Restricted Boltzman Machines (RBMs) have been successfully used in recommender systems. However, as with most of other collaborative filtering techniques, it cannot solve cold start problems for there is no rating for a new item. In this paper, we first apply conditional RBM (CRBM) which could take extra information into account and show that CRBM could solve cold start problem very well, especially for rating prediction task. CRBM naturally combine the content and collaborative data under a single framework which could be fitted effectively. Experiments show that CRBM can be compared favourably with matrix factorization models, while hidden features learned from the former models are more easy to be interpreted.
Another matrix factorization based model is the regression-based latent factor model (RLFM). RLFM simultaneously incorporate user features, item features, into a single modeling framework. Different from @cite_18 , where the latent factors' learning phase and mapping phase are separated, a Gaussian prior with a feature-base regression was added to the latent factors for regularization. RLFM provided a modeling framework through hierarchical models which add more flexibility to the factorization methods.
@cite_18
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Multiview representations reveal the fundamental attributes of the studied instances from different perspectives. Some common perspectives are reviewed by multiple views simultaneously, while some specific ones are reflected by individual views. That is, there are two kinds of properties embedded in the multiview data: 1) consistency and 2) complementarity. Different from most multiview learning approaches only focusing on either consistency or complementarity, this paper proposes a novel semisupervised multiview learning algorithm, called partially shared latent factor (PSLF) learning, which jointly exploits both consistent and complementary information among multiple views. In PSLF, a nonnegative matrix factorization (NMF)-based formulation is adopted to learn a compact and comprehensive partially shared latent representation, which is composed of common latent factors shared by multiple views and some specific latent factors to each view. With the learned representations of multiview data, we introduce a robust sparse regression model to predict the cluster labels of labeled data. By integrating the NMF-based model and the regression model, we obtain a unified formulation and propose a multiplicative-based alternative algorithm for optimization. In addition, PSLF can learn the weights of different views adaptively according to the reconstruction precisions of data matrices. Our experimental study indicates different multiview data that contains consistent and complementary information in different degrees. In addition, the encouraging results of the proposed algorithm are achieved in comparison with the state-of-the-art algorithms on real-world data sets. Recommender problems with large and dynamic item pools are ubiquitous in web applications like content optimization, online advertising and web search. Despite the availability of rich item meta-data, excess heterogeneity at the item level often requires inclusion of item-specific "factors" (or weights) in the model. However, since estimating item factors is computationally intensive, it poses a challenge for time-sensitive recommender problems where it is important to rapidly learn factors for new items (e.g., news articles, event updates, tweets) in an online fashion. In this paper, we propose a novel method called FOBFM (Fast Online Bilinear Factor Model) to learn item-specific factors quickly through online regression. The online regression for each item can be performed independently and hence the procedure is fast, scalable and easily parallelizable. However, the convergence of these independent regressions can be slow due to high dimensionality. The central idea of our approach is to use a large amount of historical data to initialize the online models based on offline features and learn linear projections that can effectively reduce the dimensionality. We estimate the rank of our linear projections by taking recourse to online model selection based on optimizing predictive likelihood. Through extensive experiments, we show that our method significantly and uniformly outperforms other competitive methods and obtains relative lifts that are in the range of 10-15 in terms of predictive log-likelihood, 200-300 for a rank correlation metric on a proprietary My Yahoo! dataset; it obtains 9 reduction in root mean squared error over the previously best method on a benchmark MovieLens dataset using a time-based train test data split. Collaborative filtering (CF) has been widely employed within recommender systems to solve many real-world problems. Learning effective latent factors plays the most important role in collaborative filtering. Traditional CF methods based upon matrix factorization techniques learn the latent factors from the user-item ratings and suffer from the cold start problem as well as the sparsity problem. Some improved CF methods enrich the priors on the latent factors by incorporating side information as regularization. However, the learned latent factors may not be very effective due to the sparse nature of the ratings and the side information. To tackle this problem, we learn effective latent representations via deep learning. Deep learning models have emerged as very appealing in learning effective representations in many applications. In particular, we propose a general deep architecture for CF by integrating matrix factorization with deep feature learning. We provide a natural instantiations of our architecture by combining probabilistic matrix factorization with marginalized denoising stacked auto-encoders. The combined framework leads to a parsimonious fit over the latent features as indicated by its improved performance in comparison to prior state-of-art models over four large datasets for the tasks of movie book recommendation and response prediction. We propose a novel latent factor model to accurately predict response for large scale dyadic data in the presence of features. Our approach is based on a model that predicts response as a multiplicative function of row and column