David M. Blei

JMLR Journal 2026 Journal Article

Extending Mean-Field Variational Inference via Entropic Regularization: Theory and Computation

• Bohan Wu
• David M. Blei

Variational inference (VI) has emerged as a popular method for approximate inference for high-dimensional Bayesian models. In this paper, we propose a novel VI method that extends the naive mean field via entropic regularization, referred to as $\Xi$-variational inference ($\Xi$-VI). $\Xi$-VI has a close connection to the entropic optimal transport problem and benefits from the computationally efficient Sinkhorn algorithm. We show that $\Xi$-variational posteriors effectively recover the true posterior dependency, where the likelihood function is downweighted by a regularization parameter. We analyze the role of dimensionality of the parameter space on the accuracy of $\Xi$-variational approximation and the computational complexity of computing the approximate distribution, providing a rough characterization of the statistical-computational trade-off in $\Xi$-VI, where higher statistical accuracy requires greater computational effort. We also investigate the frequentist properties of $\Xi$-VI and establish results on consistency, asymptotic normality, high-dimensional asymptotics, and algorithmic stability. We provide sufficient criteria for our algorithm to achieve polynomial-time convergence. Finally, we show the inferential benefits of using $\Xi$-VI over mean-field VI and other competing methods, such as normalizing flow, on simulated and real datasets. [abs] [ pdf ][ bib ] &copy JMLR 2026. ( edit, beta )

JMLR Journal 2026 Journal Article

Hierarchical Causal Models

• Eli N. Weinstein
• David M. Blei

Causal questions often arise in settings where data are hierarchical: subunits are nested within units. Consider students in schools, cells in patients, or cities in states. In these settings, unit-level variables (e.g., a school's budget) may affect subunit-level outcomes (e.g., student test scores), and subunit-level characteristics may aggregate to influence unit-level outcomes. In this paper, we show how to analyze hierarchical data for causal inference. We introduce hierarchical causal models, which extend structural causal models and graphical models by incorporating inner plates to represent nested data structures. We develop a graphical identification technique for these models that generalizes do-calculus. We show that hierarchical data can enable causal identification even when it would be impossible with non-hierarchical data--for example, when only unit-level summaries are available. We develop estimation strategies, including using hierarchical Bayesian models. We illustrate our results in simulation and through a reanalysis of the classic "eight schools" study. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2026. ( edit, beta )

ICLR Conference 2025 Conference Paper

Can Generative AI Solve Your In-Context Learning Problem? A Martingale Perspective

• Andrew Jesson
• Nicolas Beltran-Velez
• David M. Blei

This work is about estimating when a conditional generative model (CGM) can solve an in-context learning (ICL) problem. An in-context learning (ICL) problem comprises a CGM, a dataset, and a prediction task. The CGM could be a multi-modal foundation model; the dataset, a collection of patient histories, test results, and recorded diagnoses; and the prediction task to communicate a diagnosis to a new patient. A Bayesian interpretation of ICL assumes that the CGM computes a posterior predictive distribution over an unknown Bayesian model defining a joint distribution over latent explanations and observable data. From this perspective, Bayesian model criticism is a reasonable approach to assess the suitability of a given CGM for an ICL problem. However, such approaches---like posterior predictive checks (PPCs)---often assume that we can sample from the likelihood and posterior defined by the Bayesian model, which are not explicitly given for contemporary CGMs. To address this, we show when ancestral sampling from the predictive distribution of a CGM is equivalent to sampling datasets from the posterior predictive of the assumed Bayesian model. Then we develop the generative predictive $p$-value, which enables PPCs and their cousins for contemporary CGMs. The generative predictive $p$-value can be used in a statistical decision procedure to determine when the model is appropriate for an ICL problem. Our method only requires generating queries and responses from a CGM and evaluating its response log probability. Using large language models, we empirically evaluate our method on tasks involving tabular data, imaging data, and natural language data.

UAI Conference 2025 Conference Paper

HDP-Flow: Generalizable Bayesian Nonparametric Model for Time Series State Discovery

• Sana Tonekaboni
• Tina Behrouzi
• Addison Weatherhead
• Emily B. Fox
• David M. Blei
• Anna Goldenberg

We introduce HDP-Flow, a Bayesian nonparametric (BNP) model for unsupervised state discovery in dynamic, non-stationary time series data. Unlike prior work that assumes fixed states, HDPFlow models evolving datasets with unknown and variable latent states. By integrating the adaptability of BNP models with the expressive power of normalizing flows, HDP-Flow effectively models dynamic, non-stationary patterns, while learning transferable states across datasets with wellcalibrated uncertainty. We propose a scalable variational algorithm to enable efficient inference, addressing the limitations of traditional sampling-based BNP methods. HDP-Flow outperforms existing approaches in latent state identification and provides probabilistic insight into state distributions and transition dynamics. Evaluating HDP-Flow across two wearable datasets demonstrates transferability of states across diverse sub-populations, validating its robustness and generalizability.

UAI Conference 2024 Conference Paper

Amortized Variational Inference: When and Why?

• Charles C. Margossian
• David M. Blei

In a probabilistic latent variable model, factorized (or mean-field) variational inference (F-VI) fits a separate parametric distribution for each latent variable. Amortized variational inference (A-VI) instead learns a common inference function, which maps each observation to its corresponding latent variable’s approximate posterior. Typically, A-VI is used as a cog in the training of variational autoencoders, however it stands to reason that A-VI could also be used as a general alternative to F-VI. In this paper we study when and why A-VI can be used for approximate Bayesian inference. We derive conditions on a latent variable model which are necessary, sufficient, and verifiable under which A-VI can attain F-VI’s optimal solution, thereby closing the amortization gap. We prove these conditions are uniquely verified by simple hierarchical models, a broad class that encompasses many models in machine learning. We then show, on a broader class of models, how to expand the domain of AVI’s inference function to improve its solution, and we provide examples, e. g. hidden Markov models, where the amortization gap cannot be closed.

