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David Blei

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58 papers

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NeurIPS Conference 2025 Conference Paper

Fisher meets Feynman: score-based variational inference with a product of experts

Diana Cai
Robert Gower
David Blei
Lawrence Saul

We introduce a highly expressive yet distinctly tractable family for black-box variational inference (BBVI). Each member of this family is a weighted product of experts (PoE), and each weighted expert in the product is proportional to a multivariate $t$-distribution. These products of experts can model distributions with skew, heavy tails, and multiple modes, but to use them for BBVI, we must be able to sample from their densities. We show how to do this by reformulating these products of experts as latent variable models with auxiliary Dirichlet random variables. These Dirichlet variables emerge from a Feynman identity, originally developed for loop integrals in quantum field theory, that expresses the product of multiple fractions (or in our case, $t$-distributions) as an integral over the simplex. We leverage this simplicial latent space to draw weighted samples from these products of experts---samples which BBVI then uses to find the PoE that best approximates a target density. Given a collection of experts, we derive an iterative procedure to optimize the exponents that determine their geometric weighting in the PoE. At each iteration, this procedure minimizes a regularized Fisher divergence to match the scores of the variational and target densities at a batch of samples drawn from the current approximation. This minimization reduces to a convex quadratic program, and we prove under general conditions that these updates converge exponentially fast to a near-optimal weighting of experts. We conclude by evaluating this approach on a variety of synthetic and real-world target distributions.

NeurIPS Conference 2025 Conference Paper

Quantifying Uncertainty in the Presence of Distribution Shifts

Yuli Slavutsky
David Blei

Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially when test-time covariates differ from those seen during training, as occurs with selection bias or shifts over time. To address this, we propose a Bayesian framework for uncertainty estimation that explicitly accounts for covariate shifts. Unlike conventional approaches that rely on fixed priors, a key idea of our method is an adaptive prior, conditioned on both training and new covariates. This prior naturally increases uncertainty for inputs that lie far from the training distribution in regions where predictive performance is likely to degrade. To efficiently approximate the resulting posterior predictive distribution, we employ amortized variational inference. Finally, we construct synthetic environments by drawing small bootstrap samples from the training data, simulating a range of plausible covariate shifts using only the original dataset. We evaluate our method on both synthetic and real-world data, demonstrating that it yields substantially improved uncertainty estimates under distribution shift compared to existing approaches.

TMLR Journal 2024 Journal Article

CAREER: A Foundation Model for Labor Sequence Data

Keyon Vafa
Emil Palikot
Tianyu Du
Ayush Kanodia
Susan Athey
David Blei

Labor economists regularly analyze employment data by fitting predictive models to small, carefully constructed longitudinal survey datasets. Although machine learning methods offer promise for such problems, these survey datasets are too small to take advantage of them. In recent years large datasets of online resumes have also become available, providing data about the career trajectories of millions of individuals. However, standard econometric models cannot take advantage of their scale or incorporate them into the analysis of survey data. To this end we develop CAREER, a foundation model for job sequences. CAREER is first fit to large, passively-collected resume data and then fine-tuned to smaller, better-curated datasets for economic inferences. We fit CAREER to a dataset of 24 million job sequences from resumes, and adjust it on small longitudinal survey datasets. We find that CAREER forms accurate predictions of job sequences, outperforming econometric baselines on three widely-used economics datasets. We further find that CAREER can be used to form good predictions of other downstream variables. For example, incorporating CAREER into a wage model provides better predictions than the econometric models currently in use.

NeurIPS Conference 2024 Conference Paper

Estimating the Hallucination Rate of Generative AI

Andrew Jesson
Nicolas Beltran-Velez
Quentin Chu
Sweta Karlekar
Jannik Kossen
Yarin Gal
John P. Cunningham
David Blei

This paper presents a method for estimating the hallucination rate for in-context learning (ICL) with generative AI. In ICL, a conditional generative model (CGM) is prompted with a dataset and a prediction question and asked to generate a response. One interpretation of ICL assumes that the CGM computes the posterior predictive of an unknown Bayesian model, which implicitly defines a joint distribution over observable datasets and latent mechanisms. This joint distribution factorizes into two components: the model prior over mechanisms and the model likelihood of datasets given a mechanism. With this perspective, we define a \textit{hallucination} as a generated response to the prediction question with low model likelihood given the mechanism. We develop a new method that takes an ICL problem and estimates the probability that a CGM will generate a hallucination. Our method only requires generating prediction questions and responses from the CGM and evaluating its response log probability. We empirically evaluate our method using large language models for synthetic regression and natural language ICL tasks.

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TMLR Journal 2024 Journal Article

Population Priors for Matrix Factorization

Sohrab Salehi
Achille Nazaret
Sohrab P Shah
David Blei

We develop an empirical Bayes prior for probabilistic matrix factorization. Matrix factorization models each cell of a matrix with two latent variables, one associated with the cell's row and one associated with the cell's column. How to set the priors of these two latent variables? Drawing from empirical Bayes principles, we consider estimating the priors from data, to find those that best match the populations of row and column latent vectors. Thus we develop the twin population prior. We develop a variational inference algorithm to simultaneously learn the empirical priors and approximate the corresponding posterior. We evaluate this approach with both synthetic and real-world data on diverse applications: movie ratings, book ratings, single-cell gene expression data, and musical preferences. Without needing to tune Bayesian hyperparameters, we find that the twin population prior leads to high-quality predictions, outperforming manually tuned priors.

NeurIPS Conference 2024 Conference Paper

Treeffuser: probabilistic prediction via conditional diffusions with gradient-boosted trees

Nicolas Beltran-Velez
Alessandro A. Grande
Achille Nazaret
Alp Kucukelbir
David Blei

Probabilistic prediction aims to compute predictive distributions rather than single point predictions. These distributions enable practitioners to quantify uncertainty, compute risk, and detect outliers. However, most probabilistic methods assume parametric responses, such as Gaussian or Poisson distributions. When these assumptions fail, such models lead to bad predictions and poorly calibrated uncertainty. In this paper, we propose Treeffuser, an easy-to-use method for probabilistic prediction on tabular data. The idea is to learn a conditional diffusion model where the score function is estimated using gradient-boosted trees. The conditional diffusion model makes Treeffuser flexible and non-parametric, while the gradient-boosted trees make it robust and easy to train on CPUs. Treeffuser learns well-calibrated predictive distributions and can handle a wide range of regression tasks---including those with multivariate, multimodal, and skewed responses. We study Treeffuser on synthetic and real data and show that it outperforms existing methods, providing better calibrated probabilistic predictions. We further demonstrate its versatility with an application to inventory allocation under uncertainty using sales data from Walmart. We implement Treeffuser in https: //github. com/blei-lab/treeffuser.

