Speaker: Carlos-Misael Madrid-Padilla (Washington University in St. Louis)

 

Title: Temporal Spatial Model via Trend Filtering

 

 

Abstract: This talk explores the estimation of nonparametric regression functions in the presence of temporal-spatial dependencies. In such a context, trend filtering, a nonparametric estimator, is studied. To the best of our knowledge, this estimator has not previously been examined in a similar context. In the univariate case, the signals considered are assumed to have a k-th weak derivative with bounded total variation, allowing for a general degree of smoothness. In the multivariate setting, we study a variant of the K-nearest neighbor fused lasso estimator. For this case, the function is required to have bounded variation and satisfy a property that extends a piecewise Lipschitz continuity criterion, or the function is assumed to be piecewise Lipschitz. To enable efficient computation, we developed an ADMM algorithm. By aligning with lower bounds, the minimax optimality of the univariate and multivariate estimators is shown. A unique phase transition phenomenon, previously unprecedented in trend filtering studies, emerges through the analysis. Both simulation studies and real data applications underscore the superior performance of the method when compared with established techniques in the existing literature.

 

Bio:

Carlos-Misael Madrid-Padilla is a tenure-track Assistant Professor in the Department of Statistics and Data Science at Washington University in St. Louis. He earned a Ph.D. in Mathematics at the Department of Mathematics at the University of Notre Dame under the supervision of Dr. Daren Wang. During the first two years of his Ph.D., he received a master's degree in mathematics under the supervision of Dr. Alex Himonas.  His research interests include high-dimensional statistics, nonparametric statistics, change point detection, causal inference, Bayes methodology, etc.