ICML Conference 2024 Conference Paper

Batch and match: black-box variational inference with a score-based divergence

• Diana Cai
• Chirag Modi 0002
• Loucas Pillaud-Vivien
• Charles C. Margossian
• Robert M. Gower
• David M. Blei
• Lawrence K. Saul

Most leading implementations of black-box variational inference (BBVI) are based on optimizing a stochastic evidence lower bound (ELBO). But such approaches to BBVI often converge slowly due to the high variance of their gradient estimates and their sensitivity to hyperparameters. In this work, we propose batch and match (BaM), an alternative approach to BBVI based on a score-based divergence. Notably, this score-based divergence can be optimized by a closed-form proximal update for Gaussian variational families with full covariance matrices. We analyze the convergence of BaM when the target distribution is Gaussian, and we prove that in the limit of infinite batch size the variational parameter updates converge exponentially quickly to the target mean and covariance. We also evaluate the performance of BaM on Gaussian and non-Gaussian target distributions that arise from posterior inference in hierarchical and deep generative models. In these experiments, we find that BaM typically converges in fewer (and sometimes significantly fewer) gradient evaluations than leading implementations of BBVI based on ELBO maximization.

NeurIPS Conference 2024 Conference Paper

EigenVI: score-based variational inference with orthogonal function expansions

• Diana Cai
• Chirag Modi
• Charles C. Margossian
• Robert M. Gower
• David M. Blei
• Lawrence K. Saul

We develop EigenVI, an eigenvalue-based approach for black-box variational inference (BBVI). EigenVI constructs its variational approximations from orthogonal function expansions. For distributions over $\mathbb{R}^D$, the lowest order term in these expansions provides a Gaussian variational approximation, while higher-order terms provide a systematic way to model non-Gaussianity. These approximations are flexible enough to model complex distributions (multimodal, asymmetric), but they are simple enough that one can calculate their low-order moments and draw samples from them. EigenVI can also model other types of random variables (e. g. , nonnegative, bounded) by constructing variational approximations from different families of orthogonal functions. Within these families, EigenVI computes the variational approximation that best matches the score function of the target distribution by minimizing a stochastic estimate of the Fisher divergence. Notably, this optimization reduces to solving a minimum eigenvalue problem, so that EigenVI effectively sidesteps the iterative gradient-based optimizations that are required for many other BBVI algorithms. (Gradient-based methods can be sensitive to learning rates, termination criteria, and other tunable hyperparameters. ) We use EigenVI to approximate a variety of target distributions, including a benchmark suite of Bayesian models from posteriordb. On these distributions, we find that EigenVI is more accurate than existing methods for Gaussian BBVI.

UAI Conference 2024 Conference Paper

Extremely Greedy Equivalence Search

• Achille Nazaret
• David M. Blei

The goal of causal discovery is to learn a directed acyclic graph from data. One of the most well-known methods for this problem is Greedy Equivalence Search (GES). GES searches for the graph by incrementally and greedily adding or removing edges to maximize a model selection criterion. It has strong theoretical guarantees on infinite data but can fail in practice on finite data. In this paper, we first identify some of the causes of GES’s failure, finding that it can get blocked in local optima, especially in denser graphs. We then propose eXtremely Greedy Equivalent Search (XGES), which involves a new heuristic to improve the search strategy of GES while retaining its theoretical guarantees. In particular, XGES favors deleting edges early in the search over inserting edges, which reduces the possibility of the search ending in local optima. A further contribution of this work is an efficient algorithmic formulation of XGES (and GES). We benchmark XGES on simulated datasets with known ground truth. We find that XGES consistently outperforms GES in recovering the correct graphs, and it is 10 times faster.

NeurIPS Conference 2024 Conference Paper

Hypothesis Testing the Circuit Hypothesis in LLMs

• Claudia Shi
• Nicolas Beltran-Velez
• Achille Nazaret
• Carolina Zheng
• Adrià Garriga-Alonso
• Andrew Jesson
• Maggie Makar
• David M. Blei

Large language models (LLMs) demonstrate surprising capabilities, but we do not understand how they are implemented. One hypothesis suggests that these capabilities are primarily executed by small subnetworks within the LLM, known as circuits. But how can we evaluate this hypothesis? In this paper, we formalize a set of criteria that a circuit is hypothesized to meet and develop a suite of hypothesis tests to evaluate how well circuits satisfy them. The criteria focus on the extent to which the LLM's behavior is preserved, the degree of localization of this behavior, and whether the circuit is minimal. We apply these tests to six circuits described in the research literature. We find that synthetic circuits -- circuits that are hard-coded in the model -- align with the idealized properties. Circuits discovered in Transformer models satisfy the criteria to varying degrees. To facilitate future empirical studies of circuits, we created the \textit{circuitry} package, a wrapper around the \textit{TransformerLens} library, which abstracts away lower-level manipulations of hooks and activations. The software is available at \url{https: //github. com/blei-lab/circuitry}.

JMLR Journal 2024 Journal Article

Optimization-based Causal Estimation from Heterogeneous Environments

• Mingzhang Yin
• Yixin Wang
• David M. Blei

This paper presents a new optimization approach to causal estimation. Given data that contains covariates and an outcome, which covariates are causes of the outcome, and what is the strength of the causality? In classical machine learning (ML), the goal of optimization is to maximize predictive accuracy. However, some covariates might exhibit a non-causal association with the outcome. Such spurious associations provide predictive power for classical ML, but they prevent us from causally interpreting the result. This paper proposes CoCo, an optimization algorithm that bridges the gap between pure prediction and causal inference. CoCo leverages the recently-proposed idea of environments, datasets of covariates/response where the causal relationships remain invariant but where the distribution of the covariates changes from environment to environment. Given datasets from multiple environments—and ones that exhibit sufficient heterogeneity—CoCo maximizes an objective for which the only solution is the causal solution. We describe the theoretical foundations of this approach and demonstrate its effectiveness on simulated and real datasets. Compared to classical ML and existing methods, CoCo provides more accurate estimates of the causal model and more accurate predictions under interventions. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2024. ( edit, beta )

ICML Conference 2024 Conference Paper

Stable Differentiable Causal Discovery

• Achille Nazaret
• Justin Hong
• Elham Azizi
• David M. Blei

Inferring causal relationships as directed acyclic graphs (DAGs) is an important but challenging problem. Differentiable Causal Discovery (DCD) is a promising approach to this problem, framing the search as a continuous optimization. But existing DCD methods are numerically unstable, with poor performance beyond tens of variables. In this paper, we propose Stable Differentiable Causal Discovery (SDCD), a new method that improves previous DCD methods in two ways: (1) It employs an alternative constraint for acyclicity; this constraint is more stable, both theoretically and empirically, and fast to compute. (2) It uses a training procedure tailored for sparse causal graphs, which are common in real-world scenarios. We first derive SDCD and prove its stability and correctness. We then evaluate it with both observational and interventional data and in both small-scale and large-scale settings. We find that SDCD outperforms existing methods in convergence speed and accuracy, and can scale to thousands of variables.