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TMLR Journal 2023 Journal Article

Adjusting Machine Learning Decisions for Equal Opportunity and Counterfactual Fairness

Yixin Wang
Dhanya Sridhar
David Blei

Machine learning (ML) methods have the potential to automate high-stakes decisions, such as bail admissions or credit lending, by analyzing and learning from historical data. But these algorithmic decisions may be unfair: in learning from historical data, they may replicate discriminatory practices from the past. In this paper, we propose two algorithms that adjust fitted ML predictors to produce decisions that are fair. Our methods provide post-hoc adjustments to the predictors, without requiring that they be retrained. We consider a causal model of the ML decisions, define fairness through counterfactual decisions within the model, and then form algorithmic decisions that capture the historical data as well as possible but are provably fair. In particular, we consider two definitions of fairness. The first is ``equal counterfactual opportunity,'' where the counterfactual distribution of the decision is the same regardless of the protected attribute; the second is counterfactual fairness. We evaluate the algorithms, and the trade-off between accuracy and fairness, on datasets about admissions, income, credit, and recidivism.

NeurIPS Conference 2023 Conference Paper

Data Augmentations for Improved (Large) Language Model Generalization

Amir Feder
Yoav Wald
Claudia Shi
Suchi Saria
David Blei

The reliance of text classifiers on spurious correlations can lead to poor generalization at deployment, raising concerns about their use in safety-critical domains such as healthcare. In this work, we propose to use counterfactual data augmentation, guided by knowledge of the causal structure of the data, to simulate interventions on spurious features and to learn more robust text classifiers. We show that this strategy is appropriate in prediction problems where the label is spuriously correlated with an attribute. Under the assumptions of such problems, we discuss the favorable sample complexity of counterfactual data augmentation, compared to importance re-weighting. Pragmatically, we match examples using auxiliary data, based on diff-in-diff methodology, and use a large language model (LLM) to represent a conditional probability of text. Through extensive experimentation on learning caregiver-invariant predictors of clinical diagnoses from medical narratives and on semi-synthetic data, we demonstrate that our method for simulating interventions improves out-of-distribution (OOD) accuracy compared to baseline invariant learning algorithms.

NeurIPS Conference 2023 Conference Paper

Evaluating the Moral Beliefs Encoded in LLMs

Nino Scherrer
Claudia Shi
Amir Feder
David Blei

This paper presents a case study on the design, administration, post-processing, and evaluation of surveys on large language models (LLMs). It comprises two components: (1) A statistical method for eliciting beliefs encoded in LLMs. We introduce statistical measures and evaluation metrics that quantify the probability of an LLM "making a choice", the associated uncertainty, and the consistency of that choice. (2) We apply this method to study what moral beliefs are encoded in different LLMs, especially in ambiguous cases where the right choice is not obvious. We design a large-scale survey comprising 680 high-ambiguity moral scenarios (e. g. , "Should I tell a white lie? ") and 687 low-ambiguity moral scenarios (e. g. , "Should I stop for a pedestrian on the road? "). Each scenario includes a description, two possible actions, and auxiliary labels indicating violated rules (e. g. , "do not kill"). We administer the survey to 28 open- and closed-source LLMs. We find that (a) in unambiguous scenarios, most models ``choose" actions that align with commonsense. In ambiguous cases, most models express uncertainty. (b) Some models are uncertain about choosing the commonsense action because their responses are sensitive to the question-wording. (c) Some models reflect clear preferences in ambiguous scenarios. Specifically, closed-source models tend to agree with each other.

NeurIPS Conference 2023 Conference Paper

Nonparametric Identifiability of Causal Representations from Unknown Interventions

Julius von Kügelgen
Michel Besserve
Liang Wendong
Luigi Gresele
Armin Kekić
Elias Bareinboim
David Blei
Bernhard Schölkopf

We study causal representation learning, the task of inferring latent causal variables and their causal relations from high-dimensional functions (“mixtures”) of the variables. Prior work relies on weak supervision, in the form of counterfactual pre- and post-intervention views or temporal structure; places restrictive assumptions, such as linearity, on the mixing function or latent causal model; or requires partial knowledge of the generative process, such as the causal graph or intervention targets. We instead consider the general setting in which both the causal model and the mixing function are nonparametric. The learning signal takes the form of multiple datasets, or environments, arising from unknown interventions in the underlying causal model. Our goal is to identify both the ground truth latents and their causal graph up to a set of ambiguities which we show to be irresolvable from interventional data. We study the fundamental setting of two causal variables and prove that the observational distribution and one perfect intervention per node suffice for identifiability, subject to a genericity condition. This condition rules out spurious solutions that involve fine-tuning of the intervened and observational distributions, mirroring similar conditions for nonlinear cause-effect inference. For an arbitrary number of variables, we show that at least one pair of distinct perfect interventional domains per node guarantees identifiability. Further, we demonstrate that the strengths of causal influences among the latent variables are preserved by all equivalent solutions, rendering the inferred representation appropriate for drawing causal conclusions from new data. Our study provides the first identifiability results for the general nonparametric setting with unknown interventions, and elucidates what is possible and impossible for causal representation learning without more direct supervision.

NeurIPS Conference 2023 Conference Paper

Practical and Asymptotically Exact Conditional Sampling in Diffusion Models

Luhuan Wu
Brian Trippe
Christian Naesseth
David Blei
John P. Cunningham

Diffusion models have been successful on a range of conditional generation tasks including molecular design and text-to-image generation. However, these achievements have primarily depended on task-specific conditional training or error-prone heuristic approximations. Ideally, a conditional generation method should provide exact samples for a broad range of conditional distributions without requiring task-specific training. To this end, we introduce the Twisted Diffusion Sampler, or TDS. TDS is a sequential Monte Carlo (SMC) algorithm that targets the conditional distributions of diffusion models through simulating a set of weighted particles. The main idea is to use twisting, an SMC technique that enjoys good computational efficiency, to incorporate heuristic approximations without compromising asymptotic exactness. We first find in simulation and in conditional image generation tasks that TDS provides a computational statistical trade-off, yielding more accurate approximations with many particles but with empirical improvements over heuristics with as few as two particles. We then turn to motif-scaffolding, a core task in protein design, using a TDS extension to Riemannian diffusion models; on benchmark tasks, TDS allows flexible conditioning criteria and often outperforms the state-of-the-art, conditionally trained model. Code can be found in https: //github. com/blt2114/twisted diffusion sampler

TMLR Journal 2023 Journal Article

Revisiting Topic-Guided Language Models

Carolina Zheng
Keyon Vafa
David Blei

A recent line of work in natural language processing has aimed to combine language models and topic models. These \textit{topic-guided language models} augment neural language models with topic models, unsupervised learning methods that can discover document-level patterns of word use. This paper compares the effectiveness of these methods in a standardized setting. We study four topic-guided language models and two baselines, evaluating the held-out predictive performance of each model on four corpora. Surprisingly, we find that \textit{none of these methods outperform a standard LSTM language model baseline}, and most fail to learn good topics. Further, we train a probe of the neural language model that shows that the baseline's hidden states already encode topic information. We make public all code used for this study.

