Related papers: Multiple-Instance Learning: Radon-Nikodym Approach…
In the setting of nonparametric regression, we propose and study a combination of stochastic gradient methods with Nystr\"om subsampling, allowing multiple passes over the data and mini-batches. Generalization error bounds for the studied…
We propose a method for variable selection in multiple regression with random predictors. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating suitable permutation and…
We consider a regression setting where observations are collected in different environments modeled by different data distributions. The field of out-of-distribution (OOD) generalization aims to design methods that generalize better to test…
Human learners have the natural ability to use knowledge gained in one setting for learning in a different but related setting. This ability to transfer knowledge from one task to another is essential for effective learning. In this paper,…
Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of…
Many state-of-the-art algorithms for solving hard combinatorial problems in artificial intelligence (AI) include elements of stochasticity that lead to high variations in runtime, even for a fixed problem instance. Knowledge about the…
We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…
Random feature ridge regression is often analyzed in the high-dimensional regime under the homogeneous sampling model $x_i=\Sigma^{1/2}x_i'$, where the vectors $x_i'$ have iid entries and the same covariance matrix $\Sigma$ is shared by all…
We study the problem of distribution to real-value regression, where one aims to regress a mapping $f$ that takes in a distribution input covariate $P\in \mathcal{I}$ (for a non-parametric family of distributions $\mathcal{I}$) and outputs…
In contrast to classical reinforcement learning (RL), distributional RL algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or…
In this paper, we deal with the problem of reconstruction from Radon random samples in local shift-invariant signal space. Different from sampling after Radon transform, we consider sampling before Radon transform, where the sample set is…
Consider the regression problem where the response $Y\in\mathbb{R}$ and the covariate $X\in\mathbb{R}^d$ for $d\geq 1$ are \textit{unmatched}. Under this scenario, we do not have access to pairs of observations from the distribution of $(X,…
In this paper, we study the problem of estimating uniformly well the mean values of several distributions given a finite budget of samples. If the variance of the distributions were known, one could design an optimal sampling strategy by…
We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…
In this paper, we study the information transmission problem under the distributed learning framework, where each worker node is merely permitted to transmit a $m$-dimensional statistic to improve learning results of the target node.…
Let $X=(X_1,X_2, X_3)$ be a Gaussian random vector such that $X\sim \mathcal{N} (0,\Sigma)$. We consider the problem of determining the matrix $\Sigma$, up to permutation, based on the knowledge of the distribution of…
The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…
Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…
Consider the (almost surely) unique Radon partition of a set of $n$ random Gaussian vectors in $\mathbb R^{n-2}$; choose one of the two parts of this partition uniformly at random, and for $0 \le k \le n$, let $p_k$ denote the probability…