This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When additive in linear models have only bounded second moments, we show that iteratively reweighted ?1-penalized adaptive Huber estimator satisfies exponential deviation bounds oracle properties, i...

We propose a general approach to regression on digitized multidimensional signals that can pose severe challenges to standard statistical methods. The main contribution of this work is to build a two-dimensional coefficient surface that allows for interaction across the indexing plane of the regressor array. We aim to use the estimated coefficient surface for reliable (scalar) prediction. We as...

This paper studies the generalized functional linear model with a scalar response and a functional predictor. The response given the functional predictor is assumed to come from the distribution of an exponential family. A penalized likelihood approach is proposed to estimate the unknown intercept and coefficient function in the model. Inference tools such as point-wise confidence intervals of ...

Personalization is becoming an important aspect of many predictive applications. We introduce a penalized regression method which inherently implements personalization. Personalized angle (PAN) constructs coefficients that are specific to the covariate vector for one producing prediction, thus personalizing model itself. This achieved by penalizing normalized prediction given vector. The theref...