregon Trail until then.


text:
// Copyright (c) Microsoft Corporation. All rights reserved.
// Licensed under the MIT License.

using System;
using System.Threading.Tasks;
using Azure.AI.FormRecognizer.Models;
using Azure.AI.FormRecognizer.Tests;
using Azure.AI.FormRecognizer.Training;
using Azure.Core.TestFramework;
using NUnit.Framework;

namespace Azure.AI.FormRecognizer.Samples
{
    /// <summary>
    /// Samples that are used in the associated README.md file.
    /// </summary>
    public partial class Snippets : SamplesBase<FormRecognizerTestEnvironment>
    {
        [Test]
        public void CreateFormRecognizerClient()
        {
            #region Snippet:CreateFormRecognizerClient
#if SNIPPET
            string endpoint = "<endpoint>";
            string apiKey = "<apiKey>";
#else
            string endpoint = TestEnvironment.Endpoint;
            string apiKey = TestEnvironment.ApiKey;
#endif
            var credential = new AzureKeyCredential(apiKey);
            var client = new FormRecognizerClient(new Uri(endpoint), credential);
            #endregion
        }

        [Test]
        public void CreateFormRecognizerClientTokenCredential()
        {
            #region Snippet:CreateFormRecognizerClientTokenCredential
#if SNIPPET
            string endpoint = "<endpoint>";
#else
            string endpoint = TestEnvironment.Endpoint;
#endif
            var client = new FormRecognizerClient(new Uri(endpoint), new DefaultAzureCredential());
            #endregion
        }

        [Test]
        public void CreateFormTrainingClient()
        {
            #region Snippet:CreateFormTrainingClient
#if SNIPPET
            string endpoint = "<endpoint>";
            string apiKey = "<apiKey>";
#else
            string endpoint = TestEnvironment.Endpoint;
            string apiKey = TestEnvironment.ApiKey;
#endif
            var credential = new AzureKeyCredential(apiKey);
            var client = new FormTrainingClient(new Uri(endpoint), credential);
            #endregion
        }

        [Test]
        public async Task BadRequestSnippet()
        {
            string endpoint = TestEnvironment.Endpoint;
            string apiKey = TestEnvironment.ApiKey;

            var credential = new AzureKeyCredential(apiKey);
            var client = new FormRecognizerClient(new Uri(endpoint), credential);

            #region Snippet:FormRecognizerBadRequest
            try
            {
                RecognizedFormCollection receipts = await client.StartRecognizeReceiptsFromUri(new Uri("http://invalid.uri")).WaitForCompletionAsync();
            }
            catch (RequestFailedException e)
            {
                Console.WriteLine(e.ToString());
            }
            #endregion
        }
    }
}

redpajama_set_name: RedPajamaGithub


text:
Gina Chua es una periodista de Singapur que se desempeña como editora ejecutiva de la startup de medios Semafor. Anteriormente fue la editora ejecutiva de la agencia de noticias Reuters. Chua es una de las periodistas abiertamente transgénero de más alto rango en los Estados Unidos.

Biografía
Nacida en Singapur, Chua asistió a la escuela secundaria en Filipinas. Estudió en la Universidad de Chicago, obteniendo una licenciatura en matemáticas, y en la Universidad de Columbia, donde obtuvo una maestría en periodismo. Se mudó a la ciudad de Nueva York en 2005. Chua transicionó a fines de 2020.

Carrera profesional
Chua trabajó en Singapore Broadcasting Corporation y Straits Times, fue reportera de The Wall Street Journal en Manila y Hanoi, y luego se desempeñó como editora en jefe de The Wall Street Journal Asia (también conocido en un momento como The Asian Wall Street Journal) y South China Morning Post. También fue editora principal de The Wall Street Journal en Nueva York.

Chua comenzó a trabajar como editora de Reuters en 2011. Fue nombrada editora ejecutiva de la agencia en abril de 2021.

Chua cofundó los Premios Sigma de periodismo de datos con Aron Pilhofer en 2020. Ha impartido clases a nivel de pregrado y posgrado, y cursos breves de capacitación sobre los modelos comerciales del periodismo, reportajes asistidos por computadora y aritmética en la Universidad de Nueva York, la Universidad de Hong Kong y la Universidad Tecnológica de Nanyang. También creó fondos para una beca para periodistas asiáticos a una maestría en reportajes económicos y de negocios en la Universidad de Nueva York.

En 2021, Chua fue nombrada ganadora inaugural del premio Impact Award de la Online News Association por "su dedicación a la innovación en la narración visual y su firme compromiso de asesorar a los periodistas y abordar los problemas estructurales de la industria".

En marzo de 2022, Chua anunció que dejaría su puesto de editora ejecutiva en Reuters para convertirse en editora ejecutiva de Semafor, una empresa emergente de medios fundada por el periodista Ben Smith y el exdirector ejecutivo de Bloomberg Media Group, Justin B. Smith.

Referencias

Alumnado de la Universidad de Chicago
Personas LGBT de Singapur
Periodistas transgénero
Escritores transgénero
Mujeres periodistas

redpajama_set_name: RedPajamaWikipedia


text:
Q: Is NodaTime compatible with NetCoreApp 1.0? I have dotnet core app that I'm working on that is cross-platform. I wanted to use Noda as a utility in my project but get the following error even tho I have nodatime defined as a dependency in my project:
 System.IO.FileNotFoundException: Could not load file or assembly 'NodaTimestrong text, Version=2.0.0.0, Culture=neutral, PublicKeyToken=4226afe0d9b296d1'. The system cannot find the file specified.
      File name: 'NodaTime, Version=2.0.0.0, Culture=neutral, PublicKeyToken=4226afe0d9b296d1'
         at project.ef.CalendarHelper.ValidateTimeZone(String timezoneTypeName)
         at project.ef.CalendarHelper.

Here are the project config files:
API PROJECT
{
  "buildOptions": {
    "preserveCompilationContext": true,
    "emitEntryPoint": true,
    "warningsAsErrors": true,
    "debugType": "portable",
  "copyToOutput": {
      "include": [
        "config.json",
        "Certificate.pfx"
      ]
    }
  },
  "dependencies": {
    "AspNet.Security.OAuth.Introspection": "1.0.0-alpha2-final",
    "AspNet.Security.OAuth.Validation": "1.0.0-alpha2-final",
    "Microsoft.AspNetCore.Diagnostics": "1.0.0",
    "Microsoft.AspNetCore.Mvc": "1.0.0",
    "Microsoft.AspNetCore.Mvc.Formatters.Json": "1.0.0",
    "Microsoft.AspNetCore.Mvc.Cors": "1.0.0",
    "Microsoft.AspNetCore.Server.Kestrel": "1.0.0",
    "Microsoft.Extensions.Configuration.CommandLine": "1.0.0",
    "Microsoft.Extensions.Configuration.EnvironmentVariables": "1.0.0",
    "Microsoft.Extensions.Configuration.Json": "1.0.0",
    "Microsoft.Extensions.Logging.Console": "1.0.0",
    "Microsoft.Extensions.Logging.Debug": "1.0.0",
    "Microsoft.EntityFrameworkCore.Design": {
        "type": "build",
        "version": "1.0.0-preview2-final"
    },
    "Microsoft.NETCore.App": "1.0.0",
    "project.ef": "1.0.0-*"
  },
  "tools": {
      "Microsoft.EntityFrameworkCore.Tools": "1.0.0-preview2-final"
  },
  "frameworks": {
    "netcoreapp1.0": {
      "imports": [ "portable-dnxcore50+net45+win8+wp8+wpa81" ]
    }
  },
  "publishOptions": {
    "include": [
      "config.json"
    ]
  },
  "runtimes": {
      "win10-x64": {},
      "osx.10.11-x64": {},
      "ubuntu.14.04-x64": {}
  }
}

EF PROJECT
{
  "dependencies": {
    "NETStandard.Library": "1.6.0",
    "Npgsql.EntityFrameworkCore.PostgreSQL": "1.0.1",
    "Npgsql.EntityFrameworkCore.PostgreSQL.Design": "1.0.1",
    "project.Internal.ERP": "1.1.0-*",
    "project.models": "1.0.0-*",
    "NodaTime": "2.0.0-alpha-*"
  },
  "frameworks": {
    "netstandard1.6": {
      "imports": [
        "dnxcore50",
        "portable-net451+win8"
      ]
    }
  }
}