TMLR Journal 2023 Journal Article

Transport Score Climbing: Variational Inference Using Forward KL and Adaptive Neural Transport

Liyi Zhang
David Blei
Christian A Naesseth

Variational inference often minimizes the ``reverse'' Kullbeck-Leibler (KL) $D_{KL}(q||p)$ from the approximate distribution $q$ to the posterior $p$. Recent work studies the ``forward'' KL $D_{KL}(p||q)$, which unlike reverse KL does not lead to variational approximations that underestimate uncertainty. Markov chain Monte Carlo (MCMC) methods were used to evaluate the expectation in computing the forward KL. This paper introduces Transport Score Climbing (TSC), a method that optimizes $D_{KL}(p||q)$ by using Hamiltonian Monte Carlo (HMC) but running the HMC chain on a transformed, or warped, space. A function called the transport map performs the transformation by acting as a change-of-variable from the latent variable space. TSC uses HMC samples to dynamically train the transport map while optimizing $D_{KL}(p||q)$. TSC leverages synergies, where better transport maps lead to better HMC sampling, which then leads to better transport maps. We demonstrate TSC on synthetic and real data, including using TSC to train variational auto-encoders. We find that TSC achieves competitive performance on the experiments.

NeurIPS Conference 2023 Conference Paper

Variational Inference with Gaussian Score Matching

Chirag Modi
Robert Gower
Charles Margossian
Yuling Yao
David Blei
Lawrence Saul

Variational inference (VI) is a method to approximate the computationally intractable posterior distributions that arise in Bayesian statistics. Typically, VI fits a simple parametric distribution to be close to the target posterior, optimizing an appropriate objective such as the evidence lower bound (ELBO). In this work, we present a new approach to VI. Our method is based on the principle of score matching---namely, that if two distributions are equal then their score functions (i. e. , gradients of the log density) are equal at every point on their support. With this principle, we develop score-matching VI, an iterative algorithm that seeks to match the scores between the variational approximation and the exact posterior. At each iteration, score-matching VI solves an inner optimization, one that minimally adjusts the current variational estimate to match the scores at a newly sampled value of the latent variables. We show that when the variational family is a Gaussian, this inner optimization enjoys a closed-form solution, which we call Gaussian score matching VI (GSM-VI). GSM-VI is a ``black box'' variational algorithm in that it only requires a differentiable joint distribution, and as such it can be applied to a wide class of models. We compare GSM-VI to black box variational inference (BBVI), which has similar requirements but instead optimizes the ELBO. We first study how GSM-VI behaves as a function of the problem dimensionality, the condition number of the target covariance matrix (when the target is Gaussian), and the degree of mismatch between the approximating and exact posterior distribution. We then study GSM-VI on a collection of real-world Bayesian inference problems from the posteriorDB database of datasets and models. We find that GSM-VI is faster than BBVI and equally or more accurate. Specifically, over a wide range of target posteriors, GSM-VI requires 10-100x fewer gradient evaluations than BBVI to obtain a comparable quality of approximation.

CLeaR Conference 2022 Conference Paper

Estimating Social Influence from Observational Data

Dhanya Sridhar
Caterina De Bacco
David Blei

We consider the problem of estimating social influence, the effect that a person’s behavior has on the future behavior of their peers. The key challenge is that shared behavior between friends could be equally explained by influence or by two other confounding factors: 1) latent traits that caused people to both become friends and engage in the behavior, and 2) latent preferences for the behavior. This paper addresses the challenges of estimating social influence with three contributions. First, we formalize social influence as a causal effect, one which requires inferences about hypothetical interventions. Second, we develop Poisson Influence Factorization (PIF), a method for estimating social influence from observational data. PIF fits probabilistic factor models to networks and behavior data to infer variables that serve as substitutes for the confounding latent traits. Third, we develop assumptions under which PIF recovers estimates of social influence. We empirically study PIF with semi-synthetic and real data from Last. fm, and conduct a sensitivity analysis. We find that PIF estimates social influence most accurately compared to related methods and remains robust under some violations of its assumptions.

TMLR Journal 2022 Journal Article

Identifiable Deep Generative Models via Sparse Decoding

Gemma Elyse Moran
Dhanya Sridhar
Yixin Wang
David Blei

We develop the sparse VAE for unsupervised representation learning on high-dimensional data. The sparse VAE learns a set of latent factors (representations) which summarize the associations in the observed data features. The underlying model is sparse in that each observed feature (i.e. each dimension of the data) depends on a small subset of the latent factors. As examples, in ratings data each movie is only described by a few genres; in text data each word is only applicable to a few topics; in genomics, each gene is active in only a few biological processes. We prove such sparse deep generative models are identifiable: with infinite data, the true model parameters can be learned. (In contrast, most deep generative models are not identifiable.) We empirically study the sparse VAE with both simulated and real data. We find that it recovers meaningful latent factors and has smaller heldout reconstruction error than related methods.

JMLR Journal 2021 Journal Article

A general linear-time inference method for Gaussian Processes on one dimension

Jackson Loper
David Blei
John P. Cunningham
Liam Paninski

Gaussian Processes (GPs) provide powerful probabilistic frameworks for interpolation, forecasting, and smoothing, but have been hampered by computational scaling issues. Here we investigate data sampled on one dimension (e.g., a scalar or vector time series sampled at arbitrarily-spaced intervals), for which state-space models are popular due to their linearly-scaling computational costs. It has long been conjectured that state-space models are general, able to approximate any one-dimensional GP. We provide the first general proof of this conjecture, showing that any stationary GP on one dimension with vector-valued observations governed by a Lebesgue-integrable continuous kernel can be approximated to any desired precision using a specifically-chosen statespace model: the Latent Exponentially Generated (LEG) family. This new family offers several advantages compared to the general state-space model: it is always stable (no unbounded growth), the covariance can be computed in closed form, and its parameter space is unconstrained (allowing straightforward estimation via gradient descent). The theorem’s proof also draws connections to Spectral Mixture Kernels, providing insight about this popular family of kernels. We develop parallelized algorithms for performing inference and learning in the LEG model, test the algorithm on real and synthetic data, and demonstrate scaling to datasets with billions of samples. [abs] [ pdf ][ bib ] &copy JMLR 2021. ( edit, beta )

