Graduate

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

ISL Colloquium presents "Finding Global Minima via Kernel Approximations"

Topic: 
Finding Global Minima via Kernel Approximations
Abstract / Description: 

We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precision level typically rely on explicitly constructing an approximation of the function which is then minimized with algorithms that have exponential running-time complexity. In this paper, we consider an approach that jointly models the function to approximate and finds a global minimum. This is done by using infinite sums of square smooth functions and has strong links with polynomial sum-of-squares hierarchies. Leveraging recent representation properties of reproducing kernel Hilbert spaces, the infinite-dimensional optimization problem can be solved by subsampling in time polynomial in the number of function evaluations, and with theoretical guarantees on the obtained minimum. (Joint work with Alessandro Rudi and Ulysse Marteau-Ferey).

Date and Time: 
Thursday, April 1, 2021 - 10:00am

Bits & Watts' Smart Grid Seminar: Electric Grid Security

Topic: 
Electric Grid Security
Abstract / Description: 

Bits & Watts’ Smart Grid Seminar provides experts from academia, startups, research institutes, and large corporations to familiarize seminar participants with current challenges and advances in grid data analytics, economics, market design, battery storage, electrified transportation, power electronics, renewable energy. The seminar is open to Stanford students, as a 1 unit seminar course (CEE 272T/EE292T), and to the broader community.

Date and Time: 
Thursday, May 13, 2021 - 2:30pm

Bits & Watts' Smart Grid Seminar: ERCOT Frequency Regulation Ancillary Services

Topic: 
ERCOT Frequency Regulation Ancillary Services
Abstract / Description: 

Bits & Watts’ Smart Grid Seminar provides experts from academia, startups, research institutes, and large corporations to familiarize seminar participants with current challenges and advances in grid data analytics, economics, market design, battery storage, electrified transportation, power electronics, renewable energy. The seminar is open to Stanford students, as a 1 unit seminar course (CEE 272T/EE292T), and to the broader community.

Date and Time: 
Thursday, April 22, 2021 - 2:30pm

Bits & Watts' Smart Grid Seminar: Large-scale Grid Testbed

Topic: 
Large-scale Grid Testbed
Abstract / Description: 

Bits & Watts' Smart Grid Seminar provides experts from academia, startups, research institutes, and large corporations to familiarize seminar participants with current challenges and advances in grid data analytics, economics, market design, battery storage, electrified transportation, power electronics, renewable energy. The seminar is open to Stanford students, as a 1 unit seminar course (CEE 272T/EE292T), and to the broader community.

Date and Time: 
Thursday, April 15, 2021 - 2:30pm

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