5,422 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
Dirichlet belief networks for topic structure learning
Recently, considerable research effort has been devoted to developing deep
architectures for topic models to learn topic structures. Although several deep
models have been proposed to learn better topic proportions of documents, how
to leverage the benefits of deep structures for learning word distributions of
topics has not yet been rigorously studied. Here we propose a new multi-layer
generative process on word distributions of topics, where each layer consists
of a set of topics and each topic is drawn from a mixture of the topics of the
layer above. As the topics in all layers can be directly interpreted by words,
the proposed model is able to discover interpretable topic hierarchies. As a
self-contained module, our model can be flexibly adapted to different kinds of
topic models to improve their modelling accuracy and interpretability.
Extensive experiments on text corpora demonstrate the advantages of the
proposed model.Comment: accepted in NIPS 201
Marginal and simultaneous predictive classification using stratified graphical models
An inductive probabilistic classification rule must generally obey the
principles of Bayesian predictive inference, such that all observed and
unobserved stochastic quantities are jointly modeled and the parameter
uncertainty is fully acknowledged through the posterior predictive
distribution. Several such rules have been recently considered and their
asymptotic behavior has been characterized under the assumption that the
observed features or variables used for building a classifier are conditionally
independent given a simultaneous labeling of both the training samples and
those from an unknown origin. Here we extend the theoretical results to
predictive classifiers acknowledging feature dependencies either through
graphical models or sparser alternatives defined as stratified graphical
models. We also show through experimentation with both synthetic and real data
that the predictive classifiers based on stratified graphical models have
consistently best accuracy compared with the predictive classifiers based on
either conditionally independent features or on ordinary graphical models.Comment: 18 pages, 5 figure
Deep Exponential Families
We describe \textit{deep exponential families} (DEFs), a class of latent
variable models that are inspired by the hidden structures used in deep neural
networks. DEFs capture a hierarchy of dependencies between latent variables,
and are easily generalized to many settings through exponential families. We
perform inference using recent "black box" variational inference techniques. We
then evaluate various DEFs on text and combine multiple DEFs into a model for
pairwise recommendation data. In an extensive study, we show that going beyond
one layer improves predictions for DEFs. We demonstrate that DEFs find
interesting exploratory structure in large data sets, and give better
predictive performance than state-of-the-art models
Defining the hundred year flood: a Bayesian approach for using historic data to reduce uncertainty in flood frequency estimates
This paper describes a Bayesian statistical model for estimating flood frequency by combining uncertain annual maximum (AMAX) data from a river gauge with estimates of flood peak discharge from various historic sources that predate the period of instrument records. Such historic flood records promise to expand the time series data needed for reducing the uncertainty in return period estimates for extreme events, but the heterogeneity and uncertainty of historic records make them difficult to use alongside Flood Estimation Handbook and other standard methods for generating flood frequency curves from gauge data. Using the flow of the River Eden in Carlisle, Cumbria, UK as a case study, this paper develops a Bayesian model for combining historic flood estimates since 1800 with gauge data since 1967 to estimate the probability of low frequency flood events for the area taking account of uncertainty in the discharge estimates. Results show a reduction in 95% confidence intervals of roughly 50% for annual exceedance probabilities of less than 0.0133 (return periods over 75 years) compared to standard flood frequency estimation methods using solely systematic data. Sensitivity analysis shows the model is sensitive to 2 model parameters both of which are concerned with the historic (pre-systematic) period of the time series. This highlights the importance of adequate consideration of historic channel and floodplain changes or possible bias in estimates of historic flood discharges. The next steps required to roll out this Bayesian approach for operational flood frequency estimation at other sites is also discussed
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