NeurIPS Conference 2021 Conference Paper

Posterior Collapse and Latent Variable Non-identifiability

Yixin Wang
David Blei
John P. Cunningham

Variational autoencoders model high-dimensional data by positinglow-dimensional latent variables that are mapped through a flexibledistribution parametrized by a neural network. Unfortunately, variational autoencoders often suffer from posterior collapse: theposterior of the latent variables is equal to its prior, rendering thevariational autoencoder useless as a means to produce meaningfulrepresentations. Existing approaches to posterior collapse oftenattribute it to the use of neural networks or optimization issues dueto variational approximation. In this paper, we consider posteriorcollapse as a problem of latent variable non-identifiability. We provethat the posterior collapses if and only if the latent variables arenon-identifiable in the generative model. This fact implies thatposterior collapse is not a phenomenon specific to the use of flexibledistributions or approximate inference. Rather, it can occur inclassical probabilistic models even with exact inference, which wealso demonstrate. Based on these results, we propose a class oflatent-identifiable variational autoencoders, deep generative modelswhich enforce identifiability without sacrificing flexibility. Thismodel class resolves the problem of latent variablenon-identifiability by leveraging bijective Brenier maps andparameterizing them with input convex neural networks, without specialvariational inference objectives or optimization tricks. Acrosssynthetic and real datasets, latent-identifiable variationalautoencoders outperform existing methods in mitigating posteriorcollapse and providing meaningful representations of the data.

NeurIPS Conference 2020 Conference Paper

Markovian Score Climbing: Variational Inference with KL(p||q)

Christian Naesseth
Fredrik Lindsten
David Blei

Modern variational inference (VI) uses stochastic gradients to avoid intractable expectations, enabling large-scale probabilistic inference in complex models. VI posits a family of approximating distributions q and then finds the member of that family that is closest to the exact posterior p. Traditionally, VI algorithms minimize the “exclusive Kullback-Leibler (KL)” KL(q||p), often for computational convenience. Recent research, however, has also focused on the “inclusive KL” KL(p||q), which has good statistical properties that makes it more appropriate for certain inference problems. This paper develops a simple algorithm for reliably minimizing the inclusive KL using stochastic gradients with vanishing bias. This method, which we call Markovian score climbing (MSC), converges to a local optimum of the inclusive KL. It does not suffer from the systematic errors inherent in existing methods, such as Reweighted Wake-Sleep and Neural Adaptive Sequential Monte Carlo, which lead to bias in their final estimates. We illustrate convergence on a toy model and demonstrate the utility of MSC on Bayesian probit regression for classification as well as a stochastic volatility model for financial data.

NeurIPS Conference 2019 Conference Paper

Adapting Neural Networks for the Estimation of Treatment Effects

Claudia Shi
David Blei
Victor Veitch

This paper addresses the use of neural networks for the estimation of treatment effects from observational data. Generally, estimation proceeds in two stages. First, we ﬁt models for the expected outcome and the probability of treatment (propensity score). Second, we plug these ﬁtted models into a downstream estimator. Neural networks are a natural choice for the models in the ﬁrst step. Our question is: how can we adapt the design and training of the neural networks used in this ﬁrst step in order to improve the quality of the ﬁnal estimate of the treatment effect? We propose two adaptations based on insights from the statistical literature on the estimation of treatment effects. The ﬁrst is a new architecture, the Dragonnet, that exploits the sufﬁciency of the propensity score for estimation adjustment. The second is a regularization procedure, targeted regularization, that induces a bias towards models that have non-parametrically optimal asymptotic properties ‘out-of-the-box’. Studies on benchmark datasets for causal inference show these adaptations outperform existing methods.

NeurIPS Conference 2019 Conference Paper

Poisson-Randomized Gamma Dynamical Systems

Aaron Schein
Scott Linderman
Mingyuan Zhou
David Blei
Hanna Wallach

This paper presents the Poisson-randomized gamma dynamical system (PRGDS), a model for sequentially observed count tensors that encodes a strong inductive bias toward sparsity and burstiness. The PRGDS is based on a new motif in Bayesian latent variable modeling, an alternating chain of discrete Poisson and continuous gamma latent states that is analytically convenient and computationally tractable. This motif yields closed-form complete conditionals for all variables by way of the Bessel distribution and a novel discrete distribution that we call the shifted confluent hypergeometric distribution. We draw connections to closely related models and compare the PRGDS to these models in studies of real-world count data sets of text, international events, and neural spike trains. We find that a sparse variant of the PRGDS, which allows the continuous gamma latent states to take values of exactly zero, often obtains better predictive performance than other models and is uniquely capable of inferring latent structures that are highly localized in time.

NeurIPS Conference 2019 Conference Paper

Using Embeddings to Correct for Unobserved Confounding in Networks

Victor Veitch
Yixin Wang
David Blei

We consider causal inference in the presence of unobserved confounding. We study the case where a proxy is available for the unobserved confounding in the form of a network connecting the units. For example, the link structure of a social network carries information about its members. We show how to effectively use the proxy to do causal inference. The main idea is to reduce the causal estimation problem to a semi-supervised prediction of both the treatments and outcomes. Networks admit high-quality embedding models that can be used for this semi-supervised prediction. We show that the method yields valid inferences under suitable (weak) conditions on the quality of the predictive model. We validate the method with experiments on a semi-synthetic social network dataset.

NeurIPS Conference 2019 Conference Paper

Variational Bayes under Model Misspecification

Yixin Wang
David Blei

Variational Bayes (VB) is a scalable alternative to Markov chain Monte Carlo (MCMC) for Bayesian posterior inference. Though popular, VB comes with few theoretical guarantees, most of which focus on well-specified models. However, models are rarely well-specified in practice. In this work, we study VB under model misspecification. We prove the VB posterior is asymptotically normal and centers at the value that minimizes the Kullback-Leibler (KL) divergence to the true data-generating distribution. Moreover, the VB posterior mean centers at the same value and is also asymptotically normal. These results generalize the variational Bernstein--von Mises theorem [29] to misspecified models. As a consequence of these results, we find that the model misspecification error dominates the variational approximation error in VB posterior predictive distributions. It explains the widely observed phenomenon that VB achieves comparable predictive accuracy with MCMC even though VB uses an approximating family. As illustrations, we study VB under three forms of model misspecification, ranging from model over-/under-dispersion to latent dimensionality misspecification. We conduct two simulation studies that demonstrate the theoretical results.

NeurIPS Conference 2017 Conference Paper

Context Selection for Embedding Models

Liping Liu
Francisco Ruiz
Susan Athey
David Blei

Word embeddings are an effective tool to analyze language. They have been recently extended to model other types of data beyond text, such as items in recommendation systems. Embedding models consider the probability of a target observation (a word or an item) conditioned on the elements in the context (other words or items). In this paper, we show that conditioning on all the elements in the context is not optimal. Instead, we model the probability of the target conditioned on a learned subset of the elements in the context. We use amortized variational inference to automatically choose this subset. Compared to standard embedding models, this method improves predictions and the quality of the embeddings.

