text:
package io.citrine.lolo.transformers.standardizer

import io.citrine.lolo.api.TrainingRow
import io.citrine.lolo.linear.{GuessTheMeanLearner, LinearRegressionLearner}
import io.citrine.lolo.stats.functions.Friedman
import io.citrine.lolo.trees.classification.ClassificationTreeLearner
import io.citrine.lolo.{DataGenerator, SeedRandomMixIn}
import org.junit.Test

@Test
class StandardizerTest extends SeedRandomMixIn {

  val data: Seq[TrainingRow[Double]] =
    DataGenerator.generate(1024, 12, noise = 0.1, function = Friedman.friedmanSilverman, rng = rng).data
  val weights: Vector[Double] = Vector.fill(data.size)(if (rng.nextBoolean()) rng.nextDouble() else 0.0)
  // Creating another dataset which has 1 feature that has 0 variance.
  val dataWithConstant: Seq[TrainingRow[Double]] = data.map(_.mapInputs(x => 0 +: x))

  val weightedData: Seq[TrainingRow[Double]] = data.zip(weights).map { case (row, w) => row.withWeight(w) }
  val weightedDataWithConstant: Seq[TrainingRow[Double]] =
    dataWithConstant.zip(weights).map { case (row, w) => row.withWeight(w) }

  @Test
  def testStandardMeanAndVariance(): Unit = {
    val inputs = data.map(_.inputs)
    val inputTransforms = Standardization.buildMulti(inputs)

    val standardInputs = inputs.map(input => Standardization.applyMulti(input, inputTransforms))
    standardInputs.head.indices.foreach { i =>
      val values = standardInputs.map(_(i).asInstanceOf[Double])
      val mean = values.sum / values.size
      assert(mean < 1.0e-9, s"Standard input ${i} has non-zero mean ${mean}")

      val variance = values.map(Math.pow(_, 2)).sum / values.size
      assert(Math.abs(variance - 1.0) < 1.0e-9, s"Standard input ${i} has non-unit variance ${variance}")
    }

    val outputs = data.map(_.label)
    val outputTransform = Standardization.build(outputs)
    val standardOutputs = outputs.map(outputTransform.apply)

    val mean = standardOutputs.sum / standardOutputs.size
    assert(mean < 1.0e-9, s"Standard output has non-zero mean ${mean}")

    val variance = standardOutputs.map(Math.pow(_, 2)).sum / standardOutputs.size
    assert(Math.abs(variance - 1.0) < 1.0e-9, s"Standard output has non-unit variance ${variance}")
  }

  /**
    * Guess the mean should be invariant under standardization
    */
  @Test
  def testStandardGTM(): Unit = {
    val learner = GuessTheMeanLearner()
    val model = learner.train(data, rng = rng).model
    val result = model.transform(data.map(_.inputs)).expected

    val standardLearner = RegressionStandardizer(GuessTheMeanLearner())
    val standardModel = standardLearner.train(data, rng = rng).model
    val standardResult = standardModel.transform(data.map(_.inputs)).expected

    result.zip(standardResult).foreach {
      case (free: Double, standard: Double) =>
        assert(Math.abs(free - standard) < 1.0e-9, s"${free} and ${standard} should be the same")
    }
  }

  /**
    * Linear regression should be invariant under standardization
    */
  @Test
  def testStandardLinear(): Unit = {
    val learner = LinearRegressionLearner()
    val model = learner.train(weightedData).model
    val result = model.transform(data.map(_.inputs))
    val expected = result.expected
    val gradient = result.gradient

    val standardLearner = RegressionStandardizer(learner)
    val standardModel = standardLearner.train(weightedData).model
    val standardResult = standardModel.transform(data.map(_.inputs))
    val standardExpected = standardResult.expected
    val standardGradient = standardResult.gradient

    expected.zip(standardExpected).foreach {
      case (free: Double, standard: Double) =>
        assert(Math.abs(free - standard) < 1.0e-9, s"${free} and ${standard} should be the same")
    }

    gradient.get.zip(standardGradient.get).foreach {
      case (free, standard) =>
        val diff = free.zip(standard).map { case (f, s) => Math.abs(f - s) }.max
        assert(diff < 1.0e-9, "Gradients should be the same")
    }
  }

  /**
    * When the variance of a particular feature is 0
    *
    * @author Astha Garg
    */
  @Test
  def testStandardWithConstantFeature(): Unit = {
    val learner = LinearRegressionLearner()
    val model = learner.train(weightedDataWithConstant).model
    val result = model.transform(dataWithConstant.map(_.inputs))
    val expected = result.expected
    val gradient = result.gradient

    val standardLearner = RegressionStandardizer(learner)
    val standardModel = standardLearner.train(weightedDataWithConstant).model
    val standardResult = standardModel.transform(dataWithConstant.map(_.inputs))
    val standardExpected = standardResult.expected
    val standardGradient = standardResult.gradient

    gradient.get.toList.flatten.zip(standardGradient.get.toList.flatten).foreach {
      case (free: Double, standard: Double) =>
        assert(
          Math.abs(free - standard) < 1.0e-9,
          s"Failed test for gradient. ${free} and ${standard} gradients should be the same"
        )
    }

    // The gradient wrt the first constant feature is ill-defined without regularization
    gradient.get.zip(standardGradient.get).foreach {
      case (free, standard) =>
        val diff = free.zip(standard).map { case (f, s) => Math.abs(f - s) }.max
        assert(diff < 1.0e-9, s"Gradients should be the same. The diff is $diff")
    }

    // This test fails ~30% of the time when nRows=30, but its not clear why.
    expected.zip(standardExpected).foreach {
      case (free: Double, standard: Double) =>
        assert(
          Math.abs(free - standard) < 1.0e-9,
          s"Failed test for expected. ${free} and ${standard} should be the same"
        )
    }
  }

  /**
    * Ridge regression should depend on standardization
    */
  @Test
  def testStandardRidge(): Unit = {
    val learner = LinearRegressionLearner(regParam = Some(1.0))
    val model = learner.train(data).model
    val result = model.transform(data.map(_.inputs)).expected

    val standardLearner = RegressionStandardizer(learner)
    val standardModel = standardLearner.train(data).model
    val standardResult = standardModel.transform(data.map(_.inputs)).expected

    result.zip(standardResult).foreach {
      case (free: Double, standard: Double) =>
        assert(Math.abs(free - standard) > 1.0e-9, s"${free} and ${standard} should NOT be the same")
    }
  }

  @Test
  def testStandardClassification(): Unit = {
    val trainingData = DataGenerator
      .generate(2048, 12, noise = 0.1, function = Friedman.friedmanSilverman, rng = rng)
      .withBinnedLabels(bins = 2)
      .data

    val learner = ClassificationTreeLearner()
    val model = learner.train(trainingData).model
    val result = model.transform(trainingData.map(_.inputs)).expected

    val standardLearner = ClassificationStandardizer(learner)
    val standardModel = standardLearner.train(trainingData).model
    val standardResult = standardModel.transform(trainingData.map(_.inputs)).expected
    result.zip(standardResult).foreach {
      case (free: String, standard: String) =>
        assert(free == standard, s"Standard classification tree should be the same")
    }
  }
}


When asked whether he is concerned by the number of injuries suffered camp, he told :I 't know whether that's the case. It's no secret, however, he hopes to land the younger Lawsons and any other top players from their hometown who might want to join them. You can't Cheap NFL Jerseys Free Shipping tell by hair, but I have a nice lump under there, Millsap said. The Bills went into the season with the challenge of splitting carries between Jackson and Spiller. 3) One thing that could hamper trade-deadline movement: Mediocrity has kept more teams close enough to believe they can make a run. a 96 win, forcing a seventh and deciding game.
NHL player , 35. I can still play fearless. A lot of effort put , but the end, we http://www.officialpanthersfootballshops.com/YOUTH+JAMES+BRADBERRY+JERSEY didn't feel like this was going to work out, coach Bill Belichick told reporters, per ESPN's Reiss.
This game Cheap NFL Jerseys Free Shipping will be close and could the Mountaineers going home early. The registration donation is $7 per vehicle, or $6 with a canned good.
Fans of the Cleveland Cavaliers are for a very Cheap Jerseys For Sale long, and potentially very painful .
I think even the guys felt it after the game yesterday. The team didn't make it to a bowl at all 2011, though Gratz played well enough as a 12-game starter to garner second-team All-Big East honors from league coaches. This was a situation that shouldn't have caught Jones or any defender by surprise. 's behind conference champion . The bright lights, the unique sound of the pipe organ, the vendor yelling 'beer ', I soaked it all .
However, it Wholesale Jerseys was the scout's effusive Wholesale Jerseys praise of Richardson that stood out most mind. him or hate him, was a big part of what happened Rio. Looking at some of the excerpts that have been released, the Chairman doesn't hold anything back. 's value with the Authentic T. J. Leaf Jersey Pacers and elsewhere has been buoyed by his ability to guard Cheap Jerseys For Sale multiple positions, a benefit the evolving game. Let's say you have a comfortable lead enough categories to ride to a likely win. He said, ' is on the phone.' Why was on the phone? she asks proudly, before addressing the baby.
celebrated his 600th win as manager of the A's – tied for third-most franchise history behind and Tony LaRussa . Hayward detailed his schedule and http://www.pacersprostore.com/WOMENS-T-J-LEAF-JERSEY.html success thus far a post on his official website while also praising his team's ability to push forward his absence. Good Morning Football 's Brandt recently called Luck the NFL's forgotten superstar. When he finally — and very NFL Jerseys Paypal reluctantly — retired 1979, only and Beliveau had more goals for the Canadiens. The blocked punt that etched Steve Gleason into Saints lore and became symbolic of New Orleans' resilience the face of disaster is now immortalized a nine-foot statue outside the Superdome after a formal unveiling on a rain-soaked Friday afternoon. That's only going to make us bigger and better the longer run. No one lives forever, but I wish some of the great ones could. #78-Truex Jr. was eligible, and qualified, for up to $2 million performance bonuses, and earned additional $240 from the league – $150 for coming second voting for the Calder Trophy, and $90 for placing seventh the NHL for goals scored the regular , with 36.
7fav Tracked leader 2nd, travelled well to lead narrowly 2f out, ridden 1f out, kept on, headed final 50 yards, 2nd of 5 2l behind NFL Jerseys Paypal Silver Service at Curragh 6f hcp gf Jul. He should be a second-day bargain. writer Robert Kirkman has even stated a Reddit AMA that he's a fan of the series saying, R.R. If I wanted to, I know I could. Fifth-year senior James Bradberry Womens Jersey Pujals threw for 358 yards and a touchdown for Holy , from the Football Championship Subdivision, which led 20 late the third quarter.


text:
Cebu travel guide
View Philippines travel guide
The island-province of Cebu is a good springboard for island-hopping in the Visayas. Located in the centre of the Philippine archipelago, it offers travellers easy access to the caves and lagoons of Gato and Kalanggaman, dive spots in Mactan, Moalboal, Badian and Olango, as well as Carmen, Oslob and Argao beaches.
The region's metropolitan area is the second largest in the country and, along with its adjacent Mactan Island, has become a bustling package-tour destination. Travellers will find casinos, golf courses, shopping malls, balmy weather, sandy beaches and all-inclusive resort hotels. They should consider visiting in January, when Cebu stages the Sinulog Festival. The celebration involves singing, dancing, dazzling costumes and Christian imagery.
Cebu is also the country's oldest Spanish colonial city and has several historic landmarks. These include the original cross planted by Magellan in 1521, when he baptised the first group of Filipino natives into the Catholic faith. The cross is now housed in a roofed kiosk in Magallanes Street. Downtown Cebu is dominated by Colon Street, which is the country's oldest street and dates back to the 16th century.
Basilica Minore de Santo Nino
The Basilica Minore de Santo Nino (Basilica of the Holy Child) houses an icon of the infant Jesus. Distinguished as the country's oldest religious relic, it has miraculously survived fire and numerous catastrophes since the Portuguese explorer Ferdinand Magellan first presented it to Queen Juana of Cebu in 1521. The church itself was originally built in 1565, and rebuilt in 1602 after a fire. Its façade is a striking blend of Romanesque, neo-classical and Islamic architecture, while its interior is sumptuously decorated. Visitors will find the Santo Nino in the chapel. They can also purchase souvenirs and religious articles at a small shop, and view church artefacts in a small museum, which is located in the Pilgrim Center's basement.
Santo Nino Basilica, Cebu Philippines Department of Tourism
Located in Cebu City's wharf area, Fort San Pedro was the centre of the country's first Spanish settlement. Established in 1565, it began as a single triangular bastion, and was expanded and fortified over the next 200 years. The fort has also served a variety of purposes, seeing use as a watch-tower to counter pirate attacks in the 1700s, a prison for local rebels during the Philippine Revolution, and a US army barracks. Today, the fort has been turned into a museum park, where visitors can encounter the island's history. The small, well-preserved site often hosts cultural events, and student guides are usually on hand to show travellers around and provide background. Tours are free, though tips are appreciated.
Fort San Pedro Ramirez72
Jumalon Museum
The late lepidopterist, Professor Julian Jumalon, created this private institution, which is part museum, art gallery and miniature nature reserve. It houses his impressive butterfly collection, as well as the art he produced. Visitors usually gravitate towards the collection of unusual mosaics, which are made up of butterfly wings and depict scenes and people from Cebu. That said, the outdoor section is ordinarily rated as the attraction's highlight, where many live specimens flit about. The garden is full of plants that attract butterflies. Some species have been released into the grounds, while others have been bred in captivity. Travellers will find guides on hand. Tours are free, though tips are appreciated.
Website: www.jumalonbutterflysanctuary.com
Citrus Butterfly George Parrilla
Casa Gorordo Museum
The Casa Gorordo Museum was originally the home of the first Filipino Bishop of Cebu. Four generations of the Gorordo family lived in the house between 1863 and 1979. Today, the restored abode is a recreation of a typical, well-off Filipino home of the mid-to-late 19th century. Its furnishings include paintings, household items, antique furniture, and religious relics. Almost everything is authentic to the period. Most items lack labels, though this actually deepens the sense that visitors are exploring a genuine home, rather than a museum. Guided tours are sometimes available at the museum, but visitors should arrange their own if they'd enjoy a guide's commentary and they want guarantees. That said, just wandering the old house is fascinating. Visitors can buy small souvenirs on site.
Casa Gorordo Joe Coyle
Travellers can easily reach a number of beaches and islets from the Cebu metropolitan area. Mactan Island is one of the best options. It links to Cebu City via a bridge and is home to many resorts, most of which offer full scuba services and watersports facilities. Divers will relish exploring Kansatik's underwater mountain, and should also try Sogod and Moalboal, which are world-renowned dive destinations. Kalanggaman Island and Capitancillo Islet have tremendous coral reefs as well. Travellers should certainly visit Argao's picture-perfect beaches, given that they're only around two hours' drive outside Cebu. Animal lovers can venture to the sea-snake breeding ground, Gato Islet. Travellers should note that while the snakes are not aggressive, they are highly venomous. They should seek immediate attention if bitten. Bird watchers will enjoy Olango Island's pristine white sandy beaches.
Sunset Roy Chan
The Chocolate Hills
The Chocolate Hills are Bohol Province's most famous tourist attraction, and are widely regarded as one of the top 10 things to see in the country. Nature lovers will enjoy the area's conical hills, which number somewhere between 1200 and 1800. The geological marvels were formed from grass-covered limestone and turn chocolate-brown near the end of the dry season (April or May). At this time, they start to resemble enormous molehills. The UNESCO World Heritage Site is among the most alien landscapes travellers will encounter on earth. An excursion to the Chocolate Hills is a must for anyone on holiday in the Philippines. Travellers should note that climbing up to the viewing platform means scaling a steep stairway, which may be tiring for the unfit or the elderly. It's well worth the effort, though. The hills are particularly lovely in the early morning hours or at sunset.
Website: www.chocolatehills.net
Chocolate Hills edward musiak
The island province of Bohol lies southeast of Cebu and is one of the loveliest destinations in the Visayas island group. Travellers will find tremendous natural attractions, such as the world's rarest seashells. Animal lovers should look out for the tarsier, which is a huge-eyed, insect-eating monkey. When fully grown, it's roughly the size of a fist. Visitors will also enjoy the world-famous Chocolate Hills. The surreal series of between 1200 and 1800 hills resembles scoops of chocolate ice-cream and is Bohol's greatest natural attraction. The weathering of coral deposits formed it many millennia ago, when the land was still beneath the sea. Otherwise, visitors can look forward to the region's glorious beaches and top-class scuba-diving sites. Indeed, Panglao Island frequently graces lists of the world's top ten diving destinations.
Coconuts on Bohol georgeparrilla
Tourists will encounter a number of fascinating colonial buildings and historical attractions in the country's oldest city, Cebu. The destination's list of popular sightseeing spots includes the Basilica Minore del Santo Nino, which houses the oldest religious relic in the Philippines, and the old coastal Spanish fortress, Fort San Pedro. Travellers can also visit an ornate Taoist Temple and Casa Gorordo Museum: a restored 19th-century Filipino home.
Sun chaser will enjoy the region's magnificent white-sand beaches, while snorkelers and scuba divers can explore an enchanting underwater world. Mactan Island, Olango Island and Kansatik are all easily accessible from the city.
Cebu is also the gateway to a stunning part of the Philippines. Bohol Island lies to the southeast of the city and is home to the remarkable Chocolate Hills and Tarsier monkeys - one of the world's smallest primates. Travellers can venture to the small village of Oslob as well, and experience the deep joy of swimming with whale sharks.

redpajama_set_name: RedPajamaCommonCrawl