A: Noda Time 1.x only targets PCLs. You may be able to get it to work with netcoreapp1.0, but I'm not going to guarantee it.
But Noda Time 2.0 targets netstandard1.1, so should be fine. That's only available as an alpha release right now, but it works fine:
project.json contents:
{
  "buildOptions": {
    "emitEntryPoint": true
  },
  "dependencies": {
    "NodaTime": "2.0.0-alpha20160729"
  },
  "frameworks": {
    "netcoreapp1.0": {
      "dependencies": {
        "Microsoft.NETCore.App": {
          "type": "platform",
          "version": "1.0.1"
        }
      }
    }
  }
}

Program.cs contents:
using System;
using NodaTime;

public class Program
{
    public static void Main(string[] args)
    {
        Console.WriteLine(SystemClock.Instance.GetCurrentInstant());
    }
}

That runs with no problems.

redpajama_set_name: RedPajamaStackExchange


text:
Soap Opera News
Bold And The Beautiful Spoilers Friday, June 14: Thomas Makes Threats – Ridge Worries About His Marriage
SpoilersThe Bold and The Beautiful
By hellodrdavis	 On Jun 13, 2019
The Bold and the Beautiful spoilers for Friday, June 14, tease that Thomas Forrester (Matthew Atkinson) will have a tough job ahead of him. He made the snap decision to keep the secret about Beth Spencer being alive from Steffy Forrester (Jaqueline MacInnes Wood), Hope Logan (Annika Noelle), and Liam Spencer (Scott Clifton). And now he'll have some work to do to make sure that the secret stays a secret.
As B&B viewers know, Florence "Flo" Fulton (Katrina Bowden), Zoe Buckingham (Kiara Barnes), and Xander Avant (Adain Bradley) also know the Beth secret, and they fully expected Thomas to tell his sister and Hope the truth.
But since Thomas decided at the last minute to keep the secret to himself, he's going to have to get to Flo, Zoe, and Xander right away and fill them in on his decision.
Bold And The Beautiful Spoilers – Trio Is Going To Be In Shock
The trio is going to be shocked to discover that Thomas wants to keep Beth's existence from Hope and Liam. They'll probably have a lot of questions, but it looks like Thomas is going to try to lay down the law. According to B&B spoilers, Thomas will threaten Flo, Zoe, and Xander and insist that they keep on keeping the secret.
Bold And The Beautiful Comings And Goings: Joe LoCicero Cast As Thomas' Nefarious Associate Vincent
Of course, for Zoe, this will be a welcome demand. She wants the secret kept because she knows that she, her father Reese Buckingham (Wayne Brady), and Flo would surely be prosecuted for their actions. She'll probably readily agree to keep a lid on Beth's existence. And Flo will probably easily succumb to Thomas' threats.
But Xander is another story. He wants the truth to come out asap, and he's going to be a bit harder for Thomas to convince. But it looks like his threats will make Xander hold on to the secret for at least a while longer, as ongoing B&B spoilers indicate that the baby switch secret is going to remain a secret for the time being.
Bold And The Beautiful Spoilers – Sees The Writing On The Wall
Meanwhile, on Friday's new episode of B&B, Ridge Forrester's (Thorsten Kaye) concerns about his marriage will deepen. The situation with Steffy, Liam, Hope, and Thomas really has Brooke Forrester (Katherine Kelly Lang) upset, and she and Ridge just don't see eye-to-eye on the situation.
As B&B viewers know, Ridge would like nothing more than to see Liam and Steffy reunite and form a cohesive family with Kelly Spencer (Chloe Teperman and Zoe Pennington) and Phoebe Forrester (River Davidson and Madeline Valdez). But he's hesitant to say so for fear of upsetting Brooke, who desperately wants Hope and Liam to be together.
#BoldandBeautiful Spoilers: Thomas Controls Beth Secret Now – Zoe And Flo's Fate In His Hands @celebratesoaps https://t.co/SwSQvW94o3
— SOS/CTS/HH (@SoapOperaSpy) June 13, 2019
And it doesn't help that Ridge's son Thomas is openly pursuing Hope, which Brooke absolutely detests. It's bound to cause more conflict between Brooke and Ridge going forward, and Ridge can surely see the writing on the wall.
In the meantime, keep up with Hollywood Hiccups for all the latest news and updates on all of your favorite daytime television shows right here.
hellodrdavis
Suzanne L. Davis (aka "hellodrdavis") is a psychologist, author, and blogger. She is a former psychology professor and litigation consultant who now writes full-time. She's been an avid daytime soaps watcher for years.
The Bold And The Beautiful Spoilers: Ridge's Ultimatum, Zoe Forced To Choose Between…
The Bold And The Beautiful Spoilers: Thomas Or Finn? Which Man Will Hope Rebound…
The Bold And The Beautiful Spoilers: Will Steffy Be Honest With Liam & Finn…
Bold And The Beautiful Spoilers: Y&R Summer's Agenda In Los Angeles Is Exposed


text:
\section{Introduction}

Linear regression is one of the most frequently studied problems in the statistical sciences. It is well known that the least squares estimator fulfill several optimality criteria under normal distribution assumptions, a result that goes all the way back to Gau\ss \  \citep{Gauss}. Likewise, it is well known that the least squares estimator is not optimal when data deviate from these assumptions. A lot of attention has been attributed to developing methods that still yield sensible regression parameters in the presence of  casewise deviations. Such casewise deviations may originate from a fraction $\epsilon$ of the data having been generated from a different distribution (outliers), or the data satisfying the linear model with a non-normal error term, such as a Cauchy or Student's $t$. In these cases, robust linear regression methods generally outperform their least squares counterpart. Many different approaches to casewise robust regression have been proposed, a good overview of which can be found in reference works \citet{Huber, MaronnaMY06,maronna2019robust,RousseeuwLeroy}.

In the bulk of the literature on robust statistics, robustness is considered to be robustness against entire cases that do not satisfy model assumptions. For a univariate predictor $\mathbf{x}=(x_1,\ldots ,x_n)^T$, this approach is plausible because it corresponds to individual elements $x_i$ either fitting the assumptions or not. Conversely, assuming that outliers are complete observations of a multivariate predictor,
thus multivariate observations where each
\textcolor{black}{entry in the observation vector}
is considered as an
outlier, may not correspond to reality. In real life, the
predictor matrix often consists of single predictors
that are measurements of different physical entities, which need not generate outliers simultaneously. Imagine, for example, each column being a sensor in a manufacturing plant. Whereas it is viable to assume multivariate interplay between these sensors to be present under normal operating conditions, each of these sensors may break down independently and therefore, generate outliers individually. Another example would be gene expression in microarray data, and there are many more. Discarding whole cases in these (and other) practical situations can cause a significant loss of information in the estimation procedure, which just like harsh downweighting of entire outliers, can be surmised to increase estimation variance.

In the light of the above, to make maximal use of the non-contaminated portion of the data, in practice it is often preferable to detect outliers on a cellwise basis instead of casewise.
\textcolor{black}{This means that single entries (cells) in the data matrix are
considered as potential outliers, and not necessarily a whole row (observation).}
Up to today, this usually implies that outlier detection is done as a separate step {\em before} the remainder of the analysis. However, any outlier is only outlying with respect to a model and therefore, such a preliminary outlier detection c.q. correction step may distort the data in a way that is inconsistent with the model. There is a large gap yet to be covered in method development on cellwise robust techniques: methods that allow to detect and correct for deviating cells in a single model consistent way. Cellwise robust regression is still a nascent field of research. In this paper, a new cellwise robust M regression estimator (CRM) is proposed. In one run, it allows to estimate regression coefficients that are robust against cellwise and casewise outliers, while also providing a map of the deviating cells. The option to construct the estimator as a cellwise robust M regression as opposed to alternative paths, such as
MCD regression \citep{Rousseeuw84}, comes from the observation that robust M regression estimators have proven to yield a very good trade-off between efficiency and robustness in simulations and applications in fields as diverse as quantitative structure--property relationships (QSPR) \citep{SS-PP}, gravimetry \citep{gravimeters},
\textcolor{black}{finance} \citep{Guerard},
chemometrics \citep{SPRM}, analytical chemistry with applications to e.g. analysis of arch\ae ological glass \citep{PRM} and meteorite samples \citep{SPRM-DA}, as well as estimation of shaping coefficients for futures trading in the electricity markets \citep{MCRM}. Note though, that S-regression has also proven a valid path in this context \citep{Oellerer_Shooting}.