UAI Conference 2022 Conference Paper

Forget-me-not! Contrastive critics for mitigating posterior collapse

• Sachit Menon
• David M. Blei
• Carl Vondrick

Variational autoencoders (VAEs) suffer from posterior collapse, where the powerful neural networks used for modeling and inference optimize the objective without meaningfully using the latent representation. We introduce inference critics that detect and incentivize against posterior collapse by requiring correspondence between latent variables and the observations. By connecting the critic’s objective to the literature in self-supervised contrastive representation learning, we show both theoretically and empirically that optimizing inference critics increases the mutual information between observations and latents, mitigating posterior collapse. This approach is straightforward to implement and requires significantly less training time than prior methods, yet obtains competitive results on three established datasets. Overall, the approach lays the foundation to bridge the previously disconnected frameworks of contrastive learning and probabilistic modeling with variational autoencoders, underscoring the benefits both communities may find at their intersection.

ICML Conference 2022 Conference Paper

Variational Inference for Infinitely Deep Neural Networks

• Achille Nazaret
• David M. Blei

We introduce the unbounded depth neural network (UDN), an infinitely deep probabilistic model that adapts its complexity to the training data. The UDN contains an infinite sequence of hidden layers and places an unbounded prior on a truncation L, the layer from which it produces its data. Given a dataset of observations, the posterior UDN provides a conditional distribution of both the parameters of the infinite neural network and its truncation. We develop a novel variational inference algorithm to approximate this posterior, optimizing a distribution of the neural network weights and of the truncation depth L, and without any upper limit on L. To this end, the variational family has a special structure: it models neural network weights of arbitrary depth, and it dynamically creates or removes free variational parameters as its distribution of the truncation is optimized. (Unlike heuristic approaches to model search, it is solely through gradient-based optimization that this algorithm explores the space of truncations.) We study the UDN on real and synthetic data. We find that the UDN adapts its posterior depth to the dataset complexity; it outperforms standard neural networks of similar computational complexity; and it outperforms other approaches to infinite-depth neural networks.

ICML Conference 2021 Conference Paper

A Proxy Variable View of Shared Confounding

• Yixin Wang 0002
• David M. Blei

Causal inference from observational data can be biased by unobserved confounders. Confounders{—}the variables that affect both the treatments and the outcome{—}induce spurious non-causal correlations between the two. Without additional conditions, unobserved confounders generally make causal quantities hard to identify. In this paper, we focus on the setting where there are many treatments with shared confounding, and we study under what conditions is causal identification possible. The key observation is that we can view subsets of treatments as proxies of the unobserved confounder and identify the intervention distributions of the rest. Moreover, while existing identification formulas for proxy variables involve solving integral equations, we show that one can circumvent the need for such solutions by directly modeling the data. Finally, we extend these results to an expanded class of causal graphs, those with other confounders and selection variables.

UAI Conference 2021 Conference Paper

Invariant representation learning for treatment effect estimation

• Claudia Shi
• Victor Veitch
• David M. Blei

The defining challenge for causal inference from observational data is the presence of ‘confounders’, covariates that affect both treatment assignment and the outcome. To address this challenge, practitioners collect and adjust for the covariates, hoping that they adequately correct for confounding. However, including every observed covariate in the adjustment runs the risk of including ‘bad controls’, variables that induce bias when they are conditioned on. The problem is that we do not always know which variables in the covariate set are safe to adjust for and which are not. To address this problem, we develop Nearly Invariant Causal Estimation (NICE). NICE uses invariant risk minimization (IRM) [Arj19] to learn a representation of the covariates that, under some assumptions, strips out bad controls but preserves sufficient information to adjust for confounding. Adjusting for the learned representation, rather than the covariates themselves, avoids the induced bias and provides valid causal inferences. We evaluate NICE on both synthetic and semi-synthetic data. When the covariates contain unknown collider variables and other bad controls, NICE performs better than adjusting for all the covariates.

ICML Conference 2021 Conference Paper

Unsupervised Representation Learning via Neural Activation Coding

• Yookoon Park
• Sangho Lee 0008
• Gunhee Kim
• David M. Blei

We present neural activation coding (NAC) as a novel approach for learning deep representations from unlabeled data for downstream applications. We argue that the deep encoder should maximize its nonlinear expressivity on the data for downstream predictors to take full advantage of its representation power. To this end, NAC maximizes the mutual information between activation patterns of the encoder and the data over a noisy communication channel. We show that learning for a noise-robust activation code increases the number of distinct linear regions of ReLU encoders, hence the maximum nonlinear expressivity. More interestingly, NAC learns both continuous and discrete representations of data, which we respectively evaluate on two downstream tasks: (i) linear classification on CIFAR-10 and ImageNet-1K and (ii) nearest neighbor retrieval on CIFAR-10 and FLICKR-25K. Empirical results show that NAC attains better or comparable performance on both tasks over recent baselines including SimCLR and DistillHash. In addition, NAC pretraining provides significant benefits to the training of deep generative models. Our code is available at https: //github. com/yookoon/nac.

UAI Conference 2021 Conference Paper

variational combinatorial sequential monte carlo methods for bayesian phylogenetic inference

• Antonio Khalil Moretti
• Liyi Zhang
• Christian A. Naesseth
• Hadiah Venner
• David M. Blei
• Itsik Pe'er

Bayesian phylogenetic inference is often conducted via local or sequential search over topologies and branch lengths using algorithms such as random-walk Markov chain Monte Carlo (MCMC) or Combinatorial Sequential Monte Carlo (CSMC). However, when MCMC is used for evolutionary parameter learning, convergence requires long runs with inefficient exploration of the state space. We introduce Variational Combinatorial Sequential Monte Carlo (VCSMC), a powerful framework that establishes variational sequential search to learn distributions over intricate combinatorial structures. We then develop nested CSMC, an efficient proposal distribution for CSMC and prove that nested CSMC is an exact approximation to the (intractable) locally optimal proposal. We use nested CSMC to define a second objective, VNCSMC which yields tighter lower bounds than VCSMC. We show that VCSMC and VNCSMC are computationally efficient and explore higher probability spaces than existing methods on a range of tasks.

