8,348 research outputs found
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
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
A dual framework for low-rank tensor completion
One of the popular approaches for low-rank tensor completion is to use the
latent trace norm regularization. However, most existing works in this
direction learn a sparse combination of tensors. In this work, we fill this gap
by proposing a variant of the latent trace norm that helps in learning a
non-sparse combination of tensors. We develop a dual framework for solving the
low-rank tensor completion problem. We first show a novel characterization of
the dual solution space with an interesting factorization of the optimal
solution. Overall, the optimal solution is shown to lie on a Cartesian product
of Riemannian manifolds. Furthermore, we exploit the versatile Riemannian
optimization framework for proposing computationally efficient trust region
algorithm. The experiments illustrate the efficacy of the proposed algorithm on
several real-world datasets across applications.Comment: Aceepted to appear in Advances of Nueral Information Processing
Systems (NIPS), 2018. A shorter version appeared in the NIPS workshop on
Synergies in Geometric Data Analysis 201
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