Motivated by this assumption, in this manuscript the {\em cellwise robust M} (CRM) regression estimator is introduced. It consists of an iteratively reweighted least squares procedure, starting with weights derived from highly robust estimates, that both compensate for casewise vertical outliers and leverage points. Within each iteration, the SPADIMO \citep{SPADIMO} procedure is applied, detecting the cells that contribute most to outlyingness. The re-weighting scheme is then adapted to only downweight outlying cells. The resulting method thereby can deliver a highly robust estimate of regression coefficients (and intercept), and in a model consistent way, yield cellwise outlier detection. Because not as much information in the data is discarded, the method should be more efficient than a casewise robust estimator.

The article is organized as follows. In Section \ref{sec:Algo}, the CRM algorithm is described in detail. Section \ref{sec:Simulations} presents a simulation study comparing CRM to different approaches in terms of efficiency, as well as in terms of its capability to detect and downweight the correct set of outlying cells. In Section \ref{sec:Example}, the method is applied to a compelling example. Finally, Section \ref{sec:Outro} concludes.

\section{The CRM algorithm} \label{sec:Algo}

\subsection{Background}
The target of this section is to propose an estimator for the linear model that is robust against cellwise outliers, and as a by-product, yields a map of the detected outlying cells.

Let $\mathbf{X} \in \mathbb{R}^{n \times p}$ be a predictor matrix consisting of $n$ cases of $p$ predictor variables (or, if an intercept is considered, $p-1$ predictors, and the first column with ones for the intercept) and let $\boldsymbol{\beta} \in \mathbb{R}^p$ be a fixed, true vector of regression coefficients. Then, in the linear model, $n$ cases of a univariate dependent variable  $\mathbf{y}\in \mathbb{R}^n$
relate to the predictors as
\begin{equation}\label{eq:linmod}
\mathbf{y} = \mathbf{X} \boldsymbol{\beta} + \boldsymbol{\varepsilon},
\end{equation}
where the entries of $\boldsymbol{\varepsilon}$ are independent and identically distributed (i.i.d.) and where $E(\boldsymbol{\varepsilon}) = \mathbf{0}$ and $Cov\left(\boldsymbol{\varepsilon}\right) = \sigma^2 \mathbf{I}_n$. As signaled before, while the least squares estimator may be optimal under normality assumptions, robust regression methods should be the estimators of choice when outliers are expected to be in the data. Several classes of robust regression estimators exist \citep[see, e.g.,][]{RousseeuwLeroy,MaronnaMY06}). Performance analysis of robust estimators has several facets, but most prominently it comes down to analyzing how well the estimators perform in trading off robustness for statistical efficiency. Estimators that can resist a high fraction of outliers in the data, tend to have a higher variance than the corresponding maximum likelihood estimator, but that loss in efficiency need not be dramatic. Along other classes of methods, MM estimators
\citep{Yohai87} are known to perform well in terms of the robustness--efficiency trade-off and have, for that reason, been incorporated into mainstay implementations of robust regression, such as the function {\sf lmrob()} in the {\sf R} package {\sf robustbase} \citep{robustbase}.

To understand how MM estimators work, let us revert to least squares. By definition, least squares minimizes a loss function of squared residuals.
Consider a given estimator $\hat{\boldsymbol{\beta}}$ of $\boldsymbol{\beta}$. Then the $i$-th regression residual is defined as
$r_i(\hat{\boldsymbol{\beta}})=y_i - \mathbf{x}_i^T\hat{\boldsymbol{\beta}}$, where $\mathbf{y}=(y_1,\ldots ,y_n)^T$ and $\mathbf{x}_i$ represents the $i$-th row of the data
matrix $\mathbf{X}$, for $i=1,\ldots ,n$.
The least squares estimator of the regression coefficients is
given by the minimization problem
\begin{equation}\label{critLS}
    \hat{\boldsymbol{\beta}}_{\mathrm{LS}} = \mathop{\mbox{argmin}}_{\boldsymbol{\beta}}\sum_i{r_i(\boldsymbol{\beta})^2}.
\end{equation}
A more general definition is
\begin{equation}\label{critM}
    \hat{\boldsymbol{\beta}} = \mathop{\mbox{argmin}}_{\boldsymbol{\beta}}\sum_i
    \rho\left(\frac{r_i(\boldsymbol{\beta})}{\hat{\sigma}}\right) ,
\end{equation}
where $\hat{\sigma}$ is a robust scale estimator of the residuals, and
$\rho(r)$ is a function that is approximately quadratic for small (absolute) $r$,
but increases more slowly than $r^2$ for larger values of $r$. Moreover,
the inclusion of $\hat{\sigma}$ allows to get the same result if the response is
rescaled. This definition (\ref{critM}) is referred to as the class of M-estimators \citep{Huber}.
Not all choices of $\rho$ have practical relevance, but when diligently chosen, M-estimators can have a bounded influence regarding deviating, or even erratic values in
the response, and therefore they can be robust against vertical outliers.
The robustness properties of the resulting estimator derive back to $\rho$, or more precisely, to its derivative $\psi=\rho '$. More particularly, common practicable choices leading to robust estimators for $\psi$, such as the Huber, Hampel redescending or Hampel-Rousseeuw hyperbolic tangent functions \citep{Hampel}, depend on a set of parameters. The resulting robustness properties then become a function of the corresponding parameters. In this paper, the Hampel redescending function is chosen, with a similar motivation as to why the MM estimation path is pursued. The Hampel function, in its reweighting representation, is given by:
\begin{equation}
\label{eq:hampel}
w_H(r) = \left\{\begin{matrix
1 & & |r| \leq Q_1 \\
\frac{Q_1}{|r|} & & Q_1 < |r| \leq Q_2 \\
\frac{Q_3 - r}{Q_3 -Q_2} \frac{Q_1}{|r|} & \mbox{if} & Q_2 < |r| \leq Q_3 \\
0 & & Q_3 < |r|\end{matrix}
 \right. .
\end{equation}
It depends on a set of three parameters $Q_1$, $Q_2$ and $Q_3$. When applied to regression residuals, which for standardized data can be assumed to be standard normally distributed, sensible values for the parameters are the $0.95$, $0.975$ and $0.999$ quantiles of the standard normal distribution.

It can be shown that in practice, calculating M-estimators directly through optimizing \eqref{critM} is equivalent to running an iteratively re-weighted least squares (IRLS) procedure \citep{Green}. However, the resulting estimator will in general only be
robust against outliers in the response, i.e.~vertical outliers. In order to
achieve robustness also against outliers in the explanatory variables (leverage points),
it is important to select a robust starting estimator $\hat{\boldsymbol{\beta}}_0$.
This can be done by taking a highly robust but inefficient S-estimator \citep{RY1984},
combined with a robust M-scale estimator $\hat{\sigma}$ \citep{Huber}. The resulting robust
{\em MM} estimator inherits the $50\%$ breakdown point of the S-estimator, and
has tunable efficiency \citep[see][for more details]{MaronnaMY06}.

In this paper, robust MM estimators are now being generalized to cellwise robustness. In order to achieve this, the IRLS procedure will need a way to be able to detect which cells are outlying. Exactly for this purpose, the method of Sparse Directions of Maximal Outlyingness (SPADIMO) \citep{SPADIMO} has recently been developed. SPADIMO is a method that identifies which variables contribute most to a case being detected as an outlier. By incorporating SPADIMO into the IRLS reweighting scheme, and only downweighting cells flagged by SPADIMO, the method will be cellwise robust.

\subsection{The Algorithm}

The overarching algorithm described in this section can be seen as a way to convey cellwise robustness properties to any given robust regression method. However, robust regression methods being significantly different by construction, many details in the algorithm need to be adapted to the specific regression method. As outlined before, we have opted to develop the algorithm specifically as a cellwise extension to robust MM regression, inspired by the good robustness--efficiency tradeoff which have been shown in theory, simulation and practical
applications \citep{MaronnaMY06}.

MM regression estimators consist of two steps: at first, a highly robust initial estimate is calculated, which conveys its high breakdown point to the entire procedure. Then, the highly robust initial estimate is used as a plug-in estimator for an M-estimator, which in practice means that the initial estimate is used as a starting point for an algorithm to achieve higher efficiency by iterative reweighting. How this concept can be used to obtain an efficient and highly robust cellwise regression method is presented below in detail, and an overview of the essential steps is given in Algorithm 1.

\paragraph{Initial outlier detection}

Prior to starting the algorithm, the data should be centered and scaled. Since the data may still contain both cellwise and casewise outliers at that point, the preprocessing should be done robustly, with estimators that have a 50\% asymptotic breakdown point. Good choices for centering and scaling the data robustly would be the $L_1$ median and the $Q_n$ scale estimator \citep{RousseeuwQn}, respectively, but viable alternatives to these choices exist. Several algorithms to compute the $L_1$ median are available, and a good comparison is given in \citet{L1median_algos}.