UAI Conference 2020 Conference Paper

Adapting Text Embeddings for Causal Inference

• Victor Veitch
• Dhanya Sridhar
• David M. Blei

Does adding a theorem to a paper affect its chance of acceptance? Does labeling a post with the author’s gender affect the post popularity? This paper develops a method to estimate such causal effects from observational text data, adjusting for confounding features of the text such as the subject or writing quality. We assume that the text suffices for causal adjustment but that, in practice, it is prohibitively high-dimensional. To address this challenge, we develop causally sufficient embeddings, low- dimensional document representations that preserve sufficient information for causal identification and allow for efficient estimation of causal effects. Causally sufficient embeddings combine two ideas. The first is supervised dimensionality reduction: causal adjustment requires only the aspects of text that are predictive of both the treatment and outcome. The second is efficient language modeling: representations of text are designed to dispose of linguistically irrelevant information, and this information is also causally irrelevant. Our method adapts language models (specifically, word embeddings and topic models) to learn document embeddings that are able to predict both treatment and outcome. We study causally sufficient embeddings with semi-synthetic datasets and find that they improve causal estimation over related embedding methods. We illustrate the methods by answering the two motivating questions—the effect of a theorem on paper acceptance and the effect of a gender label on post popularity. Code and data available at github. com/vveitch/causal-text-embeddings-tf2.

YNIMG Journal 2018 Journal Article

A probabilistic approach to discovering dynamic full-brain functional connectivity patterns

• Jeremy R. Manning
• Xia Zhu
• Theodore L. Willke
• Rajesh Ranganath
• Kimberly Stachenfeld
• Uri Hasson
• David M. Blei
• Kenneth A. Norman

Recent research shows that the covariance structure of functional magnetic resonance imaging (fMRI) data – commonly described as functional connectivity – can change as a function of the participant's cognitive state (for review see Turk-Browne, 2013). Here we present a Bayesian hierarchical matrix factorization model, termed hierarchical topographic factor analysis (HTFA), for efficiently discovering full-brain networks in large multi-subject neuroimaging datasets. HTFA approximates each subject's network by first re-representing each brain image in terms of the activities of a set of localized nodes, and then computing the covariance of the activity time series of these nodes. The number of nodes, along with their locations, sizes, and activities (over time) are learned from the data. Because the number of nodes is typically substantially smaller than the number of fMRI voxels, HTFA can be orders of magnitude more efficient than traditional voxel-based functional connectivity approaches. In one case study, we show that HTFA recovers the known connectivity patterns underlying a collection of synthetic datasets. In a second case study, we illustrate how HTFA may be used to discover dynamic full-brain activity and connectivity patterns in real fMRI data, collected as participants listened to a story. In a third case study, we carried out a similar series of analyses on fMRI data collected as participants viewed an episode of a television show. In these latter case studies, we found that the HTFA-derived activity and connectivity patterns can be used to reliably decode which moments in the story or show the participants were experiencing. Further, we found that these two classes of patterns contained partially non-overlapping information, such that decoders trained on combinations of activity-based and dynamic connectivity-based features performed better than decoders trained on activity or connectivity patterns alone. We replicated this latter result with two additional (previously developed) methods for efficiently characterizing full-brain activity and connectivity patterns.

ICML Conference 2018 Conference Paper

Augment and Reduce: Stochastic Inference for Large Categorical Distributions

• Francisco J. R. Ruiz
• Michalis K. Titsias
• Adji Bousso Dieng
• David M. Blei

Categorical distributions are ubiquitous in machine learning, e. g. , in classification, language models, and recommendation systems. However, when the number of possible outcomes is very large, using categorical distributions becomes computationally expensive, as the complexity scales linearly with the number of outcomes. To address this problem, we propose augment and reduce (A&R), a method to alleviate the computational complexity. A&R uses two ideas: latent variable augmentation and stochastic variational inference. It maximizes a lower bound on the marginal likelihood of the data. Unlike existing methods which are specific to softmax, A&R is more general and is amenable to other categorical models, such as multinomial probit. On several large-scale classification problems, we show that A&R provides a tighter bound on the marginal likelihood and has better predictive performance than existing approaches.

ICML Conference 2018 Conference Paper

Black Box FDR

• Wesley Tansey
• Yixin Wang 0002
• David M. Blei
• Raul Rabadan

Analyzing large-scale, multi-experiment studies requires scientists to test each experimental outcome for statistical significance and then assess the results as a whole. We present Black Box FDR (BB-FDR), an empirical-Bayes method for analyzing multi-experiment studies when many covariates are gathered per experiment. BB-FDR learns a series of black box predictive models to boost power and control the false discovery rate (FDR) at two stages of study analysis. In Stage 1, it uses a deep neural network prior to report which experiments yielded significant outcomes. In Stage 2, a separate black box model of each covariate is used to select features that have significant predictive power across all experiments. In benchmarks, BB-FDR outperforms competing state-of-the-art methods in both stages of analysis. We apply BB-FDR to two real studies on cancer drug efficacy. For both studies, BB-FDR increases the proportion of significant outcomes discovered and selects variables that reveal key genomic drivers of drug sensitivity and resistance in cancer.

ICML Conference 2018 Conference Paper

Noisin: Unbiased Regularization for Recurrent Neural Networks

• Adji Bousso Dieng
• Rajesh Ranganath
• Jaan Altosaar
• David M. Blei

Recurrent neural networks (RNNs) are powerful models of sequential data. They have been successfully used in domains such as text and speech. However, RNNs are susceptible to overfitting; regularization is important. In this paper we develop Noisin, a new method for regularizing RNNs. Noisin injects random noise into the hidden states of the RNN and then maximizes the corresponding marginal likelihood of the data. We show how Noisin applies to any RNN and we study many different types of noise. Noisin is unbiased–it preserves the underlying RNN on average. We characterize how Noisin regularizes its RNN both theoretically and empirically. On language modeling benchmarks, Noisin improves over dropout by as much as 12. 2% on the Penn Treebank and 9. 4% on the Wikitext-2 dataset. We also compared the state-of-the-art language model of Yang et al. 2017, both with and without Noisin. On the Penn Treebank, the method with Noisin more quickly reaches state-of-the-art performance.