NeurIPS Conference 2017 Conference Paper

Hierarchical Implicit Models and Likelihood-Free Variational Inference

Dustin Tran
Rajesh Ranganath
David Blei

Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for models which encompass our understanding of the physical word. Despite this fundamental nature, the use of implicit models remains limited due to challenge in positing complex latent structure in them, and the ability to inference in such models with large data sets. In this paper, we first introduce the hierarchical implicit models (HIMs). HIMs combine the idea of implicit densities with hierarchical Bayesian modeling thereby defining models via simulators of data with rich hidden structure. Next, we develop likelihood-free variational inference (LFVI), a scalable variational inference algorithm for HIMs. Key to LFVI is specifying a variational family that is also implicit. This matches the model's flexibility and allows for accurate approximation of the posterior. We demonstrate diverse applications: a large-scale physical simulator for predator-prey populations in ecology; a Bayesian generative adversarial network for discrete data; and a deep implicit model for symbol generation.

NeurIPS Conference 2017 Conference Paper

Structured Embedding Models for Grouped Data

Maja Rudolph
Francisco Ruiz
Susan Athey
David Blei

Word embeddings are a powerful approach for analyzing language, and exponential family embeddings (EFE) extend them to other types of data. Here we develop structured exponential family embeddings (S-EFE), a method for discovering embeddings that vary across related groups of data. We study how the word usage of U. S. Congressional speeches varies across states and party affiliation, how words are used differently across sections of the ArXiv, and how the co-purchase patterns of groceries can vary across seasons. Key to the success of our method is that the groups share statistical information. We develop two sharing strategies: hierarchical modeling and amortization. We demonstrate the benefits of this approach in empirical studies of speeches, abstracts, and shopping baskets. We show how SEFE enables group-specific interpretation of word usage, and outperforms EFE in predicting held-out data.

NeurIPS Conference 2017 Conference Paper

Variational Inference via $\chi$ Upper Bound Minimization

Adji Bousso Dieng
Dustin Tran
Rajesh Ranganath
John Paisley
David Blei

Variational inference (VI) is widely used as an efficient alternative to Markov chain Monte Carlo. It posits a family of approximating distributions $q$ and finds the closest member to the exact posterior $p$. Closeness is usually measured via a divergence $D(q || p)$ from $q$ to $p$. While successful, this approach also has problems. Notably, it typically leads to underestimation of the posterior variance. In this paper we propose CHIVI, a black-box variational inference algorithm that minimizes $D_{\chi}(p || q)$, the $\chi$-divergence from $p$ to $q$. CHIVI minimizes an upper bound of the model evidence, which we term the $\chi$ upper bound (CUBO). Minimizing the CUBO leads to improved posterior uncertainty, and it can also be used with the classical VI lower bound (ELBO) to provide a sandwich estimate of the model evidence. We study CHIVI on three models: probit regression, Gaussian process classification, and a Cox process model of basketball plays. When compared to expectation propagation and classical VI, CHIVI produces better error rates and more accurate estimates of posterior variance.

NeurIPS Conference 2016 Conference Paper

Exponential Family Embeddings

Maja Rudolph
Francisco Ruiz
Stephan Mandt
David Blei

Word embeddings are a powerful approach to capturing semantic similarity among terms in a vocabulary. In this paper, we develop exponential family embeddings, which extends the idea of word embeddings to other types of high-dimensional data. As examples, we studied several types of data: neural data with real-valued observations, count data from a market basket analysis, and ratings data from a movie recommendation system. The main idea is that each observation is modeled conditioned on a set of latent embeddings and other observations, called the context, where the way the context is defined depends on the problem. In language the context is the surrounding words; in neuroscience the context is close-by neurons; in market basket data the context is other items in the shopping cart. Each instance of an embedding defines the context, the exponential family of conditional distributions, and how the embedding vectors are shared across data. We infer the embeddings with stochastic gradient descent, with an algorithm that connects closely to generalized linear models. On all three of our applications—neural activity of zebrafish, users’ shopping behavior, and movie ratings—we found that exponential family embedding models are more effective than other dimension reduction methods. They better reconstruct held-out data and find interesting qualitative structure.

NeurIPS Conference 2016 Conference Paper

Operator Variational Inference

Rajesh Ranganath
Dustin Tran
Jaan Altosaar
David Blei

Variational inference is an umbrella term for algorithms which cast Bayesian inference as optimization. Classically, variational inference uses the Kullback-Leibler divergence to define the optimization. Though this divergence has been widely used, the resultant posterior approximation can suffer from undesirable statistical properties. To address this, we reexamine variational inference from its roots as an optimization problem. We use operators, or functions of functions, to design variational objectives. As one example, we design a variational objective with a Langevin-Stein operator. We develop a black box algorithm, operator variational inference (OPVI), for optimizing any operator objective. Importantly, operators enable us to make explicit the statistical and computational tradeoffs for variational inference. We can characterize different properties of variational objectives, such as objectives that admit data subsampling---allowing inference to scale to massive data---as well as objectives that admit variational programs---a rich class of posterior approximations that does not require a tractable density. We illustrate the benefits of OPVI on a mixture model and a generative model of images.

NeurIPS Conference 2016 Conference Paper

The Generalized Reparameterization Gradient

Francisco Ruiz
Michalis Titsias RC AUEB
David Blei

The reparameterization gradient has become a widely used method to obtain Monte Carlo gradients to optimize the variational objective. However, this technique does not easily apply to commonly used distributions such as beta or gamma without further approximations, and most practical applications of the reparameterization gradient fit Gaussian distributions. In this paper, we introduce the generalized reparameterization gradient, a method that extends the reparameterization gradient to a wider class of variational distributions. Generalized reparameterizations use invertible transformations of the latent variables which lead to transformed distributions that weakly depend on the variational parameters. This results in new Monte Carlo gradients that combine reparameterization gradients and score function gradients. We demonstrate our approach on variational inference for two complex probabilistic models. The generalized reparameterization is effective: even a single sample from the variational distribution is enough to obtain a low-variance gradient.

NeurIPS Conference 2015 Conference Paper

Automatic Variational Inference in Stan

Alp Kucukelbir
Rajesh Ranganath
Andrew Gelman
David Blei

Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires tedious model-specific calculations; this makes it difficult for non-experts to use. We propose an automatic variational inference algorithm, automatic differentiation variational inference (ADVI); we implement it in Stan (code available), a probabilistic programming system. In ADVI the user provides a Bayesian model and a dataset, nothing else. We make no conjugacy assumptions and support a broad class of models. The algorithm automatically determines an appropriate variational family and optimizes the variational objective. We compare ADVI to MCMC sampling across hierarchical generalized linear models, nonconjugate matrix factorization, and a mixture model. We train the mixture model on a quarter million images. With ADVI we can use variational inference on any model we write in Stan.

