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Search Results: 1 - 10 of 445028 matches for " David M. Blei "
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A Split-Merge MCMC Algorithm for the Hierarchical Dirichlet Process
Chong Wang,David M. Blei
Computer Science , 2012,
Abstract: The hierarchical Dirichlet process (HDP) has become an important Bayesian nonparametric model for grouped data, such as document collections. The HDP is used to construct a flexible mixed-membership model where the number of components is determined by the data. As for most Bayesian nonparametric models, exact posterior inference is intractable---practitioners use Markov chain Monte Carlo (MCMC) or variational inference. Inspired by the split-merge MCMC algorithm for the Dirichlet process (DP) mixture model, we describe a novel split-merge MCMC sampling algorithm for posterior inference in the HDP. We study its properties on both synthetic data and text corpora. We find that split-merge MCMC for the HDP can provide significant improvements over traditional Gibbs sampling, and we give some understanding of the data properties that give rise to larger improvements.
Population Empirical Bayes
Alp Kucukelbir,David M. Blei
Computer Science , 2014,
Abstract: Bayesian predictive inference analyzes a dataset to make predictions about new observations. When a model does not match the data, predictive accuracy suffers. We develop population empirical Bayes (POP-EB), a hierarchical framework that explicitly models the empirical population distribution as part of Bayesian analysis. We introduce a new concept, the latent dataset, as a hierarchical variable and set the empirical population as its prior. This leads to a new predictive density that mitigates model mismatch. We efficiently apply this method to complex models by proposing a stochastic variational inference algorithm, called bumping variational inference (BUMP-VI). We demonstrate improved predictive accuracy over classical Bayesian inference in three models: a linear regression model of health data, a Bayesian mixture model of natural images, and a latent Dirichlet allocation topic model of scientific documents.
Hierarchical relational models for document networks
Jonathan Chang,David M. Blei
Statistics , 2009, DOI: 10.1214/09-AOAS309
Abstract: We develop the relational topic model (RTM), a hierarchical model of both network structure and node attributes. We focus on document networks, where the attributes of each document are its words, that is, discrete observations taken from a fixed vocabulary. For each pair of documents, the RTM models their link as a binary random variable that is conditioned on their contents. The model can be used to summarize a network of documents, predict links between them, and predict words within them. We derive efficient inference and estimation algorithms based on variational methods that take advantage of sparsity and scale with the number of links. We evaluate the predictive performance of the RTM for large networks of scientific abstracts, web documents, and geographically tagged news.
A General Method for Robust Bayesian Modeling
Chong Wang,David M. Blei
Statistics , 2015,
Abstract: Robust Bayesian models are appealing alternatives to standard models, providing protection from data that contains outliers or other departures from the model assumptions. Historically, robust models were mostly developed on a case-by-case basis; examples include robust linear regression, robust mixture models, and bursty topic models. In this paper we develop a general approach to robust Bayesian modeling. We show how to turn an existing Bayesian model into a robust model, and then develop a generic strategy for computing with it. We use our method to study robust variants of several models, including linear regression, Poisson regression, logistic regression, and probabilistic topic models. We discuss the connections between our methods and existing approaches, especially empirical Bayes and James-Stein estimation.
Variational Inference in Nonconjugate Models
Chong Wang,David M. Blei
Statistics , 2012,
Abstract: Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization algorithm. When the model is conditionally conjugate, the coordinate updates are easily derived and in closed form. However, many models of interest---like the correlated topic model and Bayesian logistic regression---are nonconjuate. In these models, mean-field methods cannot be directly applied and practitioners have had to develop variational algorithms on a case-by-case basis. In this paper, we develop two generic methods for nonconjugate models, Laplace variational inference and delta method variational inference. Our methods have several advantages: they allow for easily derived variational algorithms with a wide class of nonconjugate models; they extend and unify some of the existing algorithms that have been derived for specific models; and they work well on real-world datasets. We studied our methods on the correlated topic model, Bayesian logistic regression, and hierarchical Bayesian logistic regression.
