19,774 research outputs found
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
Stochastic Variational Inference
We develop stochastic variational inference, a scalable algorithm for
approximating posterior distributions. We develop this technique for a large
class of probabilistic models and we demonstrate it with two probabilistic
topic models, latent Dirichlet allocation and the hierarchical Dirichlet
process topic model. Using stochastic variational inference, we analyze several
large collections of documents: 300K articles from Nature, 1.8M articles from
The New York Times, and 3.8M articles from Wikipedia. Stochastic inference can
easily handle data sets of this size and outperforms traditional variational
inference, which can only handle a smaller subset. (We also show that the
Bayesian nonparametric topic model outperforms its parametric counterpart.)
Stochastic variational inference lets us apply complex Bayesian models to
massive data sets
A multi-resolution approximation for massive spatial datasets
Automated sensing instruments on satellites and aircraft have enabled the
collection of massive amounts of high-resolution observations of spatial fields
over large spatial regions. If these datasets can be efficiently exploited,
they can provide new insights on a wide variety of issues. However, traditional
spatial-statistical techniques such as kriging are not computationally feasible
for big datasets. We propose a multi-resolution approximation (M-RA) of
Gaussian processes observed at irregular locations in space. The M-RA process
is specified as a linear combination of basis functions at multiple levels of
spatial resolution, which can capture spatial structure from very fine to very
large scales. The basis functions are automatically chosen to approximate a
given covariance function, which can be nonstationary. All computations
involving the M-RA, including parameter inference and prediction, are highly
scalable for massive datasets. Crucially, the inference algorithms can also be
parallelized to take full advantage of large distributed-memory computing
environments. In comparisons using simulated data and a large satellite
dataset, the M-RA outperforms a related state-of-the-art method.Comment: 23 pages; to be published in Journal of the American Statistical
Associatio
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
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
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On Simplified Bayesian Modeling for Massive Geostatistical Datasets: Conjugacy and Beyond
With continued advances in Geographic Information Systems and related computational technologies, researchers in diverse fields like forestry, environmental health, climate sciences etc. have growing interests in analyzing large scale data sets measured at a substantial number of geographic locations. Geostatistical models used to capture the space varying relationships in such data are often accompanied by onerous computations which prohibit the analysis of large scale spatial data sets. Less burdensome alternatives proposed recently for analyzing massive spatial datasets often lead to inaccurate inference or require slow sampling process. Bayesian inference, while attractive for accommodating uncertainties through their hierarchical structures, can become computationally onerous for modeling massive spatial data sets because of their reliance on iterative estimation algorithms. My dissertation research aims at developing computationally scalable Bayesian geostatistical models that provide valid inference through highly accelerated sampling process. We also study the asymptotic properties of estimators in spatial analysis.In Chapter 2 and 3, we develop conjugate Bayesian frameworks for analyzing univariate and multivariate spatial data. We propose a conjugate latent Nearest-Neighbor Gaussian Process (NNGP) model in Chapter 2, which uses analytically tractable posterior distributions to obtain posterior inferences, including the large dimensional latent process. In Chapter 3, we focus on building conjugate Bayesian frameworks for analyzing multivariate spatial data. We utilize Matrix-Normal Inverse-Wishart(MNIW) prior to propose conjugate Bayesian frameworks and algorithms that can incorporate a family of scalable spatial modeling methodologies.In Chapter 4, we pursue general Bayesian modeling methodologies beyond a conjugate Bayesian hierarchical modeling. We build scalable versions of a hierarchical linear model of coregionalization (LMC) and spatial factor models, and propose a highly accelerated block update MCMC algorithm. Using the proposed Bayesian LMC model, we extend scalable modeling strategies for a single process into multivariate process cases. All proposed frameworks are tested on simulated data and fit to real data sets with observed locations numbering in the millions. Our contribution is to offer practicing scientists and spatial analysts practical and flexible scalable hierarchical models for analyzing massive spatial data sets.In Chapter 5, we investigate the asymptotic properties of the estimators in spatial analysis. We formally establish results on the identifiability and consistency of the nugget in spatial models based upon the Gaussian process within the framework of in-fill asymptotics, i.e. the sample size increases within a sampling domain that is bounded. We establish the identifiability of parameters in the Matern covariance function and the consistency of their maximum likelihood estimators in the presence of discontinuities due to the nugget
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