In the study of stochastic systems, the committor function describes the probability that a
system starting from an initial configuration x will reach a set B before a set A. This paper …

We study the power of query access for the fundamental task of agnostic learning under the
Gaussian distribution. In the agnostic model, no assumptions are made on the labels of the …

Accurately predicting and testing the types of Pulmonary arterial hypertension (PAH) of each
patient using cost-effective microarray-based expression data and machine learning …

The gradient of a function defined on a manifold is perhaps one of the most important
differential objects in data analysis. Most often in practice, the input function is available only …

A common belief in high-dimensional data analysis is that data are concentrated on a low-
dimensional manifold. This motivates simultaneous dimension reduction and regression on …

We developed localized sliced inverse regression for supervised dimension reduction. It has
the advantages of preventing degeneracy, increasing estimation accuracy, and automatic …

This work studies the statistical advantages of using features comprised of general linear
combinations of covariates to partition the data in randomized decision tree and forest …

The subspace segmentation problem is fundamental in many applications. The goal is to
cluster data drawn from an unknown union of subspaces. In this paper we state the problem …

Diffusion geometry techniques are useful to classify patterns and visualize high-dimensional
datasets. Building upon ideas from diffusion geometry, we outline our mathematical …

In high-dimensional classification or regression problems, the expected gradient
outerproduct (EGOP) of the unknown regression function f, namely EX (∇ f (X)·∇ f (X)), is …