NeurIPS Conference 2015 Conference Paper

Copula variational inference

Dustin Tran
David Blei
Edo Airoldi

We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the dependency that is not captured by the original variational distribution, and thus the augmented variational family guarantees better approximations to the posterior. With stochastic optimization, inference on the augmented distribution is scalable. Furthermore, our strategy is generic: it can be applied to any inference procedure that currently uses the mean-field or structured approach. Copula variational inference has many advantages: it reduces bias; it is less sensitive to local optima; it is less sensitive to hyperparameters; and it helps characterize and interpret the dependency among the latent variables.

NeurIPS Conference 2015 Conference Paper

The Population Posterior and Bayesian Modeling on Streams

James McInerney
Rajesh Ranganath
David Blei

Many modern data analysis problems involve inferences from streaming data. However, streaming data is not easily amenable to the standard probabilistic modeling approaches, which assume that we condition on finite data. We develop population variational Bayes, a new approach for using Bayesian modeling to analyze streams of data. It approximates a new type of distribution, the population posterior, which combines the notion of a population distribution of the data with Bayesian inference in a probabilistic model. We study our method with latent Dirichlet allocation and Dirichlet process mixtures on several large-scale data sets.

NeurIPS Conference 2014 Conference Paper

A Filtering Approach to Stochastic Variational Inference

Neil Houlsby
David Blei

Stochastic variational inference (SVI) uses stochastic optimization to scale up Bayesian computation to massive data. We present an alternative perspective on SVI as approximate parallel coordinate ascent. SVI trades-off bias and variance to step close to the unknown true coordinate optimum given by batch variational Bayes (VB). We define a model to automate this process. The model infers the location of the next VB optimum from a sequence of noisy realizations. As a consequence of this construction, we update the variational parameters using Bayes rule, rather than a hand-crafted optimization schedule. When our model is a Kalman filter this procedure can recover the original SVI algorithm and SVI with adaptive steps. We may also encode additional assumptions in the model, such as heavy-tailed noise. By doing so, our algorithm outperforms the original SVI schedule and a state-of-the-art adaptive SVI algorithm in two diverse domains.

NeurIPS Conference 2014 Conference Paper

Content-based recommendations with Poisson factorization

Prem Gopalan
Laurent Charlin
David Blei

We develop collaborative topic Poisson factorization (CTPF), a generative model of articles and reader preferences. CTPF can be used to build recommender systems by learning from reader histories and content to recommend personalized articles of interest. In detail, CTPF models both reader behavior and article texts with Poisson distributions, connecting the latent topics that represent the texts with the latent preferences that represent the readers. This provides better recommendations than competing methods and gives an interpretable latent space for understanding patterns of readership. Further, we exploit stochastic variational inference to model massive real-world datasets. For example, we can fit CPTF to the full arXiv usage dataset, which contains over 43 million ratings and 42 million word counts, within a day. We demonstrate empirically that our model outperforms several baselines, including the previous state-of-the-art approach.

NeurIPS Conference 2014 Conference Paper

Smoothed Gradients for Stochastic Variational Inference

Stephan Mandt
David Blei

Stochastic variational inference (SVI) lets us scale up Bayesian computation to massive data. It uses stochastic optimization to fit a variational distribution, following easy-to-compute noisy natural gradients. As with most traditional stochastic optimization methods, SVI takes precautions to use unbiased stochastic gradients whose expectations are equal to the true gradients. In this paper, we explore the idea of following biased stochastic gradients in SVI. Our method replaces the natural gradient with a similarly constructed vector that uses a fixed-window moving average of some of its previous terms. We will demonstrate the many advantages of this technique. First, its computational cost is the same as for SVI and storage requirements only multiply by a constant factor. Second, it enjoys significant variance reduction over the unbiased estimates, smaller bias than averaged gradients, and leads to smaller mean-squared error against the full gradient. We test our method on latent Dirichlet allocation with three large corpora.

NeurIPS Conference 2013 Conference Paper

Efficient Online Inference for Bayesian Nonparametric Relational Models

Dae Il Kim
Prem Gopalan
David Blei
Erik Sudderth

Stochastic block models characterize observed network relationships via latent community memberships. In large social networks, we expect entities to participate in multiple communities, and the number of communities to grow with the network size. We introduce a new model for these phenomena, the hierarchical Dirichlet process relational model, which allows nodes to have mixed membership in an unbounded set of communities. To allow scalable learning, we derive an online stochastic variational inference algorithm. Focusing on assortative models of undirected networks, we also propose an efficient structured mean field variational bound, and online methods for automatically pruning unused communities. Compared to state-of-the-art online learning methods for parametric relational models, we show significantly improved perplexity and link prediction accuracy for sparse networks with tens of thousands of nodes. We also showcase an analysis of LittleSis, a large network of who-knows-who at the heights of business and government.

NeurIPS Conference 2013 Conference Paper

Modeling Overlapping Communities with Node Popularities

Prem Gopalan
Chong Wang
David Blei

We develop a probabilistic approach for accurate network modeling using node popularities within the framework of the mixed-membership stochastic blockmodel (MMSB). Our model integrates some of the basic properties of nodes in social networks: homophily and preferential connection to popular nodes. We develop a scalable algorithm for posterior inference, based on a novel nonconjugate variant of stochastic variational inference. We evaluate the link prediction accuracy of our algorithm on eight real-world networks with up to 60, 000 nodes, and 24 benchmark networks. We demonstrate that our algorithm predicts better than the MMSB. Further, using benchmark networks we show that node popularities are essential to achieving high accuracy in the presence of skewed degree distribution and noisy links---both characteristics of real networks.

NeurIPS Conference 2012 Conference Paper

How They Vote: Issue-Adjusted Models of Legislative Behavior

Sean Gerrish
David Blei

We develop a probabilistic model of legislative data that uses the text of the bills to uncover lawmakers' positions on specific political issues. Our model can be used to explore how a lawmaker's voting patterns deviate from what is expected and how that deviation depends on what is being voted on. We derive approximate posterior inference algorithms based on variational methods. Across 12 years of legislative data, we demonstrate both improvement in heldout predictive performance and the model's utility in interpreting an inherently multi-dimensional space.

NeurIPS Conference 2012 Conference Paper

Scalable Inference of Overlapping Communities

Prem Gopalan
Sean Gerrish
Michael Freedman
David Blei
David Mimno

We develop a scalable algorithm for posterior inference of overlapping communities in large networks. Our algorithm is based on stochastic variational inference in the mixed-membership stochastic blockmodel. It naturally interleaves subsampling the network with estimating its community structure. We apply our algorithm on ten large, real-world networks with up to 60, 000 nodes. It converges several orders of magnitude faster than the state-of-the-art algorithm for MMSB, finds hundreds of communities in large real-world networks, and detects the true communities in 280 benchmark networks with equal or better accuracy compared to other scalable algorithms.

