Norton Lecture: Rong Tang
Abstract Title: Bayesian Inference for Risk Minimization via Exponentially Tilted Empirical Likelihood
Abstract: The celebrated Bernstein von-Mises theorem ensures credible regions from a Bayesian posterior to be well-calibrated when the model is correctly-specified, in the frequentist sense that their coverage probabilities tend to the nominal values as data accrue. However, this conventional Bayesian framework is known to lack robustness when the model is misspecified or partly specified, for example, in quantile regression, risk minimization based supervised/unsupervised learning and robust estimation. To alleviate this limitation, we propose a new Bayesian inferential approach that substitutes the (misspecified or partly specified) likelihoods with proper exponentially tilted empirical likelihoods plus a regularization term. Our surrogate empirical likelihood is carefully constructed by using the first-order optimality condition of empirical risk minimization as the moment condition. We show that the Bayesian posterior obtained by combining this surrogate empirical likelihood and a prior is asymptotically close to a normal distribution centering at the empirical risk minimizer with an appropriate sandwich-form covariance matrix. Consequently, the resulting Bayesian credible regions are automatically calibrated to deliver valid uncertainty quantification. Computationally, the proposed method can be easily implemented by Markov Chain Monte Carlo sampling algorithms. Our numerical results show that the proposed method tends to be more accurate than existing state-of-the-art competitors.
Norton Lecture (Honorable mention): Anamitra Chaudhuri
Abstract Title: Joint Sequential Detection and Isolation of a Dependence Structure
Abstract: The problem of joint sequential detection and isolation of the underlying dependence structure is considered in the context of multiple dependent data streams. A multiple testing framework is proposed, where each hypothesis corresponds to each possible pair of data streams, the sample size is a stopping time of the observations, and the probabilities of four kinds of error are controlled below distinct, user-specified levels. Two of these errors reflect the detection component of the formulation, whereas the other two are the isolation component. The optimal expected sample size is characterized to a first-order asymptotic approximation as the error probabilities go to 0. Different asymptotic regimes, expressing different prioritizations of the detection and isolation tasks, are considered. A novel and versatile family of testing procedures is proposed, in which two distinct, in general, statistics are computed for each hypothesis, one addressing the detection task and the other the isolation task. Tests in this family, of various computational complexities, are shown to be asymptotically optimal under different setups
Additional Student Presentations:
Lightning Talks
- Anwesha Chakravarti: Optimizing Trap Placement to Predict West Nile Virus Cases
- Yifan Chen: Statistical Leverage Score Approximation for Kernel Empirical Risk Minimization
- Robert Garrett: A multivariate space-time dynamic model for characterizing pathways following the Mt. Pinatubo eruption
- Byeongjip Kim: The Node Influence Mixed Membership Stochastic Block Models on Heterogeneous Networks
- Abhishek Ojha: A Conditional Bayesian Approach with Valid Inference for High Dimensional Logistic Regression
- Austin Warner: Online Change Diagnosis Using Physical Models
- Theren Williams: Restricted HMM for Latent Class Attribute Transitions
- Rentian Yao: On the convergence of Coordinate Wasserstein Proximal Gradient Flow
- Yubo Zhuang: Wasserstein K-means for clustering probability distributions
Paper Talks
- Alton Barbehenn: Biomarker Imputation with Empirical Bayes Tobit Matrix Estimation
- Kaustav Chakraborty: Efficient Model Fitting and Two-Sample Testing for Large Networks via Subsampling
- Hanjia Gao: Dimension-agnostic Change Point Detection
- Yuhan Li: Quasi-optimal Reinforcement Learning with Continuous Actions
- Diptarka Saha: Probabilistic Guarantees on Sensitivities of Bayesian Neural Network
- Adam Tonks: Spatiotemporal assessment of regional flooding risk across the contiguous United States using 2-D spline models
Student Awards