latent factors that are estimated through separate regressions on known row and column features. In fact, our model provides a single unified framework to address both cold and warm start scenarios that are commonplace in practical applications like recommender systems, online advertising, web search, etc. We provide scalable and accurate model fitting methods based on Iterated Conditional Mode and Monte Carlo EM algorithms. We show our model induces a stochastic process on the dyadic space with kernel (covariance) given by a polynomial function of features. Methods that generalize our procedure to estimate factors in an online fashion for dynamic applications are also considered. Our method is illustrated on benchmark datasets and a novel content recommendation application that arises in the context of Yahoo! Front Page. We report significant improvements over several commonly used methods on all datasets. Data often comes in the form of an array or matrix. Matrix factorization techniques attempt to recover missing or corrupted entries by assuming that the matrix can be written as the product of two low-rank matrices. In other words, matrix factorization approximates the entries of the matrix by a simple, fixed function---namely, the inner product---acting on the latent feature vectors for the corresponding row and column. Here we consider replacing the inner product by an arbitrary function that we learn from the data at the same time as we learn the latent feature vectors. In particular, we replace the inner product by a multi-layer feed-forward neural network, and learn by alternating between optimizing the network for fixed latent features, and optimizing the latent features for a fixed network. The resulting approach---which we call neural network matrix factorization or NNMF, for short---dominates standard low-rank techniques on a suite of benchmark but is dominated by some recent proposals that take advantage of the graph features. Given the vast range of architectures, activation functions, regularizers, and optimization techniques that could be used within the NNMF framework, it seems likely the true potential of the approach has yet to be reached. Recently, some recommendation methods try to improve the prediction results by integrating information from user's multiple types of behaviors. How to model the dependence and independence between different behaviors is critical for them. In this paper, we propose a novel recommendation model, the Group-Sparse Matrix Factorization (GSMF), which factorizes the rating matrices for multiple behaviors into the user and item latent factor space with group sparsity regularization. It can (1) select out the different subsets of latent factors for different behaviors, addressing that users' decisions on different behaviors are determined by different sets of factors; (2) model the dependence and independence between behaviors by learning the shared and private factors for multiple behaviors automatically; (3) allow the shared factors between different behaviors to be different, instead of all the behaviors sharing the same set of factors. Experiments on the real-world dataset demonstrate that our model can integrate users' multiple types of behaviors into recommendation better, compared with other state-of-the-arts. Homophily and stochastic equivalence are two primary features of interest in social networks. Recently, the multiplicative latent factor model (MLFM) is proposed to model social networks with directed links. Although MLFM can capture stochastic equivalence, it cannot model well homophily in networks. However, many real-world networks exhibit homophily or both homophily and stochastic equivalence, and hence the network structure of these networks cannot be modeled well by MLFM. In this paper, we propose a novel model, called generalized latent factor model (GLFM), for social network analysis by enhancing homophily modeling in MLFM. We devise a minorization-maximization (MM) algorithm with linear-time complexity and convergence guarantee to learn the model parameters. Extensive experiments on some real-world networks show that GLFM can effectively model homophily to dramatically outperform state-of-the-art methods. We review the method of Parallel Factor Analysis, which simultaneously fits multiple two-way arrays or ‘slices’ of a three-way array in terms of a common set of factors with differing relative weights in each ‘slice’. Mathematically, it is a straightforward generalization of the bilinear model of factor (or component) analysis (xij = ΣRr = 1airbjr) to a trilinear model (xijk = ΣRr = 1airbjrckr). Despite this simplicity, it has an important property not possessed by the two-way model: if the latent factors show adequately distinct patterns of three-way variation, the model is fully identified; the orientation of factors is uniquely determined by minimizing residual error, eliminating the need for a separate ‘rotation’ phase of analysis. The model can be used several ways. It can be directly fit to a three-way array of observations with (possibly incomplete) factorial structure, or it can be indirectly fit to the original observations by fitting a set of covariance matrices computed from the observations, with each matrix corresponding to a two-way subset of the data. Even more generally, one can simultaneously analyze covariance matrices computed from different samples, perhaps corresponding to different treatment groups, different kinds of cases, data from different studies, etc. To demonstrate the method we analyze data from an experiment on right vs. left cerebral hemispheric control of the hands during various tasks. The factors found appear to correspond to the causal influences manipulated in the experiment, revealing their patterns of influence in all three ways of the data. Several generalizations of the parallel factor analysis model are currently under development, including ones that combine parallel factors with Tucker-like factor ‘interactions’. Of key importance is the need to increase the method's robustness against nonstationary factor structures and qualitative (nonproportional) factor change. Matrix factorization (MF) models and their extensions are standard in modern recommender systems. MF models decompose the observed user-item interaction