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Search Results: 1 - 10 of 32489 matches for " John Paisley "
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A Collaborative Kalman Filter for Time-Evolving Dyadic Processes
San Gultekin,John Paisley
Computer Science , 2015,
Abstract: We present the collaborative Kalman filter (CKF), a dynamic model for collaborative filtering and related factorization models. Using the matrix factorization approach to collaborative filtering, the CKF accounts for time evolution by modeling each low-dimensional latent embedding as a multidimensional Brownian motion. Each observation is a random variable whose distribution is parameterized by the dot product of the relevant Brownian motions at that moment in time. This is naturally interpreted as a Kalman filter with multiple interacting state space vectors. We also present a method for learning a dynamically evolving drift parameter for each location by modeling it as a geometric Brownian motion. We handle posterior intractability via a mean-field variational approximation, which also preserves tractability for downstream calculations in a manner similar to the Kalman filter. We evaluate the model on several large datasets, providing quantitative evaluation on the 10 million Movielens and 100 million Netflix datasets and qualitative evaluation on a set of 39 million stock returns divided across roughly 6,500 companies from the years 1962-2014.
Variational Bayesian Inference with Stochastic Search
John Paisley,David Blei,Michael Jordan
Computer Science , 2012,
Abstract: Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This requires the ability to integrate a sum of terms in the log joint likelihood using this factorized distribution. Often not all integrals are in closed form, which is typically handled by using a lower bound. We present an alternative algorithm based on stochastic optimization that allows for direct optimization of the variational lower bound. This method uses control variates to reduce the variance of the stochastic search gradient, in which existing lower bounds can play an important role. We demonstrate the approach on two non-conjugate models: logistic regression and an approximation to the HDP.
The Discrete Infinite Logistic Normal Distribution
John Paisley,Chong Wang,David Blei
Statistics , 2011,
Abstract: We present the discrete infinite logistic normal distribution (DILN), a Bayesian nonparametric prior for mixed membership models. DILN is a generalization of the hierarchical Dirichlet process (HDP) that models correlation structure between the weights of the atoms at the group level. We derive a representation of DILN as a normalized collection of gamma-distributed random variables, and study its statistical properties. We consider applications to topic modeling and derive a variational inference algorithm for approximate posterior inference. We study the empirical performance of the DILN topic model on four corpora, comparing performance with the HDP and the correlated topic model (CTM). To deal with large-scale data sets, we also develop an online inference algorithm for DILN and compare with online HDP and online LDA on the Nature magazine, which contains approximately 350,000 articles.
Stochastic Annealing for Variational Inference
San Gultekin,Aonan Zhang,John Paisley
Statistics , 2015,
Abstract: We empirically evaluate a stochastic annealing strategy for Bayesian posterior optimization with variational inference. Variational inference is a deterministic approach to approximate posterior inference in Bayesian models in which a typically non-convex objective function is locally optimized over the parameters of the approximating distribution. We investigate an annealing method for optimizing this objective with the aim of finding a better local optimal solution and compare with deterministic annealing methods and no annealing. We show that stochastic annealing can provide clear improvement on the GMM and HMM, while performance on LDA tends to favor deterministic annealing methods.
The Stick-Breaking Construction of the Beta Process as a Poisson Process
John Paisley,David Blei,Michael I. Jordan
Statistics , 2011,
Abstract: We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying representation to derive error bounds on truncated beta processes that are tighter than those in the literature. We also develop a new MCMC inference algorithm for beta processes, based in part on our new Poisson process construction.
Stochastic Variational Inference
Matt Hoffman,David M. Blei,Chong Wang,John Paisley
Computer Science , 2012,
Abstract: 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.
Nested Hierarchical Dirichlet Processes
John Paisley,Chong Wang,David M. Blei,Michael I. Jordan
Computer Science , 2012,
Abstract: We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical topic modeling. The nHDP is a generalization of the nested Chinese restaurant process (nCRP) that allows each word to follow its own path to a topic node according to a document-specific distribution on a shared tree. This alleviates the rigid, single-path formulation of the nCRP, allowing a document to more easily express thematic borrowings as a random effect. We derive a stochastic variational inference algorithm for the model, in addition to a greedy subtree selection method for each document, which allows for efficient inference using massive collections of text documents. We demonstrate our algorithm on 1.8 million documents from The New York Times and 3.3 million documents from Wikipedia.
Bayesian Poisson Tensor Factorization for Inferring Multilateral Relations from Sparse Dyadic Event Counts
Aaron Schein,John Paisley,David M. Blei,Hanna Wallach
Computer Science , 2015,
Abstract: We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country $i$ took action $a$ toward country $j$ at time $t$"---known as dyadic events---in order to form and test theories of international relations. We represent these event data as a tensor of counts and develop Bayesian Poisson tensor factorization to infer a low-dimensional, interpretable representation of their salient patterns. We demonstrate that our model's predictive performance is better than that of standard non-negative tensor factorization methods. We also provide a comparison of our variational updates to their maximum likelihood counterparts. In doing so, we identify a better way to form point estimates of the latent factors than that typically used in Bayesian Poisson matrix factorization. Finally, we showcase our model as an exploratory analysis tool for political scientists. We show that the inferred latent factor matrices capture interpretable multilateral relations that both conform to and inform our knowledge of international affairs.
A Nested HDP for Hierarchical Topic Models
John Paisley,Chong Wang,David Blei,Michael I. Jordan
Statistics , 2013,
Abstract: We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical topic modeling. The nHDP is a generalization of the nested Chinese restaurant process (nCRP) that allows each word to follow its own path to a topic node according to a document-specific distribution on a shared tree. This alleviates the rigid, single-path formulation of the nCRP, allowing a document to more easily express thematic borrowings as a random effect. We demonstrate our algorithm on 1.8 million documents from The New York Times.
Combinatorial clustering and the beta negative binomial process
Tamara Broderick,Lester Mackey,John Paisley,Michael I. Jordan
Statistics , 2011,
Abstract: We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce a combinatorial stochastic process known as the negative binomial process (NBP) as an infinite-dimensional prior appropriate for such problems. We show that the NBP is conjugate to the beta process, and we characterize the posterior distribution under the beta-negative binomial process (BNBP) and hierarchical models based on the BNBP (the HBNBP). We study the asymptotic properties of the BNBP and develop a three-parameter extension of the BNBP that exhibits power-law behavior. We derive MCMC algorithms for posterior inference under the HBNBP, and we present experiments using these algorithms in the domains of image segmentation, object recognition, and document analysis.
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