JMLR Journal 2017 Journal Article

Automatic Differentiation Variational Inference

• Alp Kucukelbir
• Dustin Tran
• Rajesh Ranganath
• Andrew Gelman
• David M. Blei

Probabilistic modeling is iterative. A scientist posits a simple model, fits it to her data, refines it according to her analysis, and repeats. However, fitting complex models to large data is a bottleneck in this process. Deriving algorithms for new models can be both mathematically and computationally challenging, which makes it difficult to efficiently cycle through the steps. To this end, we develop ADVI. Using our method, the scientist only provides a probabilistic model and a dataset, nothing else. ADVI automatically derives an efficient variational inference algorithm, freeing the scientist to refine and explore many models. ADVI supports a broad class of models ---no conjugacy assumptions are required. We study ADVI across ten modern probabilistic models and apply it to a dataset with millions of observations. We deploy ADVI as part of Stan, a probabilistic programming system. [abs] [ pdf ][ bib ] &copy JMLR 2017. ( edit, beta )

ICML Conference 2017 Conference Paper

Evaluating Bayesian Models with Posterior Dispersion Indices

• Alp Kucukelbir
• Yixin Wang 0002
• David M. Blei

Probabilistic modeling is cyclical: we specify a model, infer its posterior, and evaluate its performance. Evaluation drives the cycle, as we revise our model based on how it performs. This requires a metric. Traditionally, predictive accuracy prevails. Yet, predictive accuracy does not tell the whole story. We propose to evaluate a model through posterior dispersion. The idea is to analyze how each datapoint fares in relation to posterior uncertainty around the hidden structure. This highlights datapoints the model struggles to explain and provides complimentary insight to datapoints with low predictive accuracy. We present a family of posterior dispersion indices (PDI) that capture this idea. We show how a PDI identifies patterns of model mismatch in three real data examples: voting preferences, supermarket shopping, and population genetics.

ICML Conference 2017 Conference Paper

Robust Probabilistic Modeling with Bayesian Data Reweighting

• Yixin Wang 0002
• Alp Kucukelbir
• David M. Blei

Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model’s assumptions and reality. We propose a way to systematically detect and mitigate mismatch of a large class of probabilistic models. The idea is to raise the likelihood of each observation to a weight and then to infer both the latent variables and the weights from data. Inferring the weights allows a model to identify observations that match its assumptions and down-weight others. This enables robust inference and improves predictive accuracy. We study four different forms of mismatch with reality, ranging from missing latent groups to structure misspecification. A Poisson factorization analysis of the Movielens 1M dataset shows the benefits of this approach in a practical scenario.

JMLR Journal 2017 Journal Article

Stochastic Gradient Descent as Approximate Bayesian Inference

• Stephan Mandt
• Matthew D. Hoffman
• David M. Blei

Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an approximate Bayesian posterior inference algorithm. Specifically, we show how to adjust the tuning parameters of constant SGD to best match the stationary distribution to a posterior, minimizing the Kullback-Leibler divergence between these two distributions. (2) We demonstrate that constant SGD gives rise to a new variational EM algorithm that optimizes hyperparameters in complex probabilistic models. (3) We also show how to tune SGD with momentum for approximate sampling. (4) We analyze stochastic-gradient MCMC algorithms. For Stochastic- Gradient Langevin Dynamics and Stochastic-Gradient Fisher Scoring, we quantify the approximation errors due to finite learning rates. Finally (5), we use the stochastic process perspective to give a short proof of why Polyak averaging is optimal. Based on this idea, we propose a scalable approximate MCMC algorithm, the Averaged Stochastic Gradient Sampler. [abs] [ pdf ][ bib ] &copy JMLR 2017. ( edit, beta )

ICML Conference 2017 Conference Paper

Zero-Inflated Exponential Family Embeddings

• Liping Liu
• David M. Blei

Word embeddings are a widely-used tool to analyze language, and exponential family embeddings (Rudolph et al. , 2016) generalize the technique to other types of data. One challenge to fitting embedding methods is sparse data, such as a document/term matrix that contains many zeros. To address this issue, practitioners typically downweight or subsample the zeros, thus focusing learning on the non-zero entries. In this paper, we develop zero-inflated embeddings, a new embedding method that is designed to learn from sparse observations. In a zero-inflated embedding (ZIE), a zero in the data can come from an interaction to other data (i. e. , an embedding) or from a separate process by which many observations are equal to zero (i. e. a probability mass at zero). Fitting a ZIE naturally downweights the zeros and dampens their influence on the model. Across many types of data—language, movie ratings, shopping histories, and bird watching logs—we found that zero-inflated embeddings provide improved predictive performance over standard approaches and find better vector representation of items.

ICML Conference 2016 Conference Paper

A Variational Analysis of Stochastic Gradient Algorithms

• Stephan Mandt
• Matthew D. Hoffman
• David M. Blei

Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show that SGD with constant rates can be effectively used as an approximate posterior inference algorithm for probabilistic modeling. Specifically, we show how to adjust the tuning parameters of SGD such as to match the resulting stationary distribution to the posterior. This analysis rests on interpreting SGD as a continuous-time stochastic process and then minimizing the Kullback-Leibler divergence between its stationary distribution and the target posterior. (This is in the spirit of variational inference.) In more detail, we model SGD as a multivariate Ornstein-Uhlenbeck process and then use properties of this process to derive the optimal parameters. This theoretical framework also connects SGD to modern scalable inference algorithms; we analyze the recently proposed stochastic gradient Fisher scoring under this perspective. We demonstrate that SGD with properly chosen constant rates gives a new way to optimize hyperparameters in probabilistic models.

ICML Conference 2016 Conference Paper

Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations

• Aaron Schein
• Mingyuan Zhou
• David M. Blei
• Hanna M. Wallach

We introduce Bayesian Poisson Tucker decomposition (BPTD) for modeling country–country interaction event data. These data consist of interaction events of the form “country i took action a toward country j at time t. ” BPTD discovers overlapping country–community memberships, including the number of latent communities. In addition, it discovers directed community–community interaction networks that are specific to “topics” of action types and temporal “regimes. ” We show that BPTD yields an efficient MCMC inference algorithm and achieves better predictive performance than related models. We also demonstrate that it discovers interpretable latent structure that agrees with our knowledge of international relations.