In the spirit of MM estimation, an initial, highly robust regression estimator is used to identify suspected casewise outliers. Here we use the MM estimator as starting point, but a good alternative would be the LTS estimator, which is also known to be an efficient and robust regression estimator \citep{fastLTS}.
Based on the robust MM regression estimator, observations are flagged as casewise outliers if their absolute standardized residuals exceed the 95\% quantile of the standard normal distribution. For each of the casewise outliers, it now has to be determined if they truly are casewise outliers, or if there is a subset of cells in them which make them outlying. In order to investigate which variables contribute most to the outlyingness of the casewise outliers, the SPADIMO \citep{SPADIMO} algorithm is applied. For those cases that contain cellwise outliers, outlying variables are imputed as if they were missing cells (see Algorithm 2). To impute the values in the outlying cells, the two nearest neighbors are detected based on the {\em clean} cells in the case. This means that, when a set $\mathcal{C}$ of $q < p$ variables have been detected as cellwise outliers in the case, the two nearest neighbors are determined in the $\mathbb{R}^{p-q}$ variate space spanned by the variables in $\{1,\ldots,p\} \backslash \mathcal{C}$. The nearest neighbor search is only carried out in the subset of cases that are not outlying, i.e.~have case weights equal to one. The cellwise outliers in the case under consideration are now being imputed with the corresponding column means of the two nearest neighbors. This imputation procedure generates modified cases with smaller residuals, which increases their case weights and by consequence, the valuable information in the non-outlying variables contributes to the model. This imputation step is not only a part of the algorithm initiation, but will also take place in each IRLS step. As such, the initial outlier detection step yields a first value of estimates for the regression coefficients $\hat{\boldsymbol{\beta}}$, as well as a first set of weighted and imputed data $\mathbf{X}_\omega$ and $\mathbf{y}_\omega$ for the explanatory
variables and the response, respectively.

\paragraph{Iterative modeling and outlier detection.}

Once an initial highly cellwise robust estimate of the regression coefficients has been obtained, a more efficient estimate can be found by using this estimate as a starting value into an iteratively reweighted least squares (IRLS) routine. Starting from the initial $\hat{\boldsymbol{\beta}}$, $\mathbf{X}_\omega$ and $\mathbf{y}_\omega$, the first IRLS update will consist of least squares regression estimates
based on the weighted data $\mathbf{X}_\omega$ and $\mathbf{y}_\omega$. In each step, the residuals are calculated, and casewise outliers are detected based on the magnitude of the residuals. For those cases flagged as outliers, variables contributing to outlyingness are found by SPADIMO, and for the cases that are not entirely outlying, the outlying cells are imputed as before. Now the residuals can be recalculated based on the newly imputed data and a new set of weights is computed. The procedure continues until
the estimated regression coefficients stabilize.

The complete algorithm is as follows:
\begin{itemize}
\item Apply robust regression (e.g.~MM regression) on the original
observations $\mathbf{x}_i$
and $y_i$, for $i=1,\ldots ,n$, to obtain the initial estimator $\hat{\boldsymbol{\beta}}$.
\item Run Algorithm 1, starting with the original observations
and the initial regression estimator.
\item Run Algorithm 1, starting with the resulting weighted and imputed
data $\mathbf{X}_{\omega}$ and $\mathbf{y}_{\omega}$ from the previous
point, and with
the least squares estimator $\hat{\boldsymbol{\beta}}$ from a regression
using these data.
\item Run Algorithm 1 with the weighted data as a result from the previous
point, and the corresponding least squares estimator, and repeat
until the mean absolute difference of the subsequent regression estimates
is smaller than a tolerance bound (e.g.~0.01).
\end{itemize}
The {\sf R} code implementations of CRM and SPADIMO are available in the {\sf R} package {\sf crmReg} at
\begin{center}
github.com/SebastiaanHoppner/CRM.
\end{center}

\begin{minipage}{\textwidth}
\noindent\makebox[\linewidth]{\rule{\textwidth}{0.4pt}}
\textbf{ Algorithm 1:} CRM Iteratively reweighted least squares algorithm.

\vspace{-2mm}
\noindent\makebox[\linewidth]{\rule{\textwidth}{0.4pt}}

\begin{enumerate}
\item Calculate residuals based on the estimator $\hat{\boldsymbol{\beta}}$:
\begin{equation*}
r_i= y_i - \mathbf{x}_i^T \hat{\boldsymbol{\beta}} \quad \text{ for } i \in \{1,...,n\}
\end{equation*}
\item Detect outliers as cases that satisfy
\begin{equation*}
     \frac{|r_i|}{c \mathop{\mbox{med}}_j |r_j|} > z_{0.95} ,
\end{equation*}
where $c=1.4826$ for consistency of the MAD, and $z_{0.95}$ is the 0.95 quantile
of the standard normal distribution.
\item For each outlying case:
\begin{itemize}
\item Apply SPADIMO and obtain outlying variables.
\item If not all variables contribute to outlyingness: Impute values in outlying variables as in Algorithm 2.
\item Denote the newly imputed data matrix by $\tilde{\mathbf{X}}$.
\end{itemize}
\item Update residuals
\begin{equation*}
\tilde{r}_i= y_i - \tilde{\mathbf{x}}_i^T \hat{\boldsymbol{\beta}} \quad \text{ for }
i =1,...,n.
\end{equation*}
\item Calculate case weights by the Hampel weight function (\ref{eq:hampel}),
\begin{equation*}
    \omega_i = w_H\left( \frac{|\tilde{r}_i|}{c \mathop{\mbox{med}}_j |\tilde{r}_j|} \right)
\end{equation*}
with $c$ as in Step 2.
\item
\textcolor{black}{
Let $\boldsymbol{\Omega}=\mbox{Diag}(\sqrt{\omega_1},\ldots ,\sqrt{\omega_n})$ be a diagonal matrix with the case weights as diagonal elements.
}
Update the (imputed) data as
\begin{equation*}
\mathbf{X}_{\omega} =\boldsymbol{\Omega} \tilde{\mathbf{X}}
\qquad \mbox{ and } \qquad
\mathbf{y}_{\omega} =\boldsymbol{\Omega} \mathbf{y} .
\end{equation*}
\end{enumerate}
\noindent\makebox[\linewidth]{\rule{\textwidth}{0.4pt}}
\text{}
\end{minipage}

\begin{minipage}{\textwidth}
\noindent\makebox[\linewidth]{\rule{\textwidth}{0.4pt}}
\textbf{ Algorithm 2:} CRM imputation algorithm.

\vspace{-2mm}
\noindent\makebox[\linewidth]{\rule{\textwidth}{0.4pt}}

\begin{enumerate}
    \item Let $i$ be the index of an outlying case ${\mathbf{x}}_i$.
    \item Let $\mathcal{C}$ be the set of $q < p$ variables detected as cellwise outliers in ${\mathbf{x}}_i$.
    \item Detect the two nearest neighbors ${\mathbf{x}}_{k_1}$ and ${\mathbf{x}}_{k_2}$ of the outlier ${\mathbf{x}}_i$ in the subspace $\{1,\cdots,p\} \backslash \mathcal{C}$ and only among observations ${\mathbf{x}}_j$ with $\omega_j = 1$.
    \item Impute outlying cells $\tilde{x}_{iq} = ({x}_{k_1q} + {x}_{k_2q})/2$ with $q\in\mathcal{C}$.
\end{enumerate}
\noindent\makebox[\linewidth]{\rule{\textwidth}{0.4pt}}
\text{}
\end{minipage}

\section{Simulation study} \label{sec:Simulations}

Cellwise robust estimation is a fairly recent development in the statistical sciences. Up to our knowledge, there is no report of a cellwise robust M-type regression estimator. With an emphasis on cellwise outlier detection, the {\em Detecting Deviating Data Cells} (DDC) method has been proposed \citep{Rousseeuw_DDC}. At this point, it is noted that DDC has been designed with the purpose to yield reliable cellwise outlier detection, {\em even when $\mathit{> 50\%}$ of the cases contain outlying cells}. The CRM method proposed here will not be robust against contamination of more than half of the data. While it does not offer the latter advantage, it does yield model consistent cell weights in combination with an increased statistical efficiency when compared to casewise robust regression methods.

In this simulation study, the performance of CRM applied to the robust coefficient estimator of an MM regression is compared to conventional MM regression, MM regression combined with DDC, ordinary least squares (OLS) regression and OLS regression combined with DDC. The simulation study establishes that CRM, as a method that intertwines cellwise robustness properties with estimating regression coefficients for the linear model in a model consistent way, significantly outperforms application of a model agnostic detection method for cellwise outliers (DDC), followed by either a classical or robust regression estimator.

