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Register a new userBPRS: Belief Propagation Based Iterative Recommender System
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Added by
Arash Einolghozati
Publication date
2012
fields
Informatics Engineering
and research's language is
English
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In this paper we introduce the first application of the Belief Propagation (BP) algorithm in the design of recommender systems. We formulate the recommendation problem as an inference problem and aim to compute the marginal probability distributions of the variables which represent the ratings to be predicted. However, computing these marginal probability functions is computationally prohibitive for large-scale systems. Therefore, we utilize the BP algorithm to efficiently compute these functions. Recommendations for each active user are then iteratively computed by probabilistic message passing. As opposed to the previous recommender algorithms, BPRS does not require solving the recommendation problem for all the users if it wishes to update the recommendations for only a single active. Further, BPRS computes the recommendations for each user with linear complexity and without requiring a training period. Via computer simulations (using the 100K MovieLens dataset), we verify that BPRS iteratively reduces the error in the predicted ratings of the users until it converges. Finally, we confirm that BPRS is comparable to the state of art methods such as Correlation-based neighborhood model (CorNgbr) and Singular Value Decomposition (SVD) in terms of rating and precision accuracy. Therefore, we believe that the BP-based recommendation algorithm is a new promising approach which offers a significant advantage on scalability while providing competitive accuracy for the recommender systems.
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We propose a nonparametric generalization of belief propagation, Kernel Belief Propagation (KBP), for pairwise Markov random fields. Messages are represented as functions in a reproducing kernel Hilbert space (RKHS), and message updates are simple linear operations in the RKHS. KBP makes none of the assumptions commonly required in classical BP algorithms: the variables need not arise from a finite domain or a Gaussian distribution, nor must their relations take any particular parametric form. Rather, the relations between variables are represented implicitly, and are learned nonparametrically from training data. KBP has the advantage that it may be used on any domain where kernels are defined (Rd, strings, groups), even where explicit parametric models are not known, or closed form expressions for the BP updates do not exist. The computational cost of message updates in KBP is polynomial in the training data size. We also propose a constant time approximate message update procedure by representing messages using a small number of basis functions. In experiments, we apply KBP to image denoising, depth prediction from still images, and protein configuration prediction: KBP is faster than competing classical and nonparametric approaches (by orders of magnitude, in some cases), while providing significantly more accurate results.
Learned neural solvers have successfully been used to solve combinatorial optimization and decision problems. More general counting variants of these problems, however, are still largely solved with hand-crafted solvers. To bridge this gap, we introduce belief propagation neural networks (BPNNs), a class of parameterized operators that operate on factor graphs and generalize Belief Propagation (BP). In its strictest form, a BPNN layer (BPNN-D) is a learned iterative operator that provably maintains many of the desirable properties of BP for any choice of the parameters. Empirically, we show that by training BPNN-D learns to perform the task better than the original BP: it converges 1.7x faster on Ising models while providing tighter bounds. On challenging model counting problems, BPNNs compute estimates 100s of times faster than state-of-the-art handcrafted methods, while returning an estimate of comparable quality.
A standard model for Recommender Systems is the Matrix Completion setting: given partially known matrix of ratings given by users (rows) to items (columns), infer the unknown ratings. In the last decades, few attempts where done to handle that objective with Neural Networks, but recently an architecture based on Autoencoders proved to be a promising approach. In current paper, we enhanced that architecture (i) by using a loss function adapted to input data with missing values, and (ii) by incorporating side information. The experiments demonstrate that while side information only slightly improve the test error averaged on all users/items, it has more impact on cold users/items.
Fast convergence speed is a desired property for training latent Dirichlet allocation (LDA), especially in online and parallel topic modeling for massive data sets. This paper presents a novel residual belief propagation (RBP) algorithm to accelerate the convergence speed for training LDA. The proposed RBP uses an informed scheduling scheme for asynchronous message passing, which passes fast-convergent messages with a higher priority to influence those slow-convergent messages at each learning iteration. Extensive empirical studies confirm that RBP significantly reduces the training time until convergence while achieves a much lower predictive perplexity than other state-of-the-art training algorithms for LDA, including variational Bayes (VB), collapsed Gibbs sampling (GS), loopy belief propagation (BP), and residual VB (RVB).
Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model for probabilistic topic modeling, which attracts worldwide interests and touches on many important applications in text mining, computer vision and computational biology. This paper represents LDA as a factor graph within the Markov random field (MRF) framework, which enables the classic loopy belief propagation (BP) algorithm for approximate inference and parameter estimation. Although two commonly-used approximate inference methods, such as variational Bayes (VB) and collapsed Gibbs sampling (GS), have gained great successes in learning LDA, the proposed BP is competitive in both speed and accuracy as validated by encouraging experimental results on four large-scale document data sets. Furthermore, the BP algorithm has the potential to become a generic learning scheme for variants of LDA-based topic models. To this end, we show how to learn two typical variants of LDA-based topic models, such as author-topic models (ATM) and relational topic models (RTM), using BP based on the factor graph representation.
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