The Issue-Adjusted Ideal Point Model
Sean M. Gerrish,David M. Blei
Computer Science , 2012,
Abstract: We develop a model of issue-specific voting behavior. This model can be used to explore lawmakers' personal voting patterns of voting by issue area, providing an exploratory window into how the language of the law is correlated with political support. We derive approximate posterior inference algorithms based on variational methods. Across 12 years of legislative data, we demonstrate both improvement in heldout prediction performance and the model's utility in interpreting an inherently multi-dimensional space.
Syntactic Topic Models
Jordan Boyd-Graber,David M. Blei
Computer Science , 2010,
Abstract: The syntactic topic model (STM) is a Bayesian nonparametric model of language that discovers latent distributions of words (topics) that are both semantically and syntactically coherent. The STM models dependency parsed corpora where sentences are grouped into documents. It assumes that each word is drawn from a latent topic chosen by combining document-level features and the local syntactic context. Each document has a distribution over latent topics, as in topic models, which provides the semantic consistency. Each element in the dependency parse tree also has a distribution over the topics of its children, as in latent-state syntax models, which provides the syntactic consistency. These distributions are convolved so that the topic of each word is likely under both its document and syntactic context. We derive a fast posterior inference algorithm based on variational methods. We report qualitative and quantitative studies on both synthetic data and hand-parsed documents. We show that the STM is a more predictive model of language than current models based only on syntax or only on topics.
Black Box Variational Inference
Rajesh Ranganath,Sean Gerrish,David M. Blei
Computer Science , 2013,
Abstract: Variational inference has become a widely used method to approximate posteriors in complex latent variables models. However, deriving a variational inference algorithm generally requires significant model-specific analysis, and these efforts can hinder and deter us from quickly developing and exploring a variety of models for a problem at hand. In this paper, we present a "black box" variational inference algorithm, one that can be quickly applied to many models with little additional derivation. Our method is based on a stochastic optimization of the variational objective where the noisy gradient is computed from Monte Carlo samples from the variational distribution. We develop a number of methods to reduce the variance of the gradient, always maintaining the criterion that we want to avoid difficult model-based derivations. We evaluate our method against the corresponding black box sampling based methods. We find that our method reaches better predictive likelihoods much faster than sampling methods. Finally, we demonstrate that Black Box Variational Inference lets us easily explore a wide space of models by quickly constructing and evaluating several models of longitudinal healthcare data.
Hierarchical Variational Models
Rajesh Ranganath,Dustin Tran,David M. Blei
Computer Science , 2015,
Abstract: Black box inference allows researchers to easily prototype and evaluate an array of models. Recent advances in variational inference allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive variational distribution which maintains efficient computation? To address this, we develop hierarchical variational models. In a hierarchical variational model, the variational approximation is augmented with a prior on its parameters, such that the latent variables are conditionally independent given this shared structure. This preserves the computational efficiency of the original approximation, while admitting hierarchically complex distributions for both discrete and continuous latent variables. We study hierarchical variational models on a variety of deep discrete latent variable models. Hierarchical variational models generalize other expressive variational distributions and maintains higher fidelity to the posterior.
Variational Gaussian Process
Dustin Tran,Rajesh Ranganath,David M. Blei
Computer Science , 2015,
Abstract: Representations offered by deep generative models are fundamentally tied to their inference method from data. Variational inference methods require a rich family of approximating distributions. We construct the variational Gaussian process (VGP), a Bayesian nonparametric model which adapts its shape to match complex posterior distributions. The VGP generates approximate posterior samples by generating latent inputs and warping them through random non-linear mappings; the distribution over random mappings is learned during inference, enabling the transformed outputs to adapt to varying complexity. We prove a universal approximation theorem for the VGP, demonstrating its representative power for learning any model. For inference we present a variational objective inspired by autoencoders and perform black box inference over a wide class of models. The VGP achieves new state-of-the-art results for unsupervised learning, inferring models such as the deep latent Gaussian model and the recently proposed DRAW.
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