6,771 research outputs found
Scalable Recommendation with Poisson Factorization
We develop a Bayesian Poisson matrix factorization model for forming
recommendations from sparse user behavior data. These data are large user/item
matrices where each user has provided feedback on only a small subset of items,
either explicitly (e.g., through star ratings) or implicitly (e.g., through
views or purchases). In contrast to traditional matrix factorization
approaches, Poisson factorization implicitly models each user's limited
attention to consume items. Moreover, because of the mathematical form of the
Poisson likelihood, the model needs only to explicitly consider the observed
entries in the matrix, leading to both scalable computation and good predictive
performance. We develop a variational inference algorithm for approximate
posterior inference that scales up to massive data sets. This is an efficient
algorithm that iterates over the observed entries and adjusts an approximate
posterior over the user/item representations. We apply our method to large
real-world user data containing users rating movies, users listening to songs,
and users reading scientific papers. In all these settings, Bayesian Poisson
factorization outperforms state-of-the-art matrix factorization methods
Large-Scale Distributed Bayesian Matrix Factorization using Stochastic Gradient MCMC
Despite having various attractive qualities such as high prediction accuracy
and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix
Factorization has not been widely adopted because of the prohibitive cost of
inference. In this paper, we propose a scalable distributed Bayesian matrix
factorization algorithm using stochastic gradient MCMC. Our algorithm, based on
Distributed Stochastic Gradient Langevin Dynamics, can not only match the
prediction accuracy of standard MCMC methods like Gibbs sampling, but at the
same time is as fast and simple as stochastic gradient descent. In our
experiments, we show that our algorithm can achieve the same level of
prediction accuracy as Gibbs sampling an order of magnitude faster. We also
show that our method reduces the prediction error as fast as distributed
stochastic gradient descent, achieving a 4.1% improvement in RMSE for the
Netflix dataset and an 1.8% for the Yahoo music dataset
Scalable Bayesian Non-Negative Tensor Factorization for Massive Count Data
We present a Bayesian non-negative tensor factorization model for
count-valued tensor data, and develop scalable inference algorithms (both batch
and online) for dealing with massive tensors. Our generative model can handle
overdispersed counts as well as infer the rank of the decomposition. Moreover,
leveraging a reparameterization of the Poisson distribution as a multinomial
facilitates conjugacy in the model and enables simple and efficient Gibbs
sampling and variational Bayes (VB) inference updates, with a computational
cost that only depends on the number of nonzeros in the tensor. The model also
provides a nice interpretability for the factors; in our model, each factor
corresponds to a "topic". We develop a set of online inference algorithms that
allow further scaling up the model to massive tensors, for which batch
inference methods may be infeasible. We apply our framework on diverse
real-world applications, such as \emph{multiway} topic modeling on a scientific
publications database, analyzing a political science data set, and analyzing a
massive household transactions data set.Comment: ECML PKDD 201
Zero-Truncated Poisson Tensor Factorization for Massive Binary Tensors
We present a scalable Bayesian model for low-rank factorization of massive
tensors with binary observations. The proposed model has the following key
properties: (1) in contrast to the models based on the logistic or probit
likelihood, using a zero-truncated Poisson likelihood for binary data allows
our model to scale up in the number of \emph{ones} in the tensor, which is
especially appealing for massive but sparse binary tensors; (2)
side-information in form of binary pairwise relationships (e.g., an adjacency
network) between objects in any tensor mode can also be leveraged, which can be
especially useful in "cold-start" settings; and (3) the model admits simple
Bayesian inference via batch, as well as \emph{online} MCMC; the latter allows
scaling up even for \emph{dense} binary data (i.e., when the number of ones in
the tensor/network is also massive). In addition, non-negative factor matrices
in our model provide easy interpretability, and the tensor rank can be inferred
from the data. We evaluate our model on several large-scale real-world binary
tensors, achieving excellent computational scalability, and also demonstrate
its usefulness in leveraging side-information provided in form of
mode-network(s).Comment: UAI (Uncertainty in Artificial Intelligence) 201
Distributed Bayesian Matrix Factorization with Limited Communication
Bayesian matrix factorization (BMF) is a powerful tool for producing low-rank
representations of matrices and for predicting missing values and providing
confidence intervals. Scaling up the posterior inference for massive-scale
matrices is challenging and requires distributing both data and computation
over many workers, making communication the main computational bottleneck.
Embarrassingly parallel inference would remove the communication needed, by
using completely independent computations on different data subsets, but it
suffers from the inherent unidentifiability of BMF solutions. We introduce a
hierarchical decomposition of the joint posterior distribution, which couples
the subset inferences, allowing for embarrassingly parallel computations in a
sequence of at most three stages. Using an efficient approximate
implementation, we show improvements empirically on both real and simulated
data. Our distributed approach is able to achieve a speed-up of almost an order
of magnitude over the full posterior, with a negligible effect on predictive
accuracy. Our method outperforms state-of-the-art embarrassingly parallel MCMC
methods in accuracy, and achieves results competitive to other available
distributed and parallel implementations of BMF.Comment: 28 pages, 8 figures. The paper is published in Machine Learning
journal. An implementation of the method is is available in SMURFF software
on github (bmfpp branch): https://github.com/ExaScience/smurf
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