NeurIPS Conference 2012 Conference Paper

Truncation-free Online Variational Inference for Bayesian Nonparametric Models

Chong Wang
David Blei

We present a truncation-free online variational inference algorithm for Bayesian nonparametric models. Unlike traditional (online) variational inference algorithms that require truncations for the model or the variational distribution, our method adapts model complexity on the fly. Our experiments for Dirichlet process mixture models and hierarchical Dirichlet process topic models on two large-scale data sets show better performance than previous online variational inference algorithms.

NeurIPS Conference 2011 Conference Paper

Spatial distance dependent Chinese restaurant processes for image segmentation

Soumya Ghosh
Andrei Ungureanu
Erik Sudderth
David Blei

The distance dependent Chinese restaurant process (ddCRP) was recently introduced to accommodate random partitions of non-exchangeable data. The ddCRP clusters data in a biased way: each data point is more likely to be clustered with other data that are near it in an external sense. This paper examines the ddCRP in a spatial setting with the goal of natural image segmentation. We explore the biases of the spatial ddCRP model and propose a novel hierarchical extension better suited for producing "human-like" segmentations. We then study the sensitivity of the models to various distance and appearance hyperparameters, and provide the first rigorous comparison of nonparametric Bayesian models in the image segmentation domain. On unsupervised image segmentation, we demonstrate that similar performance to existing nonparametric Bayesian models is possible with substantially simpler models and algorithms.

NeurIPS Conference 2010 Conference Paper

Estimating Spatial Layout of Rooms using Volumetric Reasoning about Objects and Surfaces

Abhinav Gupta
Martial Hebert
Takeo Kanade
David Blei

There has been a recent push in extraction of 3D spatial layout of scenes. However, none of these approaches model the 3D interaction between objects and the spatial layout. In this paper, we argue for a parametric representation of objects in 3D, which allows us to incorporate volumetric constraints of the physical world. We show that augmenting current structured prediction techniques with volumetric reasoning significantly improves the performance of the state-of-the-art.

NeurIPS Conference 2010 Conference Paper

Nonparametric Density Estimation for Stochastic Optimization with an Observable State Variable

Lauren Hannah
Warren Powell
David Blei

We study convex stochastic optimization problems where a noisy objective function value is observed after a decision is made. There are many stochastic optimization problems whose behavior depends on an exogenous state variable which affects the shape of the objective function. Currently, there is no general purpose algorithm to solve this class of problems. We use nonparametric density estimation for the joint distribution of state-outcome pairs to create weights for previous observations. The weights effectively group similar states. Those similar to the current state are used to create a convex, deterministic approximation of the objective function. We propose two solution methods that depend on the problem characteristics: function-based and gradient-based optimization. We offer two weighting schemes, kernel based weights and Dirichlet process based weights, for use with the solution methods. The weights and solution methods are tested on a synthetic multi-product newsvendor problem and the hour ahead wind commitment problem. Our results show Dirichlet process weights can offer substantial benefits over kernel based weights and, more generally, that nonparametric estimation methods provide good solutions to otherwise intractable problems.

NeurIPS Conference 2010 Conference Paper

Online Learning for Latent Dirichlet Allocation

Matthew Hoffman
Francis Bach
David Blei

We develop an online variational Bayes (VB) algorithm for Latent Dirichlet Allocation (LDA). Online LDA is based on online stochastic optimization with a natural gradient step, which we show converges to a local optimum of the VB objective function. It can handily analyze massive document collections, including those arriving in a stream. We study the performance of online LDA in several ways, including by fitting a 100-topic topic model to 3. 3M articles from Wikipedia in a single pass. We demonstrate that online LDA finds topic models as good or better than those found with batch VB, and in a fraction of the time.

NeurIPS Conference 2009 Conference Paper

A Bayesian Analysis of Dynamics in Free Recall

Richard Socher
Samuel Gershman
Per Sederberg
Kenneth Norman
Adler Perotte
David Blei

We develop a probabilistic model of human memory performance in free recall experiments. In these experiments, a subject first studies a list of words and then tries to recall them. To model these data, we draw on both previous psychological research and statistical topic models of text documents. We assume that memories are formed by assimilating the semantic meaning of studied words (represented as a distribution over topics) into a slowly changing latent context (represented in the same space). During recall, this context is reinstated and used as a cue for retrieving studied words. By conceptualizing memory retrieval as a dynamic latent variable model, we are able to use Bayesian inference to represent uncertainty and reason about the cognitive processes underlying memory. We present a particle filter algorithm for performing approximate posterior inference, and evaluate our model on the prediction of recalled words in experimental data. By specifying the model hierarchically, we are also able to capture inter-subject variability.

NeurIPS Conference 2009 Conference Paper

Decoupling Sparsity and Smoothness in the Discrete Hierarchical Dirichlet Process

Chong Wang
David Blei

We present a nonparametric hierarchical Bayesian model of document collections that decouples sparsity and smoothness in the component distributions (i. e. , the ``topics). In the sparse topic model (STM), each topic is represented by a bank of selector variables that determine which terms appear in the topic. Thus each topic is associated with a subset of the vocabulary, and topic smoothness is modeled on this subset. We develop an efficient Gibbs sampler for the STM that includes a general-purpose method for sampling from a Dirichlet mixture with a combinatorial number of components. We demonstrate the STM on four real-world datasets. Compared to traditional approaches, the empirical results show that STMs give better predictive performance with simpler inferred models.

NeurIPS Conference 2009 Conference Paper

Reading Tea Leaves: How Humans Interpret Topic Models

Jonathan Chang
Sean Gerrish
Chong Wang
Jordan Boyd-Graber
David Blei

Probabilistic topic models are a popular tool for the unsupervised analysis of text, providing both a predictive model of future text and a latent topic representation of the corpus. Practitioners typically assume that the latent space is semantically meaningful. It is used to check models, summarize the corpus, and guide exploration of its contents. However, whether the latent space is interpretable is in need of quantitative evaluation. In this paper, we present new quantitative methods for measuring semantic meaning in inferred topics. We back these measures with large-scale user studies, showing that they capture aspects of the model that are undetected by previous measures of model quality based on held-out likelihood. Surprisingly, topic models which perform better on held-out likelihood may infer less semantically meaningful topics.

NeurIPS Conference 2009 Conference Paper

Variational Inference for the Nested Chinese Restaurant Process

Chong Wang
David Blei

The nested Chinese restaurant process (nCRP) is a powerful nonparametric Bayesian model for learning tree-based hierarchies from data. Since its posterior distribution is intractable, current inference methods have all relied on MCMC sampling. In this paper, we develop an alternative inference technique based on variational methods. To employ variational methods, we derive a tree-based stick-breaking construction of the nCRP mixture model, and a novel variational algorithm that efficiently explores a posterior over a large set of combinatorial structures. We demonstrate the use of this approach for text and hand written digits modeling, where we show we can adapt the nCRP to continuous data as well.