\subsection{Simulation setting}

The data for the simulation study are generated from a $p$-dimensional multivariate normal distribution with center $\boldsymbol{\mu}=(0,\dots,0)^T$ and covariance matrix $\boldsymbol{\Sigma}$. The covariance matrix is a matrix of zeros, with ones in the diagonal and 0.5 in the first off-diagonal, so $\boldsymbol{\Sigma}_{i, i}=1$ for $i=1, \ldots, p$, $\boldsymbol{\Sigma}_{j, j+1}=\boldsymbol{\Sigma}_{j+1, j}=0.5$ for $j=1, \ldots, p-1$ and $\boldsymbol{\Sigma}$ is zero elsewhere. The number of variables is set to $p=50$ and $n=400$ cases are generated, resulting in the data matrix $\mathbf{X}\in\mathbb{R}^{n\times p}$.

Let $\boldsymbol{\beta}$ be a vector of length $p$ of random values from a standard normal distribution, normalized to length 10 and the intercept $\beta_0 = 10$. The error term $\boldsymbol{\epsilon}$ is a vector of length $n$ of random values from a normal distribution with mean 0 and standard deviation 0.5.

Then, the response is generated for clean data as follows:
\begin{equation}
    \mathbf{y} = \mathbf{1}_n\beta_0 + \mathbf{X}  \boldsymbol{\beta} + \boldsymbol{\epsilon},
\end{equation}
so the clean data consists of $(\mathbf{y}, \mathbf{X})$ and the regression coefficients are $(\beta_0, \boldsymbol{\beta})$. A pairwise scatterplot of the response variable
$\mathbf{y}$ and the first four predictor variables in $\mathbf{X}$ is shown in Figure \ref{fig:pairs_clean_data}.
\begin{figure}[t]
\centering
\includegraphics[width=0.6\textwidth]{pairs_clean_data}
~
\vspace*{-5mm}
\caption{Pairwise scatterplot of the response variable $\mathbf{y}$ and the first four predictor variables in $\mathbf{X}$.}
\label{fig:pairs_clean_data}
\end{figure}

\subsection{Adding contamination}
\label{sec:contam}

Contamination is added to the data matrix $\mathbf{X}$, and the contaminated matrix is denoted as $\mathbf{X}^c$. For the contamination we randomly select a fraction of $r=5\%$ of the observations in $\mathbf{X}$, so $r \cdot n=20$ rows of $\mathbf{X}$ are randomly selected. These $20$ observations will be contaminated and are called casewise outliers.
\textcolor{black}{
Here, the fraction of contamination is fixed; note that in Section~\ref{sec:breakdown}, the effect of the fraction of contamination will be investigated.
}
Let $I^c\subset\{1, \ldots, n\}$ denote the random subset of 20 selected case indices. To generate cellwise outliers, for each selected case $i\in I^c$, $\check{r}=10\%$ of the predictor variables are randomly picked. So for each casewise outlier, $\check{r} \cdot p=5$ randomly selected cells will be contaminated. For each $i\in I^c$, let $J_i^c\subset\{1, \ldots, p\}$ denote the subset of 5 selected variable indices. The total number of contaminated cells in $\mathbf{X}^c$ will be $r\cdot \check{r}\cdot n\cdot p=100$.

Cellwise contamination in variable $j$ is achieved by adding to its mean value $\overline{x}_j$, $k=6$ times the standard deviation $s_j$ of variable $j$ plus a random value $e$ of the standard normal distribution. The contaminated matrix is $\mathbf{X}^c$ with
\[x^c_{ij}=\overline{x}_j + ks_j + e = \overline{x}_j + k\sqrt{\frac{1}{n-1}\sum_{l=1}^{n}(x_{lj} - \overline{x}_j)^2} + e\]
for all $i\in I^c$ and $j\in J^c_i$. The contaminated data consists of $(\mathbf{y}, \mathbf{X}^c)$ where a casewise outlier is considered an observation which has contaminated cells. Figure \ref{fig:pairs_contaminated_data} shows a pairwise scatterplot of the response variable $\mathbf{y}$ and the first four predictor variables in $\mathbf{X}^c$. The casewise outliers are in red and the uncontaminated cases are in blue.
\begin{figure}[t]
	\centering
	\includegraphics[width=0.6\textwidth]{pairs_contaminated_data}
	~
\vspace*{-5mm}
	\caption{Pairwise scatterplot of the response variable $\mathbf{y}$ and the first four predictor variables in $\mathbf{X}^c$. The casewise outliers are in red and the uncontaminated cases are in blue.}
	\label{fig:pairs_contaminated_data}
\end{figure}

\textcolor{black}{
Section~\ref{sec:varyk} will also contain simulation results where $k$ is varied within a certain range.
}

\subsection{Regression methods}

The following linear regression methods have been fit to the contaminated data $(\mathbf{y}, \mathbf{X}^c)$: CRM (with MM regression as a starting estimate), simple MM regression and OLS regression. The following parameter settings for the CRM regression estimation were used: the maximal number of iterations was set to 100, the relative tolerance for converging the regression coefficients was set to 0.01, the outlyingness factor for SPADIMO was set to 1.5; SPADIMO sparsity was allowed to vary as $\eta \in \{0.1,0.2,\cdots,0.9\}$ \citep{SPADIMO}. The authors  also suggest these settings as the default values in the \texttt{R} implementation.

For the methods that are sequential combinations of DDC with regression methods, the workflow goes as follows. At first, the Detect Deviating Cells (DDC) method is applied to the contaminated data matrix $\mathbf{X}^c$ , which returns a DDC-imputed matrix, further denoted $\mathbf{X}^{DDC}$. Then, MM and OLS regression are fit to $(\mathbf{y}, \mathbf{X}^{DDC})$.

\subsection{Evaluation}

Four different criteria are assessed to evaluate the relative performance of the three approaches.

At first, the most obvious performance criterion for any regression method is predictive performance on independent test data. To evaluate the prediction performance, the mean squared error of prediction (MSEP) is calculated over the set of uncontaminated cases:
\begin{equation}\label{eq:msep}
\text{MSEP}= \frac{1}{n_{clean}}\sum_{i \in I}(\hat{y}_i-y_i)^2
\end{equation}
where $I$ contains the indices of clean, uncontaminated cases ($I$ is the complementary set of $I^c$) and $n_{clean}$ is the number of uncontaminated cases.

Secondly, it is interesting to know how much the individual regression coefficients, estimated by the three methods, deviate from the truth. To assess bias for the individual regression coefficients, the mean absolute error (MAE)
\begin{equation}\label{eq:mae}
\text{MAE}=\frac{1}{p}\sum_{j=1}^{p}|\hat{\beta}_j-\beta_j|
\end{equation}
is reported.

CRM and DDC each generate an imputed matrix of $\mathbf{X}^c$, denoted as $\mathbf{X}^{imp}$. In the case of DDC, $\mathbf{X}^{imp}=\mathbf{X}^{DDC}$. It is very informative to compare how close to the true values each of these methods come when imputing the cellwise outliers. We report the performance of each imputed matrix $\mathbf{X}^{imp}$ as the root mean squared error of imputation (RMSEI) between the simulated uncontaminated matrix $\mathbf{X}$ and imputation of CRM and DDC:
\begin{equation}
\text{RMSEI}(\mathbf{X}^{imp}, \mathbf{X})=\sqrt{\frac{1}{np}\sum_{i=1}^{n}\sum_{j=1}^{p}(x_{ij}^{imp} - x_{ij})^2}
\end{equation}

Finally, it is an interesting question to investigate the quality of identification of cellwise outliers by CRM. The latter is reported as:
\begin{itemize}
    \item the {\em recall} (also called hit rate or true positive rate): of all cellwise outliers, how many have actually been detected as outliers (and therefore imputed) by CRM
    \item the precision: of all cells that were flagged as outliers by CRM, how many actually were cellwise outliers
\end{itemize}

\subsection{Results}

In what follows, the simulation results will be shown, illustrating the results according to the four evaluation criteria described in the previous section.
Each result reported is the aggregate across hundred repeats. These aggregates are illustrated as boxplots  in Figures \ref{fig:boxplot_MSEP}, \ref{fig:boxplot_MAE}  and \ref{fig:boxplot_RMSEI_Precision_Recall}. The average result for each method is printed at the bottom and the best result is shown in bold.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.7\textwidth]{boxplot_MSEP}
~
\vspace*{-5mm}
\caption{\label{fig:boxplot_MSEP} Boxplot of MSEP for each of the regression methods. The average result for each method is printed at the bottom where the best result is shown in bold.}
\end{figure}

