Minimax rate for optimal transport regression between distributions

Nearly Optimal Minimax Estimator for High Dimensional Sparse Linear Regression

We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints (`q constraint with 0 < q ≤ 1) in the high-dimensional setting. We first present a family of estimators, called the projected nearest neighbor estimator and show, by using results from Convex Geometry, that such estimator is within a logarithmic ...

Hausdorff Distances Between Distributions Using Optimal Transport and Mathematical Morphology

In this paper we address the question of defining and computing Hausdorff distances between distributions in a general sense. We exhibit some links between Prokhorov-Lévy distances and dilation-based distances. In particular, mathematical morphology provides an elegant way to deal with periodic distributions. The case of possibility distributions is addressed using fuzzy mathematical morphology...

Minimax-optimal semi-supervised regression on unknown manifolds

We consider the problem of semi-supervised regression when the predictor variables are drawn from an unknown manifold. A simple approach to this problem is to first use both the labeled and unlabeled data to estimate the manifold geodesic distance between pairs of points, and then apply a k nearest neighbor regressor based on these distance estimates. We prove that given sufficiently many unlab...

Minimax-optimal semi-supervised regression on unknown manifolds: supplementary material

Robust Minimax Probability Machine Regression Robust Minimax Probability Machine Regression

We formulate regression as maximizing the minimum probability (Ω) that the true regression function is within ±2 of the regression model. Our framework starts by posing regression as a binary classification problem, such that a solution to this single classification problem directly solves the original regression problem. Minimax probability machine classification (Lanckriet et al., 2002a) is u...