Propensity score weighting is often utilized to achieve covariate balance when comparing treatment groups in observational studies. Here we define a general class of balancing weights that balance the weighted covariate distribution between groups. This class includes the commonly used inverse-probability weights, but we illustrate here why these weights can be problematic if covariates...
Model-free knockoffs: high-dimensional variable selection that controls the false discovery rate
Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a nonlinear fashion, such as when the response is binary. Although this modeling problem has been extensively studied, it remains unclear how to effectively control the fraction of false discoveries even in high-dimensional logistic regression, not to mention general high-dimensional nonlinear models. To address such a practical problem, we...
Non-identifiability and Posterior Exploration in Non-negative Matrix Factorization
Non-negative matrix factorization (NMF) is a popular model for data exploration: each data point can be thought of as a convex, linear combination of a set of bases, and the bases represent something important about the structure of the data. I will first talk about non-identifiability in NMF -- which can thwart interpretation -- including some counter-intuitive examples of how factorizations may not be unique. Next, I will describe on-going work in my group on how to combine some of...
Bayesian analysis of high-dimensional graphical models often leads to posterior distributions that are computationally intractable. Similar issues arise with other classes of statistical models. In this talk I will advocate the use of more general loss functions in the Bayesian machinery. The idea is not new, but I will present some new results on the contraction properties of the resulting quasi-posterior distributions...
