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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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Stochastics and Statistics Seminar

Understanding Machine Learning with Statistical Physics

Lenka Zdeborová (Institute of Theoretical Physics, CNRS)
E18-304

Abstract: The affinity between statistical physics and machine learning has long history, this is reflected even in the machine learning terminology that is in part adopted from physics. Current theoretical challenges and open questions about deep learning and statistical learning call for unified account of the following three ingredients: (a) the dynamics of the learning algorithm, (b) the architecture of the neural networks, and (c) the structure of the data. Most existing theories are not taking in account all of…

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Stability of a Fluid Model for Fair Bandwidth Sharing with General File Size Distributions

Ruth J Williams (University of California, San Diego)
E18-304

Abstract: Massoulie and Roberts introduced a stochastic model for a data communication network where file sizes are generally distributed and the network operates under a fair bandwidth sharing policy.  It has been a standing problem to prove stability of this general model when the average load on the system is less than the network's capacity. A crucial step in an approach to this problem is to prove stability of an associated measure-valued fluid model. We shall describe prior work on this question done under various strong assumptions and…

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IDS.190 Topics in Bayesian Modeling and Computation

A Causal Exposure Response Function with Local Adjustment for Confounding: A study of the health effects of long-term exposure to low levels of fine particulate matter

Francesca Dominici (Harvard University)
E18-304

Abstract:   In the last two decades, ambient levels of air pollution have declined substantially. Yet, as mandated by the Clean Air Act, we must continue to address the following question: is exposure to levels of air pollution that are well below the National Ambient Air Quality Standards (NAAQS) harmful to human health? Furthermore, the highly contentious nature surrounding environmental regulations necessitates casting this question within a causal inference framework. Several parametric and semi-parametric regression modeling approaches have been used to…

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Stochastics and Statistics Seminar

Automated Data Summarization for Scalability in Bayesian Inference

Tamara Broderick (MIT)
E18-304

Abstract: Many algorithms take prohibitively long to run on modern, large data sets. But even in complex data sets, many data points may be at least partially redundant for some task of interest. So one might instead construct and use a weighted subset of the data (called a “coreset”) that is much smaller than the original dataset. Typically running algorithms on a much smaller data set will take much less computing time, but it remains to understand whether the output…

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