From Figure \ref{fig:boxplot_MSEP}, one can derive that DDC based imputation as a preprocessing step to regression methods does not improve predictive performance. In fact, just applying least squares regression without DDC preprocessing predicts better. However, due to the presence of outliers, both robust regression methods, CRM and MM,
clearly outperform least squares. In terms of predictive power,
Figure~\ref{fig:boxplot_MSEP} is reassuring in the sense that CRM performs equally well as the robust benchmark method, MM regression.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.7\textwidth]{boxplot_MAE}
~
\vspace*{-5mm}
\caption{\label{fig:boxplot_MAE} Boxplot of MAE for each of the regression methods.}
\end{figure}

Regarding bias in the regression coefficients, Figure \ref{fig:boxplot_MAE} shows that, not unexpectedly, the OLS regression coefficients are most biased in the presence of cellwise outliers. However, again applying DDC as a preprocessing step prior to either OLS or MM regression, performs much worse than casewise or cellwise robust M regression.
The MAE for CRM regression is slightly smaller than that of plain MM regression,
and thus CRM has a slightly higher statistical efficiency than
its casewise counterpart.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.7\textwidth]{boxplot_RMSEI_Precision_Recall}
~
\vspace*{-5mm}
\caption{\label{fig:boxplot_RMSEI_Precision_Recall}(Left) Boxplot of RMSEI for CRM and DDC. (Right) Precision and recall of detected cellwise outliers by CRM.}
\end{figure}

The subplots in Figure \ref{fig:boxplot_RMSEI_Precision_Recall} illustrate CRM's performance at imputing the true values for the cellwise outliers. In this respect, CRM beats DDC by a wide margin (left subplot). This is in line with CRM having a better predictive performance and a lower bias in the regression coefficients. Essentially, this tells us that much of CRM's superior performance shown in Figures \ref{fig:boxplot_MSEP} and \ref{fig:boxplot_MAE} can be attributed to it yielding a much more truthful intermediate imputation. Finally, the right panel in Figure \ref{fig:boxplot_RMSEI_Precision_Recall} shows that CRM imputation does well detecting and imputing cells that are cellwise outliers in reality, but it may sometimes impute a few too many.

On average it took 11.5 seconds to execute the CRM algorithm across the hundred repeats. The execution times were measured on an Intel core i5 with 2.7 GHz and 8 GB RAM.

\subsection{Simulation results for varying magnitude of contamination}
\label{sec:varyk}

\textcolor{black}{
The way how the data cells were contaminated was described in Section~\ref{sec:contam},
where the magnitude of the contamination was controlled by the parameter $k$ as a
multiple of the standard deviation of the respective variable.
In this section we report simulation results when this parameter is varied
as $k\in\{0, 1, 2, \ldots, 8\}$, and thus we focus on the effect where the cells
are getting more and more extreme, starting from the variable average.
Figures~\ref{fig:MSEP_MAE}--\ref{fig:precision_recall} present the average
results across 10 simulation replications.
}

\textcolor{black}{
The results in Figure~\ref{fig:MSEP_MAE} indicate that already the situation
$k=0$, where the cells are replaced by the column means, creates outliers which
are identified by CRM and MM regression, as well as by DDC. There is clearly a
strong effect on the prediction error (MSEP) and on the quality of the parameter
estimates (MAE) of the non-robust OLS estimator
if the contamination gets more extreme. All other estimators do not show a
clear effect when $k$ is varied. However, Figures~\ref{fig:RMSEI_curves} and
\ref{fig:precision_recall} provide more insight: increasing $k$ leads to higher
precision and recall for CRM. In other words, CRM can only correctly identify the
outlying cells (and not declare others as outliers)
if they are outlying clearly enough. With $k=0$, precision and
recall are still very low. On the other hand, the resulting error from imputation
(RMSEI) for CRM is in the same range for $k$ varying from 0 to 6, and
only for bigger $k$ it increases slightly, maybe due to an overfit effect,
but is still clearly smaller than that of DDC.
}

\begin{figure}[htbp]
\centering
\includegraphics[width=0.49\textwidth]{MSEP_curves.pdf}
\hfill
\includegraphics[width=0.49\textwidth]{MAE_curves.pdf}
~
\vspace*{-5mm}
\caption{\label{fig:MSEP_MAE} \textcolor{black}{Average MSEP (left) and
MAE (right) for each of the regression methods for different values of $k$, controlling the magnitude of the outlyingness.}}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[width=0.5\textwidth]{RMSEI_curves.pdf}
~
\vspace*{-5mm}
\caption{\label{fig:RMSEI_curves} \textcolor{black}{Average RMSEI for CRM and DDC for different values of $k$, controlling the magnitude of the outlyingness.}}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[width=0.65\textwidth]{precision_recall2.pdf}
~
\vspace*{-5mm}
\caption{\label{fig:precision_recall} \textcolor{black}{Average precision (left) and average recall (right) of detected cellwise outliers by CRM for different values of $k$, controlling the magnitude of the outlyingness.}}
\end{figure}

\subsection{Simulation results for breakdown}
\label{sec:breakdown}

\textcolor{black}{
In the simulation settings considered so far, the fraction of contamination has
been fixed at 5\% (see Section~\ref{sec:contam}). It will now gradually be increased, while keeping all other parameters unchanged (here, $k=6$ is chosen again).
Thus, more and more out of the 400 observations are contaminated, where
in each observation 10\% of the cells are randomly being picked for contamination.
Figure~\ref{fig:breakdown} shows the average of the results for MAE from all
previously considered regression methods, starting from no contamination, up to
50\% (in steps of 5\%). This reveals the breakdown behavior of the methods.
The OLS estimator is the most efficient when no contamination is present, but its
bias increases quickly when more and more contamination is added.
The DDC-based methods are almost not affected by the amount of contamination, because
DDC is highly robust, but they lead to a comparably large bias for small percentages of contamination. MM-regression and CRM
behave very similarly, but CRM seems to have a slightly smaller bias. Finally, note that the robustness
behavior of both methods depends on tuning parameters; in case of CRM this depends
on the parameters of the Hampel function, which could be adjusted if necessary.
}

\begin{figure}[htbp]
\centering
\includegraphics[width=0.6\textwidth]{MAE_breakdown.pdf}
~
\vspace*{-5mm}
\caption{\label{fig:breakdown} \textcolor{black}{Breakdown behavior of the different
regression methods: the fraction of contamination (10\% in each observation) is
increased from 0 to 50\%.}}
\end{figure}

\section{Real data example} \label{sec:Example}

The target of this analysis is to have a predictive model for cholesterol based on the nutrients contained in individual products. The data were taken from the Swiss nutrition data base 2015 \citep{SNT}. The original data set consists of nutrients on more than 40 components and 965 generic food products. We will focus on the first 193 products which do not contain any missing values and consider the variables in Table \ref{tab:nutrients_variables} where \verb|cholesterol| is the response variable. Since all of these 6 variables are skewed right, they were logarithmically transformed first.

\begin{table}[htbp]
\centering
\caption{Variables of the nutrients data.}
\label{tab:nutrients_variables}

\vspace*{2mm}
\begin{tabular}{l l}
\hline
 Variable & Description   \\ \hline
\verb|cholesterol| & cholesterol in milligram per 100g edible portion  \\
\verb|energy_kcal| & energy in kcal per 100g edible portion   \\
\verb|protein| & protein in gram per 100g edible portion  \\
\verb|water| & water in gram per 100g edible portion  \\
\verb|carbohydrates| & carbohydrates in gram per 100g edible portion  \\
\verb|sugars| & sugars in gram per 100g edible portion  \\
\hline
\end{tabular}
\end{table}

These data are a good example of data where one would expect the cellwise robust estimation technique to outperform the casewise one. While it is variable to assume a multivariate interplay between these variables in real life systems, these variables are measured independently. Moreover, biological effects can generate deviating behavior independently. It is therefore plausible to assume the necessity for multiple regression and corresponding multivariate effects taking place between the inputs, yet the mechanisms that generate outliers can be assumed to be largely independent.