ICML Conference 2016 Conference Paper

Hierarchical Variational Models

• Rajesh Ranganath
• Dustin Tran
• David M. Blei

Black box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive variational distribution that maintains efficient computation? To address this, we develop hierarchical variational models (HVMs). HVMs augment a variational approximation with a prior on its parameters, which allows it to capture complex structure for both discrete and continuous latent variables. The algorithm we develop is black box, can be used for any HVM, and has the same computational efficiency as the original approximation. We study HVMs on a variety of deep discrete latent variable models. HVMs generalize other expressive variational distributions and maintains higher fidelity to the posterior.

UAI Conference 2016 Conference Paper

Overdispersed Black-Box Variational Inference

• Francisco J. R. Ruiz
• Michalis K. Titsias
• David M. Blei

We introduce overdispersed black-box variational inference, a method to reduce the variance of the Monte Carlo estimator of the gradient in black-box variational inference. Instead of taking samples from the variational distribution, we use importance sampling to take samples from an overdispersed distribution in the same exponential family as the variational approximation. Our approach is general since it can be readily applied to any exponential family distribution, which is the typical choice for the variational approximation. We run experiments on two non-conjugate probabilistic models to show that our method effectively reduces the variance, and the overhead introduced by the computation of the proposal parameters and the importance weights is negligible. We find that our overdispersed importance sampling scheme provides lower variance than black-box variational inference, even when the latter uses twice the number of samples. This results in faster convergence of the black-box inference procedure.

ICLR Conference 2016 Conference Paper

Variational Gaussian Process

• Dustin Tran
• Rajesh Ranganath
• David M. Blei

Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric variational family, 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 auto-encoders 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.

UAI Conference 2015 Conference Paper

Population Empirical Bayes

• Alp Kucukelbir
• David M. Blei

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.

UAI Conference 2015 Conference Paper

Scalable Recommendation with Hierarchical Poisson Factorization

• Prem Gopalan
• Jake M. Hofman
• David M. Blei

We develop hierarchical Poisson matrix factorization (HPF), a novel method for providing users with high quality recommendations based on implicit feedback, such as views, clicks, or purchases. In contrast to existing recommendation models, HPF has a number of desirable properties. First, we show that HPF more accurately captures the long-tailed user activity found in most consumption data by explicitly considering the fact that users have finite attention budgets. This leads to better estimates of users’ latent preferences, and therefore superior recommendations, compared to competing methods. Second, HPF learns these latent factors by only explicitly considering positive examples, eliminating the often costly step of generating artificial negative examples when fitting to implicit data. Third, HPF is more than just one method— it is the simplest in a class of probabilistic models with these properties, and can easily be extended to include more complex structure and assumptions. We develop a variational algorithm for approximate posterior inference for HPF that scales up to large data sets, and we demonstrate its performance on a wide variety of real-world recommendation problems—users rating movies, listening to songs, reading scientific papers, and reading news articles.

UAI Conference 2015 Conference Paper

The Survival Filter: Joint Survival Analysis with a Latent Time Series

• Rajesh Ranganath
• Adler J. Perotte
• Noémie Elhadad
• David M. Blei

Survival analysis is a core task in applied statistics, which models time-to-failure or time-to-event data. In the clinical domain, for example, meaningful events are defined as the onset of different diseases for a given patient. Survival analysis is limited, however, for analyzing modern electronic health records. Patients often have a wide range of diseases, and there are complex interactions among the relative risks of different events. To this end, we develop the survival filter model, a time-series model for joint survival analysis that models multiple patients and multiple diseases. We develop a scalable variational inference algorithm and apply our method to a large data set of longitudinal patient records. The survival filter gives good predictive performance when compared to two baselines and identifies clinically meaningful patterns of disease interaction.

YNIMG Journal 2014 Journal Article

Decomposing spatiotemporal brain patterns into topographic latent sources

• Samuel J. Gershman
• David M. Blei
• Kenneth A. Norman
• Per B. Sederberg

This paper extends earlier work on spatial modeling of fMRI data to the temporal domain, providing a framework for analyzing high temporal resolution brain imaging modalities such as electroencapholography (EEG). The central idea is to decompose brain imaging data into a covariate-dependent superposition of functions defined over continuous time and space (what we refer to as topographic latent sources). The continuous formulation allows us to parametrically model spatiotemporally localized activations. To make group-level inferences, we elaborate the model hierarchically by sharing sources across subjects. We describe a variational algorithm for parameter estimation that scales efficiently to large data sets. Applied to three EEG data sets, we find that the model produces good predictive performance and reproduces a number of classic findings. Our results suggest that topographic latent sources serve as an effective hypothesis space for interpreting spatiotemporal brain imaging data.

ICML Conference 2014 Conference Paper

The Inverse Regression Topic Model

• Maxim Rabinovich
• David M. Blei

\citettaddy13mnir proposed multinomial inverse regression (MNIR) as a new model of annotated text based on the influence of metadata and response variables on the distribution of words in a document. While effective, MNIR has no way to exploit structure in the corpus to improve its predictions or facilitate exploratory data analysis. On the other hand, traditional probabilistic topic models (like latent Dirichlet allocation) capture natural heterogeneity in a collection but do not account for external variables. In this paper, we introduce the inverse regression topic model (IRTM), a mixed-membership extension of MNIR that combines the strengths of both methodologies. We present two inference algorithms for the IRTM: an efficient batch estimation algorithm and an online variant, which is suitable for large corpora. We apply these methods to a corpus of 73K Congressional press releases and another of 150K Yelp reviews, demonstrating that the IRTM outperforms both MNIR and supervised topic models on the prediction task. Further, we give examples showing that the IRTM enables systematic discovery of in-topic lexical variation, which is not possible with previous supervised topic models.

ICML Conference 2013 Conference Paper

An Adaptive Learning Rate for Stochastic Variational Inference

• Rajesh Ranganath
• Chong Wang 0002
• David M. Blei
• Eric P. Xing

Stochastic variational inference finds good posterior approximations of probabilistic models with very large data sets. It optimizes the variational objective with stochastic optimization, following noisy estimates of the natural gradient. Operationally, stochastic inference iteratively subsamples from the data, analyzes the subsample, and updates parameters with a decreasing learning rate. However, the algorithm is sensitive to that rate, which usually requires hand-tuning to each application. We solve this problem by developing an adaptive learning rate for stochastic inference. Our method requires no tuning and is easily implemented with computations already made in the algorithm. We demonstrate our approach with latent Dirichlet allocation applied to three large text corpora. Inference with the adaptive learning rate converges faster and to a better approximation than the best settings of hand-tuned rates.

