CHRISTIAN MUELLER 
Center for Computational Biology
Flatiron Institute, Simons Foundation
It’s Just a Matter of Perspective – Proximal Algorithms for Tuning-Insensitive and Robust Sparse Regression
ABSTRACT
Finding the maximum likelihood estimate associated with a particular statistical model is commonplace in statistics. In the high-dimensional setting, this task is often associated with solving a (convex) non-smooth optimization problem. In this talk, I introduce a model for maximum likelihood-type estimation (M-estimation) that generalizes a large class of well-known estimators, including Huber’s concomitant M-estimators and the scaled Lasso. The model, termed perspective M-estimation, leverages the observation that convex M-estimators with concomitant scale as well as various regularizers are instances of perspective functions. Such functions are amenable to proximal analysis, which leads to principled and provably convergent optimization algorithms via proximal splitting. I will show several instances of the model, including new estimators that can handle heteroscedasticity in the data. The model also extends to novel regression models with compositional covariates. Compositional (or relative abundance) data are commonplace in biology, including microbiome research. I will show examples on synthetic test cases and applications to microbiome data.
This is joint work with Patrick Combettes.
Friday, 11/2/18, BLOC 113, 11:30 AM