matrix into user and item latent factors. In this paper, we propose a co-factorization model, CoFactor, which jointly decomposes the user-item interaction matrix and the item-item co-occurrence matrix with shared item latent factors. For each pair of items, the co-occurrence matrix encodes the number of users that have consumed both items. CoFactor is inspired by the recent success of word embedding models (e.g., word2vec) which can be interpreted as factorizing the word co-occurrence matrix. We show that this model significantly improves the performance over MF models on several datasets with little additional computational overhead. We provide qualitative results that explain how CoFactor improves the quality of the inferred factors and characterize the circumstances where it provides the most significant improvements. The problem of topic modeling can be seen as a generalization of the clustering problem, in that it posits that observations are generated due to multiple latent factors (e.g., the words in each document are generated as a mixture of several active topics, as opposed to just one). This increased representational power comes at the cost of a more challenging unsupervised learning problem of estimating the topic probability vectors (the distributions over words for each topic), when only the words are observed and the corresponding topics are hidden. We provide a simple and efficient learning procedure that is guaranteed to recover the parameters for a wide class of mixture models, including the popular latent Dirichlet allocation (LDA) model. For LDA, the procedure correctly recovers both the topic probability vectors and the prior over the topics, using only trigram statistics (i.e., third order moments, which may be estimated with documents containing just three words). The method, termed Excess Correlation Analysis (ECA), is based on a spectral decomposition of low order moments (third and fourth order) via two singular value decompositions (SVDs). Moreover, the algorithm is scalable since the SVD operations are carried out on @math matrices, where @math is the number of latent factors (e.g. the number of topics), rather than in the @math -dimensional observed space (typically @math ). Finding latent factors of the data using matrix factorizations is a tried-and-tested approach in data mining. But finding shared factors over multiple matrices is more novel problem. Specifically, given two matrices, we want to find a set of factors shared by these two matrices and sets of factors specific for the matrices. Not only does such decomposition reveal what is common between the two matrices, it also eliminates the need of explaining that common part twice, thus concentrating the non-shared factors to uniquely specific parts of the data. This paper studies a problem called Joint Subspace Boolean Matrix Factorization asking exactly that: a set of shared factors and sets of specific factors. Furthermore, the matrix factorization is based on the Boolean arithmetic. This restricts the presented approach suitable to only binary matrices. The benefits, however, include much sparser factor matrices and greater interpretability of the results. The paper presents three algorithms for finding the Joint Subspace Boolean Matrix Factorization, an MDLbased method for selecting the subspaces’ dimensionality, and throughout experimental evaluation of the proposed algorithms. Regularized matrix factorization models are known to generate high quality rating predictions for recommender systems. One of the major drawbacks of matrix factorization is that once computed, the model is static. For real-world applications dynamic updating a model is one of the most important tasks. Especially when ratings on new users or new items come in, updating the feature matrices is crucial. In this paper, we generalize regularized matrix factorization (RMF) to regularized kernel matrix factorization (RKMF). Kernels provide a flexible method for deriving new matrix factorization methods. Furthermore with kernels nonlinear interactions between feature vectors are possible. We propose a generic method for learning RKMF models. From this method we derive an online-update algorithm for RKMF models that allows to solve the new-user new-item problem. Our evaluation indicates that our proposed online-update methods are accurate in approximating a full retrain of a RKMF model while the runtime of online-updating is in the range of milliseconds even for huge datasets like Netflix. Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in statistics, machine learning, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint mixed relaxations (i.e., l 1 -norm and trace norm) under certain conditions. However, all current provable algorithms suffer from superlinear per-iteration cost, which severely limits their applicability to large-scale problems. In this paper, we propose a scalable, provable and structured robust bilinear factorization (RBF) method to recover low-rank and sparse matrices from missing and grossly corrupted data, i.e., robust matrix completion (RMC), or incomplete and grossly corrupted measurements, i.e., compressive principal component pursuit (CPCP). Specifically, we first present two small-scale matrix trace norm regularized bilinear factorization models for RMC and CPCP problems, in which repetitively calculating SVD of a large-scale matrix is replaced by updating two much smaller factor matrices. Then, we apply the alternating direction method of multipliers (ADMM) to efficiently solve the RMC problems. Finally, we provide the convergence analysis of our algorithm, and extend it to address general CPCP problems. Experimental results verified both the efficiency and effectiveness of our method compared with the state-of-the-art methods. Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis which is based on a linear transformations between the latent space and the data space. In this paper we introduce a form of non-linear latent variable model called the Generative Topographic Mapping, for which the parameters of the model can be determined using the EM algorithm. GTM provides a principled alternative to the widely used Self-Organizing Map (SOM) of Kohonen (1982), and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from flow diagnostics for a multi-phase oil pipeline. We describe a latent variable model for supervised dimensionality reduction and distance metric learning. The model discovers linear projections of high dimensional data that shrink the distance between similarly labeled inputs and expand the distance between differently labeled ones. The model's continuous latent variables locate pairs of examples in a latent space of lower dimensionality. The model differs significantly from classical factor analysis in that the posterior distribution over these latent variables is not always multivariate Gaussian. Nevertheless we show that inference is completely tractable and derive an Expectation-Maximization (EM) algorithm for parameter estimation. We also compare the model to other approaches in distance metric learning. The model's main advantage is its simplicity: at each iteration of the EM algorithm, the distance metric is re-estimated by solving an unconstrained least-squares problem. Experiments show that these simple updates are highly effective. We propose fLDA, a novel matrix factorization method to predict ratings in recommender system applications where a "bag-of-words" representation for item meta-data is natural. Such scenarios are commonplace in web applications like content recommendation, ad targeting and web search where items are articles, ads and web pages respectively. Because of data sparseness, regularization is key to good predictive accuracy. Our method works by regularizing both user and item factors simultaneously through user features and the bag of words associated with each item. Specifically, each word in an item is associated with a discrete latent factor often referred to as the topic of the word; item topics are obtained by averaging topics across all words in an item. Then, user rating on an item is modeled as user's affinity to the item's topics where user affinity to topics (user factors) and topic assignments to words in items (item factors) are learned jointly in a supervised fashion. To avoid overfitting, user and item factors are regularized through Gaussian linear regression and Latent Dirichlet Allocation (LDA) priors respectively. We show our model is accurate, interpretable and handles both cold-start and warm-start scenarios seamlessly through a single model. The efficacy of our method is illustrated on benchmark datasets and a new dataset from Yahoo! Buzz where fLDA provides superior predictive accuracy in cold-start scenarios and is comparable to state-of-the-art methods in warm-start scenarios. As a by-product, fLDA also identifies interesting topics that explains user-item interactions. Our method also generalizes a recently proposed technique called supervised LDA (sLDA) to collaborative filtering applications. While sLDA estimates item topic vectors in a supervised fashion for a single regression, fLDA incorporates multiple regressions (one for each user) in estimating the item factors. We propose a new matrix completion algorithm— Kernelized Probabilistic Matrix Factorization (KPMF), which effectively incorporates external side information into the matrix factorization process. Unlike Probabilistic Matrix Factorization (PMF) [14], which assumes an independent latent vector for each row (and each column) with Gaussian priors, KMPF works with latent vectors spanning all rows (and columns) with Gaussian Process (GP) priors. Hence, KPMF explicitly captures the underlying (nonlinear) covariance structures across rows and columns. This crucial difference greatly boosts the performance of KPMF when appropriate side information, e.g., users’ social network in recommender systems, is incorporated. Furthermore, GP priors allow the KPMF model to fill in a row that is entirely missing in the original matrix based on the side information alone, which is not feasible for standard PMF formulation. In our paper, we mainly work on the matrix completion problem with a graph among the rows and or columns as side information, but the proposed framework can be easily used with other types of side information as well. Finally, we demonstrate the efficacy of KPMF through two different applications: 1) recommender systems and 2) image restoration. CANDECOMP PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance. Latent variable models are a fundamental modeling tool in machine learning applications, but they present significant computational and analytical challenges. The popular EM algorithm and its variants, is a much used algorithmic tool; yet our rigorous understanding of its performance is highly incomplete. Recently, work in (2014) has demonstrated that for an important class of problems, EM exhibits linear local convergence. In the high-dimensional setting, however, the M-step may not be well defined. We address precisely this setting through a unified treatment using regularization. While regularization for high-dimensional problems is by now well understood, the iterative EM algorithm requires a careful balancing of making progress towards the solution while identifying the right structure (e.g., sparsity or low-rank). In particular, regularizing the M-step using the state-of-the-art high-dimensional prescriptions (e.g., Wainwright (2014)) is not guaranteed to provide this balance. Our algorithm and analysis are linked in a way that reveals the balance between optimization and statistical errors. We specialize our general framework to sparse gaussian mixture models, high-dimensional mixed regression, and regression with missing variables, obtaining statistical guarantees for each of these examples. Latent variable models can be enriched with a multi-dimensional structure to consider the many latent factors in a text corpus, such as topic, author perspective and sentiment. We introduce factorial LDA, a multi-dimensional model in which a document is influenced by K different factors, and each word token depends on a K-dimensional vector of latent variables. Our model incorporates structured word priors and learns a sparse product of factors. Experiments on research abstracts show that our model can learn latent factors such as research topic, scientific discipline, and focus (methods vs. applications). Our modeling improvements reduce test perplexity and improve human interpretability of the discovered factors.