NeurIPS Conference 2008 Conference Paper

Mixed Membership Stochastic Blockmodels

Edo Airoldi
David Blei
Stephen Fienberg
Eric Xing

Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assumptions underlying many boilerplate models no longer hold. In this paper, we describe a class of latent variable models of such data called Mixed Membership Stochastic Blockmodels. This model extends blockmodels for relational data to ones which capture mixed membership latent relational structure, thus providing an object-specific low-dimensional representation. We develop a general variational inference algorithm for fast approximate posterior inference. We explore applications to social networks and protein interaction networks.

NeurIPS Conference 2008 Conference Paper

Relative Performance Guarantees for Approximate Inference in Latent Dirichlet Allocation

Indraneel Mukherjee
David Blei

Hierarchical probabilistic modeling of discrete data has emerged as a powerful tool for text analysis. Posterior inference in such models is intractable, and practitioners rely on approximate posterior inference methods such as variational inference or Gibbs sampling. There has been much research in designing better approximations, but there is yet little theoretical understanding of which of the available techniques are appropriate, and in which data analysis settings. In this paper we provide the beginnings of such understanding. We analyze the improvement that the recently proposed collapsed variational inference (CVB) provides over mean field variational inference (VB) in latent Dirichlet allocation. We prove that the difference in the tightness of the bound on the likelihood of a document decreases as $O(k-1) + \log m /m$, where $k$ is the number of topics in the model and $m$ is the number of words in a document. As a consequence, the advantage of CVB over VB is lost for long documents but increases with the number of topics. We demonstrate empirically that the theory holds, using simulated text data and two text corpora. We provide practical guidelines for choosing an approximation.

NeurIPS Conference 2008 Conference Paper

Syntactic Topic Models

Jordan Boyd-Graber
David Blei

We develop \name\ (STM), a nonparametric Bayesian model of parsed documents. \Shortname\ generates words that are both thematically and syntactically constrained, which combines the semantic insights of topic models with the syntactic information available from parse trees. Each word of a sentence is generated by a distribution that combines document-specific topic weights and parse-tree specific syntactic transitions. Words are assumed generated in an order that respects the parse tree. We derive an approximate posterior inference method based on variational methods for hierarchical Dirichlet processes, and we report qualitative and quantitative results on both synthetic data and hand-parsed documents.

NeurIPS Conference 2007 Conference Paper

Supervised Topic Models

Jon McAuliffe
David Blei

We introduce supervised latent Dirichlet allocation (sLDA), a statistical model of labelled documents. The model accommodates a variety of response types. We derive a maximum-likelihood procedure for parameter estimation, which relies on variational approximations to handle intractable posterior expectations. Prediction problems motivate this research: we use the fitted model to predict response values for new documents. We test sLDA on two real-world problems: movie ratings predicted from reviews, and web page popularity predicted from text descriptions. We illustrate the benefits of sLDA versus modern regularized regression, as well as versus an unsupervised LDA analysis followed by a separate regression.

NeurIPS Conference 2005 Conference Paper

Correlated Topic Models

John Lafferty
David Blei

Topic models, such as latent Dirichlet allocation (LDA), can be useful tools for the statistical analysis of document collections and other discrete data. The LDA model assumes that the words of each document arise from a mixture of topics, each of which is a distribution over the vocabulary. A limitation of LDA is the inability to model topic correlation even though, for example, a document about genetics is more likely to also be about disease than x-ray astronomy. This limitation stems from the use of the Dirichlet distribution to model the variability among the topic proportions. In this paper we develop the correlated topic model (CTM), where the topic proportions exhibit correlation via the logistic normal distribution [1]. We derive a mean-field variational inference algorithm for approximate posterior inference in this model, which is complicated by the fact that the logistic normal is not conjugate to the multinomial. The CTM gives a better fit than LDA on a collection of OCRed articles from the journal Science. Furthermore, the CTM provides a natural way of visualizing and exploring this and other unstructured data sets.

NeurIPS Conference 2004 Conference Paper

Integrating Topics and Syntax

Thomas Griffiths
Mark Steyvers
David Blei
Joshua Tenenbaum

Statistical approaches to language learning typically focus on either short-range syntactic dependencies or long-range semantic dependencies between words. We present a generative model that uses both kinds of dependencies, and can be used to simultaneously find syntactic classes and semantic topics despite having no representation of syntax or seman- tics beyond statistical dependency. This model is competitive on tasks like part-of-speech tagging and document classification with models that exclusively use short- and long-range dependencies respectively.

NeurIPS Conference 2004 Conference Paper

Sharing Clusters among Related Groups: Hierarchical Dirichlet Processes

Yee Teh
Michael Jordan
Matthew Beal
David Blei

We propose the hierarchical Dirichlet process (HDP), a nonparametric Bayesian model for clustering problems involving multiple groups of data. Each group of data is modeled with a mixture, with the number of components being open-ended and inferred automatically by the model. Further, components can be shared across groups, allowing dependencies across groups to be modeled effectively as well as conferring generaliza- tion to new groups. Such grouped clustering problems occur often in practice, e. g. in the problem of topic discovery in document corpora. We report experimental results on three text corpora showing the effective and superior performance of the HDP over previous models.

NeurIPS Conference 2003 Conference Paper

Hierarchical Topic Models and the Nested Chinese Restaurant Process

Thomas Griffiths
Michael Jordan
Joshua Tenenbaum
David Blei

We address the problem of learning topic hierarchies from data. The model selection problem in this domain is daunting—which of the large collection of possible trees to use? We take a Bayesian approach, gen- erating an appropriate prior via a distribution on partitions that we refer to as the nested Chinese restaurant process. This nonparametric prior al- lows arbitrarily large branching factors and readily accommodates grow- ing data collections. We build a hierarchical topic model by combining this prior with a likelihood that is based on a hierarchical variant of latent Dirichlet allocation. We illustrate our approach on simulated data and with an application to the modeling of NIPS abstracts.

NeurIPS Conference 2001 Conference Paper

Latent Dirichlet Allocation

David Blei
Andrew Ng
Michael Jordan

We propose a generative model for text and other collections of dis(cid: 173) crete data that generalizes or improves on several previous models including naive Bayes/unigram, mixture of unigrams [6], and Hof(cid: 173) mann's aspect model, also known as probabilistic latent semantic indexing (pLSI) [3]. In the context of text modeling, our model posits that each document is generated as a mixture of topics, where the continuous-valued mixture proportions are distributed as a latent Dirichlet random variable. Inference and learning are carried out efficiently via variational algorithms. We present em(cid: 173) pirical results on applications of this model to problems in text modeling, collaborative filtering, and text classification.