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Stochastics and Statistics Seminar

The Planted Matching Problem

Cristopher Moore (Santa Fe Institute)
E18-304

Abstract: What happens when an optimization problem has a good solution built into it, but which is partly obscured by randomness? Here we revisit a classic polynomial-time problem, the minimum perfect matching problem on bipartite graphs. If the edges have random weights in , Mézard and Parisi — and then Aldous, rigorously — showed that the minimum matching has expected weight zeta(2) = pi^2/6. We consider a “planted” version where a particular matching has weights drawn from an exponential distribution…

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IDS.190 Topics in Bayesian Modeling and Computation

Markov Chain Monte Carlo Methods and Some Attempts at Parallelizing Them

Pierre E. Jacob (Harvard University)
E18-304

IDS.190 – Topics in Bayesian Modeling and Computation Abstract: MCMC methods yield approximations that converge to quantities of interest in the limit of the number of iterations. This iterative asymptotic justification is not ideal: it stands at odds with current trends in computing hardware. Namely, it would often be computationally preferable to run many short chains in parallel, but such an approach is flawed because of the so-called "burn-in" bias.  This talk will first describe that issue and some known…

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Stochastics and Statistics Seminar

Towards Robust Statistical Learning Theory

Stanislav Minsker (USC)
E18-304

Abstract:  Real-world data typically do not fit statistical models or satisfy assumptions underlying the theory exactly, hence reducing the number and strictness of these assumptions helps to lessen the gap between the “mathematical” world and the “real” world. The concept of robustness, in particular, robustness to outliers, plays the central role in understanding this gap. The goal of the talk is to introduce the principles and robust algorithms based on these principles that can be applied in the general framework…

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IDS.190 Topics in Bayesian Modeling and Computation

Esther Williams in the Harold Holt Memorial Swimming Pool: Some Thoughts on Complexity

Daniel Simpson (University of Toronto)
E18-304

IDS.190 – Topics in Bayesian Modeling and Computation Speaker: Daniel Simpson (University of Toronto) Abstract: As data becomes more complex and computational modelling becomes more powerful, we rapidly find ourselves beyond the scope of traditional statistical theory. As we venture beyond the traditional thunderdome, we need to think about how to cope with this additional complexity in our model building.  In this talk, I will talk about a few techniques that are useful when specifying prior distributions and building Bayesian models…

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Stochastics and Statistics Seminar

Accurate Simulation-Based Parametric Inference in High Dimensional Settings

Maria-Pia Victoria-Feser, (University of Geneva)
E18-304

Abstract: Accurate estimation and inference in finite sample is important for decision making in many experimental and social fields, especially when the available data are complex, like when they include mixed types of measurements, they are dependent in several ways, there are missing data, outliers, etc. Indeed, the more complex the data (hence the models), the less accurate are asymptotic theory results in finite samples.  This is in particular the case, for example, with logistic regression, with possibly also random effects…

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IDS.190 Topics in Bayesian Modeling and Computation

Using Bagged Posteriors for Robust Inference

Jonathan Huggins (Boston University)
37-212

IDS.190 – Topics in Bayesian Modeling and Computation **PLEASE NOTE ROOM CHANGE TO BUILDING 37-212 FOR THE WEEKS OF 10/30 AND 11/6** Speaker:   Jonathan Huggins (Boston University) Abstract: Standard Bayesian inference is known to be sensitive to misspecification between the model and the data-generating mechanism, leading to unreliable uncertainty quantification and poor predictive performance. However, finding generally applicable and computationally feasible methods for robust Bayesian inference under misspecification has proven to be a difficult challenge. An intriguing approach is…

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IDS.190 Topics in Bayesian Modeling and Computation

Probabilistic Inference and Learning with Stein’s Method

Lester Mackey (Microsoft Research)
37-212

IDS.190 – Topics in Bayesian Modeling and Computation **PLEASE NOTE ROOM CHANGE TO BUILDING 37-212 FOR THE WEEKS OF 10/30 AND 11/6** Speaker: Lester Mackey (Microsoft Research) Abstract: Stein’s method is a powerful tool from probability theory for bounding the distance between probability distributions.  In this talk, I’ll describe how this tool designed to prove central limit theorems can be adapted to assess and improve the quality of practical inference procedures.  I’ll highlight applications to Markov chain sampler selection, goodness-of-fit testing, variational…

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One-shot Information Theory via Poisson Processes

Cheuk Ting Li (UC Berkeley)
E18-304

Abstract: In information theory, coding theorems are usually proved in the asymptotic regime where the blocklength tends to infinity. While there are techniques for finite blocklength analysis, they are often more complex than their asymptotic counterparts. In this talk, we study the use of Poisson processes in proving coding theorems, which not only gives sharp one-shot and finite blocklength results, but also gives significantly shorter proofs than conventional asymptotic techniques in some settings. Instead of using fixed-size random codebooks, we…

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Stochastics and Statistics Seminar

SDP Relaxation for Learning Discrete Structures: Optimal Rates, Hidden Integrality, and Semirandom Robustness

Yudong Chen (Cornell)
E18-304

Abstract: We consider the problems of learning discrete structures from network data under statistical settings. Popular examples include various block models, Z2 synchronization and mixture models. Semidefinite programming (SDP) relaxation has emerged as a versatile and robust approach to these problems. We show that despite being a relaxation, SDP achieves the optimal Bayes error rate in terms of distance to the target solution. Moreover, SDP relaxation is provably robust under the so-called semirandom model, which frustrates many existing algorithms. Our…

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IDS.190 Topics in Bayesian Modeling and Computation

Artificial Bayesian Monte Carlo Integration: A Practical Resolution to the Bayesian (Normalizing Constant) Paradox

Xiao-Li Meng (Harvard University)
E18-304

Abstract: Advances in Markov chain Monte Carlo in the past 30 years have made Bayesian analysis a routine practice. However, there is virtually no practice of performing Monte Carlo integration from the Bayesian perspective; indeed,this problem has earned the “paradox” label in the context of computing normalizing constants (Wasserman, 2013). We first use the modeling-what-we-ignore idea of Kong et al. (2003) to explain that the crux of the paradox is not with the likelihood theory, which is essentially the same…

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Massachusetts Institute of Technology
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Cambridge, MA 02139-4307
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