Related papers: On the Sample Complexity of Privately Learning Unb…

Differential privacy formalises privacy-preserving mechanisms that provide access to a database. We pose the question of whether Bayesian inference itself can be used directly to provide private access to data, with no modification. The…

Learning unbiased models on imbalanced datasets is a significant challenge. Rare classes tend to get a concentrated representation in the classification space which hampers the generalization of learned boundaries to new test examples. In…

We develop differentially private methods for estimating various distributional properties. Given a sample from a discrete distribution $p$, some functional $f$, and accuracy and privacy parameters $\alpha$ and $\varepsilon$, the goal is to…

The realizable-to-agnostic transformation (Beimel et al., 2015; Alon et al., 2020) provides a general mechanism to convert a private learner in the realizable setting (where the examples are labeled by some function in the concept class) to…

Differentially private data generation techniques have become a promising solution to the data privacy challenge -- it enables sharing of data while complying with rigorous privacy guarantees, which is essential for scientific progress in…

In this work we consider generic Gaussian Multi-index models, in which the labels only depend on the (Gaussian) $d$-dimensional inputs through their projection onto a low-dimensional $r = O_d(1)$ subspace, and we study efficient agnostic…

Although there is an extensive literature on the maxima of Gaussian processes, there are relatively few non-asymptotic bounds on their lower-tail probabilities. The aim of this paper is to develop such a bound, while also allowing for many…

This paper explores certain kinds of empirical process with respect to the components of multivariate Gaussian. We put forward some finite sample bounds which hold for multivariate Gaussian under general dependence. We give necessary and…

A new line of work, started with Dwork et al., studies the task of answering statistical queries using a sample and relates the problem to the concept of differential privacy. By the Hoeffding bound, a sample of size $O(\log k/\alpha^2)$…

This paper considers the generalization performance of differentially private convex learning. We demonstrate that the convergence analysis of Langevin algorithms can be used to obtain new generalization bounds with differential privacy…

This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…

The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major…

We prove finite-sample concentration and anti-concentration bounds for dimension estimation using Gaussian kernel sums. Our bounds provide explicit dependence on sample size, bandwidth, and local geometric and distributional parameters,…

We present a new algorithm for general reinforcement learning where the true environment is known to belong to a finite class of N arbitrary models. The algorithm is shown to be near-optimal for all but O(N log^2 N) time-steps with high…

We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning…

This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…

We study the problem of generalized uniformity testing \cite{BC17} of a discrete probability distribution: Given samples from a probability distribution $p$ over an {\em unknown} discrete domain $\mathbf{\Omega}$, we want to distinguish,…

Understanding minimal assumptions that enable learning and generalization is perhaps the central question of learning theory. Several celebrated results in statistical learning theory, such as the VC theorem and Littlestone's…

Many learning paradigms self-select training data in light of previously learned parameters. Examples include active learning, semi-supervised learning, bandits, or boosting. Rodemann et al. (2024) unify them under the framework of…

The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for…