The estimates of the regression coefficients by CRM are given in Table \ref{tab:nutrients_coefficients}. It took around 1 second to apply the CRM algorithm on this dataset. CRM indicates 30 out of 193 food products as casewise outliers having at least one contaminated outlying cell. The results are plotted as a heatmap in Figure \ref{fig:nutrients_heatmap}, where the 30 outliers are represented as rows and each contaminated/outlying cell is shown as a colored box. The anomalous cells, whose values are deviating either upwards or downwards, are colored red or blue, respectively.
It can be seen that some food products have a lot of anomalous nutrient values, whereas others only have an atypical value for a few cells. Figure \ref{fig:nutrients_heatmap_imputed} contains the nutritional data of the 30 anomalous food products where the deviating cells have been imputed by CRM. The blue cells are replaced with larger values while the red cells are imputed with smaller values (according to CRM). \textcolor{black}{A more saturated color refers to bigger differences
between the imputed and the original data values.}

\begin{table}[htbp]
\centering
\caption{Estimated regression coefficients of the nutrients data by CRM.}
\label{tab:nutrients_coefficients}

\vspace*{2mm}
\begin{tabular}{l r}
\hline
Variable & Estimated coefficient  \\ \hline
\verb|(Intercept)| & -33.73173  \\
\verb|log.energy_kcal| &  3.62970  \\
\verb|log.protein| &  0.98341  \\
\verb|log.water| & 3.78561  \\
\verb|log.carbohydrates| & 0.05336 \\
\verb|log.sugars| & -0.10999 \\
\hline
\end{tabular}
\end{table}

\begin{figure}[htbp]
\centering
\includegraphics[width=1\textwidth]{nutrients_heatmap.pdf}
~
\vspace*{-5mm}
\caption{Heatmap of outliers detected by CRM in the nutrients data. The red and blue boxes indicate the contaminated cells.}
\label{fig:nutrients_heatmap}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[width=1\textwidth]{nutrients_heatmap_imputed2.pdf}
~
\vspace*{-5mm}
\caption{Heatmap of outliers detected by CRM in the nutrients data. The red and blue boxes indicate the cells imputed by CRM, \textcolor{black}{and higher
saturation of the color refers to bigger differences to the original data}.}
\label{fig:nutrients_heatmap_imputed}
\end{figure}

A 10-fold cross validation is conducted on the nutrients data set, using
\textcolor{black}{CRM as well as OLS and MM regression, also in the version where
outliers are first replaced with the DDC method (DDC-OLS and DDC-MM).}
Figure \ref{fig:nutrients_crossvalidation2} shows that CRM clearly outperforms MM regression
\textcolor{black}{as well as the DDC-MM method}
in terms of the $10\%$ trimmed root mean squared error of prediction (RMSEP).
\textcolor{black}{
Note that trimming makes the evaluation measure robust against the
outliers~\citep{maronna2019robust}.
As Figures \ref{fig:nutrients_heatmap} and \ref{fig:nutrients_heatmap_imputed} show,
CRM only imputes the cellwise outliers, which often just amount to a single cell per case. This implies that CRM can process up to 80\% more relevant information for the outlying cases when compared to MM regression, that downweights these entire cases, some of them even to zero. Because CRM retains more uncontaminated information, it allows to make more accurate predictions.}
\textcolor{black}{There is, however, only a smaller difference between CRM
and OLS or DDC-OLS. It seems
that the outliers in the explanatory variables are not acting as bad leverage points,
and correcting them by DDC even leads to a slightly poorer prediction performance
for OLS regression. The imputation by CRM on the other hand seems much more
appropriate. Even though the predictive performance is comparable to OLS,
CRM has the advantage that it produces heatmaps of the outlying cells and the
values that they have been imputed with, see Figure~\ref{fig:nutrients_heatmap_imputed}}.
These can be of great value to the practitioner, since they allow to analyze which cells deviate per case and understand the outlier generating mechanism(s).

\begin{figure}[htbp]
\centering
\includegraphics[width=0.7\textwidth]{nutrients_crossvalidation2.pdf}
~
\vspace*{-5mm}
\caption{Boxplot of $10\%$ trimmed RMSEP values from 10-fold cross validation for each of the regression methods.}
\label{fig:nutrients_crossvalidation2}
\end{figure}

\section{Conclusions and outlook} \label{sec:Outro}

Cellwise robust M regression has been introduced as a regression method that is robust to vertical outliers and both cellwise and casewise and leverage points. Intrinsically, the method detects cells that are deviating {\em with respect to the linear model} and imputes them with more model consistent values. While CRM may not be the first method to detect deviating cells, it is the first to do so in a model consistent way for a linear model. This offers the practitioner a combined advantage of having a robust fit that reliably fits the majority of the data and producing a heatmap of suspected deviating cells, as well as model based imputations. Compared to casewise robust estimators, CRM will retain a larger fraction of uncontaminated data cells. Depending on the data, this fraction can be substantially larger. Therefore, the resulting fit is closer to the underlying model that generates the data, and the procedure is more efficient.

A simulation study has shown that CRM can generally be assumed to perform on par with a casewise robust estimator in terms of predictive power; an example prediction cholesterol from other nutrients has shown, though, that real life cases {\em can} be found for which CRM does outperform the casewise robust estimator. The simulation study has also shown that when a linear model can be assumed to have generated the data, detecting deviating cells and imputing them by CRM is a much better idea than using technique agnostic of the linear model, such as DDC, prior to regression.
\textcolor{black}{Also alternatives to DDC, for example kNN-based imputation methods,
would suffer from the same problem that they
ignore the underlying model.}
Finally, the simulation study has highlighted as well that CRM is slightly more efficient than MM at estimating individual regression coefficients.

 On a casewise basis, there is widespread consensus that outliers are only outlying with respect to a model, and therefore need to be detected by robust estimators for the corresponding model. Few experts will assume that there exists a generic {\em data cleaning} estimator that can generically detect all outliers, regardless of which model is being estimated. This has led to over forty years of research on robust statistics, that has produced robust counterparts for virtually the entire arsenal of classical statistical estimators. However, on a cellwise basis, the few approaches in the literature, such as DDC, seem to be going for generically detecting cellwise outliers. DDC has practical merit: it can be applied to data sets that contain over 50\% of casewise outliers, for which CRM would break down. That said, the majority of data sets containing cellwise outliers do not contain them in a majority of cases. In the latter situation, we argue that it is better to construct a model consistent cellwise robust estimator. The simulation study and example have corroborated this claim.

The introduction of CRM is a first step that opens the door to an entire class of model consistent cellwise robust estimators. Just like for casewise robust statistics, we would like to open up the field and see development starting on other cellwise robust statistics, such as cellwise robust principal component analysis, cellwise robust partial least squares, or cellwise robust canonical correlation analysis, just to name a few.

Another topic for further research would be inference. It has been shown that Wald type inference can be applied to MM-estimators \citep{Koller}; these results have been incorporated into the \texttt{R} package \texttt{robustbase}. It will be a promising topic of research to extend these results to the cellwise setting. Note that while analytical results on inference for the CRM parameters are still to be generated, the practitioner can always resort to the robust bootstrap, which can be computed fast \citep{FRB}.

\section*{Acknowledgments}

\textcolor{black}{The authors are grateful to two anonymous reviewer. Their suggestions
and remarks led to a substantially improved manuscript.}

\bibliographystyle{plainnat}

redpajama_set_name: RedPajamaArXiv


Caught the flu? A new app on Facebook might tell you who you probably got it from.
Down with the sniffles or the chills? While the Department of Health (DOH) says we've reached the end of the Philippines' official flu season, many people may still be feeling under the weather, given the chilly temperature, the lowest we've experienced in years. This is because of the northeast monsoon and the tail-end of a cold front. Expect the cold weather to extend well into February.
As a response to the alarming flu rise in the U.S., (more than 40 states have reported a widespread increase in flu activity), the DOH has released an advisory to the public, urging people to be wary of fever-like symptoms, including sore throat and cough. Children, pregnant women, the elderly and people with heart, kidney or lung-related problems, in particular, were indicated as most prone to the flu.
Said DOH Secretary Enrique Ona, "Influenza can be a very serious disease. It can lead to hospitalization or death". Thus, people are still urged to still be vigilant about their hygiene (proper washing of hands), coughing and sneezing etiquette (covering the mouth and nose), as well as social distancing (avoiding possibly flu-infected people, as well as steering clear of crowded places).
Speaking of which, the Facebook team recently teamed up with healthcare product company Help Remedies to come up with an app to tell you who might have infected you with the flu, or who to avoid if you aren't.