JMLR Journal 2013 Journal Article

Bayesian Canonical Correlation Analysis

• Chong Wang
• David M. Blei

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 nonconjugate. 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 data sets. We studied our methods on the correlated topic model, Bayesian logistic regression, and hierarchical Bayesian logistic regression. [abs] [ pdf ][ bib ] &copy JMLR 2013. ( edit, beta )

JMLR Journal 2013 Journal Article

Stochastic Variational Inference

• Matthew D. Hoffman
• David M. Blei
• Chong Wang
• John Paisley

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. [abs] [ pdf ][ bib ] &copy JMLR 2013. ( edit, beta )

ICML Conference 2012 Conference Paper

Nonparametric variational inference

• Samuel Gershman
• Matthew D. Hoffman
• David M. Blei

ICML Conference 2012 Conference Paper

Sparse stochastic inference for latent Dirichlet allocation

• David M. Mimno
• Matthew D. Hoffman
• David M. Blei

ICML Conference 2012 Conference Paper

Variational Bayesian Inference with Stochastic Search

• John Paisley
• David M. Blei
• Michael I. Jordan

YNIMG Journal 2011 Journal Article

A topographic latent source model for fMRI data

• Samuel J. Gershman
• David M. Blei
• Francisco Pereira
• Kenneth A. Norman

We describe and evaluate a new statistical generative model of functional magnetic resonance imaging (fMRI) data. The model, topographic latent source analysis (TLSA), assumes that fMRI images are generated by a covariate-dependent superposition of latent sources. These sources are defined in terms of basis functions over space. The number of parameters in the model does not depend on the number of voxels, enabling a parsimonious description of activity patterns that avoids many of the pitfalls of traditional voxel-based approaches. We develop a multi-subject extension where latent sources at the subject-level are perturbations of a group-level template. We evaluate TLSA according to prediction, reconstruction and reproducibility. We show that it compares favorably to a Naive Bayes model while using fewer parameters. We also describe a hypothesis testing framework that can be used to identify significant latent sources.

JMLR Journal 2011 Journal Article

Dirichlet Process Mixtures of Generalized Linear Models

• Lauren A. Hannah
• David M. Blei
• Warren B. Powell

We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new class of methods for nonparametric regression. Given a data set of input-response pairs, the DP-GLM produces a global model of the joint distribution through a mixture of local generalized linear models. DP-GLMs allow both continuous and categorical inputs, and can model the same class of responses that can be modeled with a generalized linear model. We study the properties of the DP-GLM, and show why it provides better predictions and density estimates than existing Dirichlet process mixture regression models. We give conditions for weak consistency of the joint distribution and pointwise consistency of the regression estimate. [abs] [ pdf ][ bib ] &copy JMLR 2011. ( edit, beta )

JMLR Journal 2011 Journal Article

Distance Dependent Chinese Restaurant Processes

• David M. Blei
• Peter I. Frazier

We develop the distance dependent Chinese restaurant process, a flexible class of distributions over partitions that allows for dependencies between the elements. This class can be used to model many kinds of dependencies between data in infinite clustering models, including dependencies arising from time, space, and network connectivity. We examine the properties of the distance dependent CRP, discuss its connections to Bayesian nonparametric mixture models, and derive a Gibbs sampler for both fully observed and latent mixture settings. We study its empirical performance with three text corpora. We show that relaxing the assumption of exchangeability with distance dependent CRPs can provide a better fit to sequential data and network data. We also show that the distance dependent CRP representation of the traditional CRP mixture leads to a faster-mixing Gibbs sampling algorithm than the one based on the original formulation. [abs] [ pdf ][ bib ] &copy JMLR 2011. ( edit, beta )

ICML Conference 2011 Conference Paper

Predicting Legislative Roll Calls from Text

• Sean Gerrish
• David M. Blei

ICML Conference 2011 Conference Paper

Variational Inference for Stick-Breaking Beta Process Priors

• John Paisley
• Lawrence Carin
• David M. Blei

ICML Conference 2010 Conference Paper

A Language-based Approach to Measuring Scholarly Impact

• Sean Gerrish
• David M. Blei

Identifying the most influential documents in a corpus is an important problem in many fields, from information science and historiography to text summarization and news aggregation. Unfortunately, traditional bibliometrics such as citations are often not available. We propose using changes in the thematic content of documents over time to measure the importance of individual documents within the collection. We describe a dynamic topic model for both quantifying and qualifying the impact of these documents. We validate the model by analyzing three large corpora of scientific articles. Our measurement of a document’s impact correlates significantly with its number of citations.

ICML Conference 2010 Conference Paper

Bayesian Nonparametric Matrix Factorization for Recorded Music

• Matthew D. Hoffman
• David M. Blei
• Perry R. Cook

ICML Conference 2010 Conference Paper

Distance dependent Chinese restaurant processes

• David M. Blei
• Peter I. Frazier

ICML Conference 2010 Conference Paper

The IBP Compound Dirichlet Process and its Application to Focused Topic Modeling

• Sinead A. Williamson
• Chong Wang 0002
• Katherine A. Heller
• David M. Blei

UAI Conference 2009 Conference Paper

Multilingual Topic Models for Unaligned Text

• Jordan L. Boyd-Graber
• David M. Blei

We develop the multilingual topic model for unaligned text (MuTo), a probabilistic model of text that is designed to analyze corpora composed of documents in two languages. From these documents, MuTo uses stochastic EM to simultaneously discover both a matching between the languages and multilingual latent topics. We demonstrate that MuTo is able to find shared topics on real-world multilingual corpora, successfully pairing related documents across languages. MuTo provides a new framework for creating multilingual topic models without needing carefully curated parallel corpora and allows applications built using the topic model formalism to be applied to a much wider class of corpora.

