The paper investigates the computational and statistical challenges of the calibration distance, a key metric for measuring miscalibration in probabilistic predictors. It presents an efficient algorithm for exact computation when the distribution has a uniform marginal and noiseless labels, and shows that the problem becomes NP‑hard if either assumption is dropped. The authors also provide a polynomial‑time approximation scheme for the general case and establish tight sample complexity bounds for estimating the calibration distance from data.
We study the problem of \emph{adversarially robust} PAC learning. In this framework, the learner observes independent samples from an unknown distribution over $\mathcal{X} \times \{0,1\}$, as in clas...
arXiv:2610.19652v1 Announce Type: new Abstract: Recent work has sought to transfer first-order nonconvex optimization guarantees to zeroth-order methods through gradient estimators, typically incurri...
arXiv:2509. 03734v3 Announce Type: replace-cross Abstract: In the hypothesis selection problem, we are given sample and query access to finite set of candidate distributions (hypotheses), $\mathcal{H} = \{H_1, \ldots, H_n\}$, and samples from an unknown distribution $P$, both over a domain $\mathcal{X}$.
arXiv:2609.24260v1 Announce Type: cross Abstract: We study the problem of \emph{adversarially robust} PAC learning. In this framework, the learner observes independent samples from an unknown distrib...
arXiv:2607. 22889v1 Announce Type: new Abstract: Learning the natural parameters $z \in \mathbb{R}^n$ of discrete distributions $\mu_z$ from independent samples constrained to a subset $S \subseteq \{0,1\}^n$ is a foundational challenge in high-dimensional statistics.
arXiv:2603. 16798v2 Announce Type: replace Abstract: We study mean estimation for a Gaussian distribution with identity covariance in $\mathbb{R}^d$ under a missing data scheme termed realizable $\epsilon$-contamination model.
arXiv:2606. 11149v1 Announce Type: new Abstract: We study the problem of learning a drifting concept in the presence of Massart noise.
arXiv:2604. 08438v2 Announce Type: replace Abstract: The Shapley value, and its broader family of semi-values, has received much attention in various attribution problems.
The paper presents a polynomial‑time algorithm for robustly learning Boolean concept classes with respect to a fixed distribution, achieving the optimal error rate of η + ε where η is the noise rate. It builds on Blanc’s earlier, computationally inefficient algorithm and introduces no‑regret learners to overcome the previous limitations. Additionally, the authors provide an efficient method that does not require an ERM oracle for any function class admitting sandwiching polynomials under hypercontractive distributions, including a first polynomial‑time solution for learning halfspaces with Gaussian marginals at error η + ε.
arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
The paper investigates the sample complexity of estimating the Fréchet Inception Distance (FID) between high‑dimensional Gaussian distributions when one distribution is known. It establishes tight bias and variance bounds for the empirical plug‑in estimator, shows how higher‑order extrapolation reduces bias, and introduces a new Relative Taylor Debiasing (RTD) algorithm that achieves optimal sample complexity. Experiments on synthetic data and ImageNet confirm the theoretical predictions and demonstrate RTD’s superior accuracy with limited samples.
arXiv:2606. 17319v1 Announce Type: cross Abstract: Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube.