You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Existing collaborative ranking based recommender systems tend to perform best when there is enough observed ratings for each user and the observation is made completely at random. Under this setting recommender systems can properly suggest a list of recommendations according to the user interests. However, when the observed ratings are extremely sparse (e.g. in the case of cold-start users where no rating data is available), and are not sampled uniformly at random, existing ranking methods fail to effectively leverage side information to transduct the knowledge from existing ratings to unobserved ones. We propose a semi-supervised collaborative ranking model, dubbed S @math COR , to improve the quality of cold-start recommendation. S @math COR mitigates the sparsity issue by leveraging side information about both observed and missing ratings by collaboratively learning the ranking model. This enables it to deal with the case of missing data not at random, but to also effectively incorporate the available side information in transduction. We experimentally evaluated our proposed algorithm on a number of challenging real-world datasets and compared against state-of-the-art models for cold-start recommendation. We report significantly higher quality recommendations with our algorithm compared to the state-of-the-art.

Cited Abstract(s):
[1]: Consider a typical recommendation problem. A company has historical records of products sold to a large customer base. These records may be compactly represented as a sparse customer-times-product who-bought-what" binary matrix. Given this matrix, the goal is to build a model that provides recommendations for which products should be sold next to the existing customer base. Such problems may naturally be formulated as collaborative filtering tasks. However, this is a one-class setting, that is, the only known entries in the matrix are one-valued. If a customer has not bought a product yet, it does not imply that the customer has a low propensity to potentially be interested in that product. In the absence of entries explicitly labeled as negative examples, one may resort to considering unobserved customer-product pairs as either missing data or as surrogate negative instances. In this paper, we propose an approach to explicitly deal with this kind of ambiguity by instead treating the unobserved entries as optimization variables. These variables are optimized in conjunction with learning a weighted, low-rank non-negative matrix factorization (NMF) of the customer-product matrix, similar to how Transductive SVMs implement the low-density separation principle for semi-supervised learning. Experimental results show that our approach gives significantly better recommendations in comparison to various competing alternatives on one-class collaborative filtering tasks.

[2]: Users typically rate only a small fraction of all available items. We show that the absence of ratings carries useful information for improving the top-k hit rate concerning all items, a natural accuracy measure for recommendations. As to test recommender systems, we present two performance measures that can be estimated, under mild assumptions, without bias from data even when ratings are missing not at random (MNAR). As to achieve optimal test results, we present appropriate surrogate objective functions for efficient training on MNAR data. Their main property is to account for all ratings - whether observed or missing in the data. Concerning the top-k hit rate on test data, our experiments indicate dramatic improvements over even sophisticated methods that are optimized on observed ratings only.

[3]: Advanced and effective collaborative filtering methods based on explicit feedback assume that unknown ratings do not follow the same model as the observed ones (). In this work, we build on this assumption, and introduce a novel dynamic matrix factorization framework that allows to set an explicit prior on unknown values. When new ratings, users, or items enter the system, we can update the factorization in time independent of the size of data (number of users, items and ratings). Hence, we can quickly recommend items even to very recent users. We test our methods on three large datasets, including two very sparse ones, in static and dynamic conditions. In each case, we outrank state-of-the-art matrix factorization methods that do not use a prior on unknown ratings.

[4]: A fundamental aspect of rating-based recommender systems is the observation process, the process by which users choose the items they rate. Nearly all research on collaborative filtering and recommender systems is founded on the assumption that missing ratings are missing at random. The statistical theory of missing data shows that incorrect assumptions about missing data can lead to biased parameter estimation and prediction. In a recent study, we demonstrated strong evidence for violations of the missing at random condition in a real recommender system. In this paper we present the first study of the effect of non-random missing data on collaborative ranking, and extend our previous results regarding the impact of non-random missing data on collaborative prediction.
Substantial evidence for violations of the missing at random condition in recommender systems is reported in [2] and it has been showed that incorporating an explicit model of the missing data mechanism can lead to significant improvements in prediction performance.The first study of the effect of non-random missing data on collaborative ranking is presented in [4] . [1] an EM algorithm to optimize in turn the factorization and the estimation of missing values. Recently, in [3] a novel dynamic matrix factorization framework that allows to set an explicit prior on unknown values is introduced. However their algorithm requires a careful setting of the prior rating to be practical.