UAI Conference 2008 Conference Paper

Continuous Time Dynamic Topic Models

• Chong Wang 0002
• David M. Blei
• David Heckerman

In this paper, we develop the continuous time dynamic topic model (cDTM). The cDTM is a dynamic topic model that uses Brownian motion to model the latent topics through a sequential collection of documents, where a “topic” is a pattern of word use that we expect to evolve over the course of the collection. We derive an efficient variational approximate inference algorithm that takes advantage of the sparsity of observations in text, a property that lets us easily handle many time points. In contrast to the cDTM, the original discrete-time dynamic topic model (dDTM) requires that time be discretized. Moreover, the complexity of variational inference for the dDTM grows quickly as time granularity increases, a drawback which limits fine-grained discretization. We demonstrate the cDTM on two news corpora, reporting both predictive perplexity and the novel task of time stamp prediction.

JMLR Journal 2008 Journal Article

Mixed Membership Stochastic Blockmodels

• Edoardo M. Airoldi
• David M. Blei
• Stephen E. Fienberg
• Eric P. Xing

Consider data consisting of pairwise measurements, such as presence or absence of links between pairs of objects. These data arise, for instance, in the analysis of protein interactions and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing pairwise measurements with probabilistic models requires special assumptions, since the usual independence or exchangeability assumptions no longer hold. Here we introduce a class of variance allocation models for pairwise measurements: mixed membership stochastic blockmodels. These models combine global parameters that instantiate dense patches of connectivity (blockmodel) with local parameters that instantiate node-specific variability in the connections (mixed membership). We develop a general variational inference algorithm for fast approximate posterior inference. We demonstrate the advantages of mixed membership stochastic blockmodels with applications to social networks and protein interaction networks. [abs] [ pdf ][ bib ] &copy JMLR 2008. ( edit, beta )

ICML Conference 2007 Conference Paper

Hierarchical maximum entropy density estimation

• Miroslav Dudík
• David M. Blei
• Robert E. Schapire

UAI Conference 2007 Conference Paper

Nonparametric Bayes Pachinko Allocation

• Wei Li 0010
• David M. Blei
• Andrew McCallum

ICML Conference 2006 Conference Paper

Dynamic topic models

• David M. Blei
• John D. Lafferty

A family of probabilistic time series models is developed to analyze the time evolution of topics in large document collections. The approach is to use state space models on the natural parameters of the multinomial distributions that represent the topics. Variational approximations based on Kalman filters and nonparametric wavelet regression are developed to carry out approximate posterior inference over the latent topics. In addition to giving quantitative, predictive models of a sequential corpus, dynamic topic models provide a qualitative window into the contents of a large document collection. The models are demonstrated by analyzing the OCR'ed archives of the journal Science from 1880 through 2000.

ICML Conference 2004 Conference Paper

Variational methods for the Dirichlet process

• David M. Blei
• Michael I. Jordan

Variational inference methods, including mean field methods and loopy belief propagation, have been widely used for approximate probabilistic inference in graphical models. While often less accurate than MCMC, variational methods provide a fast deterministic approximation to marginal and conditional probabilities. Such approximations can be particularly useful in high dimensional problems where sampling methods are too slow to be effective. A limitation of current methods, however, is that they are restricted to parametric probabilistic models. MCMC does not have such a limitation; indeed, MCMC samplers have been developed for the Dirichlet process (DP), a nonparametric distribution on distributions (Ferguson, 1973) that is the cornerstone of Bayesian nonparametric statistics (Escobar & West, 1995; Neal, 2000). In this paper, we develop a mean-field variational approach to approximate inference for the Dirichlet process, where the approximate posterior is based on the truncated stick-breaking construction (Ishwaran & James, 2001). We compare our approach to DP samplers for Gaussian DP mixture models.

JMLR Journal 2003 Journal Article

Latent Dirichlet Allocation

• David M. Blei
• Andrew Y. Ng
• Michael I. Jordan

We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model.

JMLR Journal 2003 Journal Article

Matching Words and Pictures

• Kobus Barnard
• Pinar Duygulu
• David Forsyth
• Nando de Freitas
• David M. Blei
• Michael I. Jordan

We present a new approach for modeling multi-modal data sets, focusing on the specific case of segmented images with associated text. Learning the joint distribution of image regions and words has many applications. We consider in detail predicting words associated with whole images (auto-annotation) and corresponding to particular image regions (region naming). Auto-annotation might help organize and access large collections of images. Region naming is a model of object recognition as a process of translating image regions to words, much as one might translate from one language to another. Learning the relationships between image regions and semantic correlates (words) is an interesting example of multi-modal data mining, particularly because it is typically hard to apply data mining techniques to collections of images. We develop a number of models for the joint distribution of image regions and words, including several which explicitly learn the correspondence between regions and words. We study multi-modal and correspondence extensions to Hofmann's hierarchical clustering/aspect model, a translation model adapted from statistical machine translation (Brown et al.), and a multi-modal extension to mixture of latent Dirichlet allocation (MoM-LDA). All models are assessed using a large collection of annotated images of real scenes. We study in depth the difficult problem of measuring performance. For the annotation task, we look at prediction performance on held out data. We present three alternative measures, oriented toward different types of task. Measuring the performance of correspondence methods is harder, because one must determine whether a word has been placed on the right region of an image. We can use annotation performance as a proxy measure, but accurate measurement requires hand labeled data, and thus must occur on a smaller scale. We show results using both an annotation proxy, and manually labeled data.

UAI Conference 2002 Conference Paper

Learning with Scope, with Application to Information Extraction and Classification

• David M. Blei
• J. Andrew Bagnell
• Andrew McCallum

In probabilistic approaches to classification and information extraction, one typically builds a statistical model of words under the assumption that future data will exhibit the same regularities as the training data. In many data sets, however, there are scope-limited features whose predictive power is only applicable to a certain subset of the data. For example, in information extraction from web pages, word formatting may be indicative of extraction category in different ways on different web pages. The difficulty with using such features is capturing and exploiting the new regularities encountered in previously unseen data. In this paper, we propose a hierarchical probabilistic model that uses both local/scope-limited features, such as word formatting, and global features, such as word content. The local regularities are modeled as an unobserved random parameter which is drawn once for each local data set. This random parameter is estimated during the inference process and then used to perform classification with both the local and global features--- a procedure which is akin to automatically retuning the classifier to the local regularities on each newly encountered web page. Exact inference is intractable and we present approximations via point estimates and variational methods. Empirical results on large collections of web data demonstrate that this method significantly improves performance from traditional models of global features alone.