Dennis and Gnasher Unleashed: The Ultimate Dennis Quiz!
How much do you know about Dennis's adventures in Dennis and Gnasher Unleashed? Find out by taking this mega quiz!
In Episode 2, 'Dare Dennis', which of these adults doesn't greet Dennis in town?
Later on, what type of sausage do Dennis and Gnasher launch?
Ain't nothing but a hot dog!
In Episode 4, 'Raiders of the Lost Sweetie', where does Dennis get his stripey Tongue Destroyer sweet from?
In Episode 5, 'Escape from Azkabash', how does Dennis's gran hurt her foot?
In that same episode, how does Dennis escape the classroom?
Also in Episode 5, What happens at the end of the Beanotown Brawny Bean Race?
In Episode 6, 'Griller Thriller', how does Dennis find Walter on the bridge?
In Episode 8, 'Night of the Living Veg', what does the winning team get for growing the biggest vegetable?
How does Dennis catch Walter cheating?
He leaves the shop price tags on!
He's caught stealing them from Aldi!
What smoothie ingredient does Dennis hate?
In Episode 9, 'The Hamazing Hamsterman', which hamster behaviour does Dennis show first?
What happens to the hamster's Numskulls?
How does Dennis get into Wilbur's lab?
In Episode 10, 'Prank Wars', what does Dennis say his nickname is?
According to Ralf, who else in Dennis's family has the 'Prank Force'?
In Episode 12, 'The Fan', which grown-up joins the Dinmakers?
Who almost replaces Dennis and the Dinmakers at their gig?
In Epsiode 13, 'Screwtop Spudswap', where does Dennis think Paul took the professor's body?
In the Episode 14, 'Are We There Yeti?', where do Dennis and his friends hide the hairy beast?
In Episode 15, 'Super Paul', what does Dennis call the toaster?
How do Dennis, Rubi and JJ get into the factory later in that story?
In Episode 16, 'The Wonder Sausage', what's the name of Dennis's super cool new best friend?
In Episode 17, 'Jurassic Bark', how does Dennis defeat the tank?
In 'The Great Beanotown Bake Off' (Episode 19), how does Dennis prepare to make the perfect pie for Pieface?
In Episode 20, 'Why So Clonely', what happens to clones when a certain amount of time has passed?
Competition: Win a Gnasher Backpack!


text:
Alfred Godet, né le  à Neuchâtel et mort le  à Neuchâtel, est un professeur et conservateur suisse.

Biographie
Alfred Godet est le fils de Charles-Henri Godet, botaniste et professeur à l'Académie de Neuchâtel. De son père, il hérite d'un goût pour les excursions alpines et les courses à travers la campagne. Il fait ses classes au Collège latin de Neuchâtel puis aux auditoires (qui remplacent l'Académie) et il est membre de la société de Belles-Lettres. Alors qu'il se destine au métier d'architecte, Alfred Godet est contraint, en raison de sa myopie, de changer de métier. Pendant près de huit années, il est précepteur, suivant les familles de ses élèves de l'Allemagne à l'Angleterre en passant par la Bohême.

Soucieux de regagner sa terre natale, Alfred Godet s'installe à Neuchâtel en 1874 et devient professeur particulier. Peu après, en 1878, il épouse Sophie Delachaux, fille du pasteur Constant Delachaux. Afin de subvenir aux besoins de son jeune ménage, Alfred Godet passe, à plus de trente ans, son brevet d'enseignant. Il devient alors maître de latin puis enseignant à la 1ère secondaire des garçons et à l'école de commerce. Féru d'histoire et d'archéologie neuchâteloises, il est l'auteur de nombreux travaux et dessins publiés dans la revue le Musée neuchâtelois (au comité de laquelle il est entré en 1887). Alfred Godet collabore aussi à divers ouvrages, dont le Neuchâtel pittoresque de Philippe Godet, son cousin, et La Suisse au  de Paul Seippel. Alfred Godet est aussi membre de la Commission fédérale des monuments historiques et membre de la Société française d'archéologie.

En 1886, Alfred Godet devient sous-conservateur du Musée historique de Neuchâtel (aujourd'hui Musée d'art et d'histoire) avant de devenir, à la mort d'Auguste Bachelin, conservateur à son tour.

Publications (non exhaustif)
 Alfred Godet, « Les poêles à moulures polychromes et monochromes de notre canton », Musée neuchâtelois, 1886, p. 149-158, p. 182-191.
 Alfred Godet, « Causerie sur les gaufres et les gaufriers », Musée neuchâtelois, 1887, p. 14-19, p. 33-38, p. 69-77.
 Alfred Godet, « L'orfèvrerie artistique dans le Pays de Neuchâtel aux  et s », Musée neuchâtelois, Neuchâtel, 1889, p. 149-156, p. 184-192, p. 215-219.
 Alfred Godet, « Nos industries neuchâteloises : les cartes à jouer », Musée neuchâtelois, 1890, p. 149-190.
 Alfred Godet, Les chansons de nos grand'mères, Neuchâtel, Attinger, 1890-1892.
 Alfred Godet, « Samuel-Ferdinand Gallot, lithographe neuchâtelois (1774-1854) », Musée neuchâtelois, Neuchâtel, 1896, p. 53-55.
 Alfred Godet, « Un tableau religieux du  au Landeron », Musée neuchâtelois, Neuchâtel, 1897, p. 308-310.
 Alfred Godet, « Notice sur le Musée historique de Neuchâtel », Musée neuchâtelois, Neuchâtel, 1898, p. 149-161.
 Alfred Godet, « Les pipes du  et du  », Anzeiger für schweizerische Altertumskunde, Zürich, 1898, n° 4, p. 7.
 Alfred Godet, « La révolution des 16, 17 et  à Couvet », Musée neuchâtelois, Neuchâtel, 1899, p. 161-170.
 Alfred Godet, « Iconographie du cinquantenaire et du tir fédéral de Neuchâtel 1898 », Musée neuchâtelois, 1899, p. 53-63, p. 80-89, p. 117-125, p. 142-149.

Notes et références

Bibliographie
 Auguste Châtelain, « Alfred Godet », Musée neuchâtelois, Neuchâtel, 1905, p. 107-122.
 C. Brun (éd.), Dictionnaire des artistes suisses, Frauenfeld, Huber, vol. 1, 1905, p. 596.

Liens externes

 Notice Alfred Godet dans le Dictionnaire historique de la Suisse

Conservateur suisse de musée
Naissance en novembre 1846
Naissance à Neuchâtel
Décès en novembre 1902
Décès à Neuchâtel
Histoire du canton de Neuchâtel
Personnalité scientifique neuchâteloise
Personnalité neuchâteloise


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Origin of the totem of the wolf.
Origin of the wolf totem.
Lockport, N.Y. : Union Print. and Pub. Co., c1884, c1883.
Scanned from a CIHM microfiche of the original publication held by Brock University, St. Catharines.
"Dedicated to the memory of Joinstaga, from whom many legends of the almost forgotten past were obtained by the author."


Because this is how I imagine people accepting their awards.
1. My day job is to keep a group of preschool children in order, and provide fun activities and opportunities for them to grow as people. On a daily basis, I have to guide young children in learning how to problem solve, resolve differences with other children, and find ways to keep them active and entertained, especially when it is becoming clear that they are getting bored. I think I can keep a few thousand adults in line for a few hours.
2. Which brings me to my next point: I am creative and inventive, which is what I would need to be in order to keep those adults entertained. My plan is to provide activities to keep the energy going, especially during the commercial breaks. There would be all sorts of games and art supplies available -- and smocks, of course, to keep all of their clothes in mint condition. The best thing about all of these activities is that everyone is a winner!
3. It is also good to let you know that I am a plateful of classy with a side of fun -- please note that the above photo is my fun side. I'm not going to lie, I do burp, but I know how to keep it professional. Curse words are not in my vocabulary when on network television, and I have excellent posture while wearing Spanx. My fun side is the part of the meal that everyone looks forward to, like fries. It's the part of me that likes to laugh, tell jokes, and be silly. I should probably mention that this side of me is actually super sized -- I do work with children for a living.
4. I can sing, dance, and act, or at least that's what my elementary music teacher would tell you from my clearly amazing performance as one of the people of the Emerald City in our school's production of The Wizard of Oz. I am known to break out into random song and dance performances be it a popular tune, or one that I've made up about putting on my shoes. While I may not be the next Judy Garland, I can be highly entertaining.
I have learned many things from working with children including the fact that everyone has impossible dreams, but no one has the right to crush them. Everyone that is part of Oscar night has had impossible dreams, and on that special night their dreams are validated despite how many times they have been crushed. Yes, the reasons for my being the next Oscar host may be rather silly, but I'd be lying to myself and you if I didn't say that a little party of me secretly wants to be the host of The Oscars.


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