Statistics and Probability Seminars

Statistics Seminar presents "Community estimation in general multilayer stochastic block models"

Topic: 
Community estimation in general multilayer stochastic block models
Abstract / Description: 

We consider the problem of estimating common community structures in multi-layer stochastic block models, where each single layer may not have sufficient signal strength to recover the full community structure. Two estimators are developed to accommodate general connectivity patterns: a least square approach and a bias-corrected spectral approach. The analyses of these estimators involve some new matrix concentration inequalities. The performance of our method and the necessity of bias removal is demonstrated in synthetic data and in microarray analysis about gene co-expression networks. Some open problems will be briefly discussed.

Date and Time: 
Tuesday, May 18, 2021 - 4:30pm

Statistics Seminar: Metropolis-Hastings via classification

Topic: 
Metropolis-Hastings via classification
Abstract / Description: 

This paper develops a Bayesian computational platform at the interface between posterior sampling and optimization in models whose marginal likelihoods are difficult to evaluate. Inspired by adversarial optimization, namely Generative Adversarial Networks (GAN), we reframe the likelihood function estimation problem as a classification problem. Pitting a Generator, who simulates fake data, against a Classifier, who tries to distinguish them from the real data, one obtains likelihood (ratio) estimators which can be plugged into the Metropolis-Hastings acceptance ratios. The resulting Markov chains generate, at a steady state, samples from an approximate posterior whose asymptotic properties we characterize. Drawing upon connections with empirical Bayes and Bayesian mis-specification, we quantify the convergence rate in terms of the contraction speed of the actual posterior and the convergence rate of the Classifier. Asymptotic normality results are also provided which justify inferential potential of our approach. We illustrate the usefulness of our approach on simulated data.

This is based on joint work with Tetsuya Kaji.

Date and Time: 
Tuesday, April 6, 2021 - 4:30pm

Statistics Seminar: Vintage factor analysis with varimax performs statistical inference

Topic: 
Vintage factor analysis with varimax performs statistical inference
Abstract / Description: 

Psychologists developed Multiple Factor Analysis to decompose multivariate data into a small number of interpretable factors without any a priori knowledge about those factors. In this form of factor analysis, the Varimax "factor rotation" is a key step to make the factors interpretable. Charles Spearman and many others objected to factor rotations because the factors seem to be rotationally invariant. This is an historical engima because factor rotations have survived and are widely popular because, empirically, they often make factors easier to interpret. We argue that the rotation makes the factors easier to interpret because, in fact, the Varimax factor rotation performs statistical inference. We show that Principal Components Analysis (PCA) with the Varimax rotation provides a unified spectral estimation strategy for a broad class of modern factor models, including the Stochastic Blockmodel and a natural variation of Latent Dirichlet Allocation (i.e., "topic modeling"). In addition, we show that Thurstone's widely employed sparsity diagnostics implicitly assess a key "leptokurtic" condition that makes the rotation statistically identifiable in these models. Taken together, this shows that the know-how of Vintage Factor Analysis performs statistical inference, reversing nearly a century of statistical thinking on the topic. With a sparse eigensolver, PCA with Varimax is both fast and stable. Combined with Thurstone's straightforward diagnostics, this vintage approach is suitable for a wide array of modern applications.

Date and Time: 
Tuesday, March 30, 2021 - 4:30pm

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