ixture models represent the superposition of statistical processes, and are natural in machine learning and statistics. In mixed regression, the relationship between input and output is given by one of possibly several different (noisy) linear functions. Thus the solution encodes a combinatorial selection problem, and hence computing it is difficult in the worst case. Even…

Most big real-world networks (social, technological, biological) are sparse. Most of networks have noticeable structure, which can be formed by clusters (communities) and hubs. When and how can a hidden structure be recovered from a sparse network? Known approaches to this problem come from a variety of disciplines – probability, combinatorics, physics, statistics, optmization, information…

Many scientific and engineering challenges---ranging from personalized medicine to customized marketing recommendations---require an understanding of treatment heterogeneity. We develop a non-parametric causal forest for estimating heterogeneous treatment effects that is closely inspired by Breiman's widely used random forest algorithm. Given a potential outcomes framework with unconfoundedness, we show that causal forests are pointwise consistent for…

Ranking, clustering, or metrically-embedding a set of items (e.g., images, documents, products) based on human judgments can shed light on preferences and human reasoning. Two common approaches to collecting data from people are rating and comparison-based systems. Ratings can be difficult to calibrate across people. Also, in certain applications, it may be far easier to…

Many optimization problems arising in high-dimensional statistics decompose naturally into a sum of several terms, where the individual terms are relatively simple but the composite objective function can only be optimized with iterative algorithms. Specifically, we are interested in optimization problems of the form F(Kx) + G(x), where K is a fixed linear transformation, while…