Understanding a user's motivations provides valuable information beyond the ability to recommend items. Quite often this can be accomplished by perusing both ratings and review texts, since it is the latter where the reasoning for specific preferences is explicitly expressed. Unfortunately matrix factorization approaches to recommendation result in large, complex models that are difficult to interpret and give recommendations that are hard to clearly explain to users. In contrast, in this paper, we attack this problem through succinct additive co-clustering. We devise a novel Bayesian technique for summing co-clusterings of Poisson distributions. With this novel technique we propose a new Bayesian model for joint collaborative filtering of ratings and text reviews through a sum of simple co-clusterings. The simple structure of our model yields easily interpretable recommendations. Even with a simple, succinct structure, our model outperforms competitors in terms of predicting ratings with reviews.
Collaborative filtering is a rich field of research. In particular, factorization models that learn a bilinear model of latent factors have proven to be effective for recommendation problems @cite_27 @cite_12 . A variety of papers have adapted frequentist intuition on factorization to Bayesian models @cite_22 @cite_0 @cite_20 @cite_24 . Of particular note are Probabilistic Matrix Factorization (PMF) and Bayesian Probabilistic Matrix Factorization (BPMF) @cite_22 , which we will compare to later. Recently, ACCAMS @cite_8 took a drastically different approach from classic bilinear models. It uses an additive model of co-clusterings to approximate matrices succinctly. While the resulting model is simple and small, its prediction quality is as good as more complex factorization models.
@cite_22 @cite_8 @cite_0 @cite_24 @cite_27 @cite_12 @cite_20
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Low-rank matrix approximation methods provide one of the simplest and most effective approaches to collaborative filtering. Such models are usually fitted to data by finding a MAP estimate of the model parameters, a procedure that can be performed efficiently even on very large datasets. However, unless the regularization parameters are tuned carefully, this approach is prone to overfitting because it finds a single point estimate of the parameters. In this paper we present a fully Bayesian treatment of the Probabilistic Matrix Factorization (PMF) model in which model capacity is controlled automatically by integrating over all model parameters and hyperparameters. We show that Bayesian PMF models can be efficiently trained using Markov chain Monte Carlo methods by applying them to the Netflix dataset, which consists of over 100 million movie ratings. The resulting models achieve significantly higher prediction accuracy than PMF models trained using MAP estimation. A popular approach to collaborative filtering is matrix factorization. In this paper we develop a non-linear probabilistic matrix factorization using Gaussian process latent variable models. We use stochastic gradient descent (SGD) to optimize the model. SGD allows us to apply Gaussian processes to data sets with millions of observations without approximate methods. We apply our approach to benchmark movie recommender data sets. The results show better than previous state-of-the-art performance. We propose a probabilistic matrix factorization model for collaborative filtering that learns from data that is missing not at random (MNAR). Matrix factorization models exhibit state-of-the-art predictive performance in collaborative filtering. However, these models usually assume that the data is missing at random (MAR), and this is rarely the case. For example, the data is not MAR if users rate items they like more than ones they dislike. When the MAR assumption is incorrect, inferences are biased and predictive performance can suffer. Therefore, we model both the generative process for the data and the missing data mechanism. By learning these two models jointly we obtain improved performance over state-of-the-art methods when predicting the ratings and when modeling the data observation process. We present the first viable MF model for MNAR data. Our results are promising and we expect that further research on NMAR models will yield large gains in collaborative filtering. Many existing approaches to collaborative filtering can neither handle very large datasets nor easily deal with users who have very few ratings. In this paper we present the Probabilistic Matrix Factorization (PMF) model which scales linearly with the number of observations and, more importantly, performs well on the large, sparse, and very imbalanced Netflix dataset. We further extend the PMF model to include an adaptive prior on the model parameters and show how the model capacity can be controlled automatically. Finally, we introduce a constrained version of the PMF model that is based on the assumption that users who have rated similar sets of movies are likely to have similar preferences. The resulting model is able to generalize considerably better for users with very few ratings. When the predictions of multiple PMF models are linearly combined with the predictions of Restricted Boltzmann Machines models, we achieve an error rate of 0.8861, that is nearly 7 better than the score of Netflix's own system.