arXiv:2604. 14614v2 Announce Type: replace-cross Abstract: We give an algorithm for PAC learning intersections of $k$ halfspaces with a $\rho$ margin to within error $\varepsilon$ that runs in time $\textsf{poly}(k, \varepsilon^{-1}, \rho^{-1}) \cdot \exp \left(O(\sqrt{n \log(1/\rho) \log k})\right)$.
arXiv:2407. 00966v3 Announce Type: replace Abstract: In traditional models of supervised learning, the goal of a learner-- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$-- is to output a hypothesis that is competitive (to within $\epsilon$) of the best fitting concept from some class.
arXiv:2004. 05813v3 Announce Type: replace-cross Abstract: Suppose that we are given independent, identically distributed random samples $x_1,\cdots,x_n$ from a mixture at most $k$ many $d$-dimensional spherical Gaussian distributions $\mu_1,\cdots,\mu_{k_0}$ of identical and known variance $\sigma^2$ in each coordinate, such that the minimum $\ell^2$ distance between two distinct centers $y_l$ and $y_j$ is greater than $2\Delta\sigma \min\{\sqrt{d},\sqrt k\}$, where $\Delta>C_0$, and $C_0$ is a sufficiently large universal constant.
arXiv:2509. 20848v2 Announce Type: replace-cross Abstract: In the classic point location problem, one is given an arbitrary dataset $X \subset \mathbb{R}^d$ of $n$ points with query access to an unknown halfspace $f : \mathbb{R}^d \to \{0,1\}$, and the goal is to learn the label of every point in $X$.
arXiv:2607. 09909v1 Announce Type: cross Abstract: We study nearest neighbor search from the perspective of data-driven algorithm design: given a dataset $P \subset \mathbb{R}^d$ of size $n$ and sample access to a query distribution over $\mathbb{R}^d$, the goal is to learn a data structure optimized for queries drawn from that specific distribution.
arXiv:2608. 04686v1 Announce Type: new Abstract: We study distributionally robust PAC learning for the $0$--$1$-loss, where adversarial perturbations of the data distribution are constrained by a Cressie--Read divergence of order $k>1$ and radius $\rho\geq 0$.
The paper investigates restricted eigenvalue (RE) bounds for norm‑regularized estimators under heavy‑tailed designs. It shows that the previously conjectured sample‑size law based on Gaussian width fails for heavy‑tailed measurements, due to a phenomenon called simultaneous threshold occupancy. The authors provide explicit counterexamples, derive worst‑case sample‑complexity bounds, and compare the behavior of heavy‑tailed versus Gaussian designs on constant‑width polyhedral descent cones.
arXiv:2608. 06363v1 Announce Type: cross Abstract: Let $H\subseteq\{-1,+1\}^X$ be a class of finite VC dimension $d\ge1$.
arXiv:2608. 10869v1 Announce Type: new Abstract: Worst-case multiclass bounds do not become smaller when the best classifier is already nearly correct: what is missing is an optimistic rate, a guarantee whose fluctuation scales with the oracle risk itself.
arXiv:2606. 29331v1 Announce Type: new Abstract: Scientific discovery via symbolic regression is often viewed as statistically and computationally intractable because the hypothesis space of expressions grows combinatorially with depth.
arXiv:2609.38834v1 Announce Type: cross Abstract: Contrastive learning is a successful paradigm for learning $d$-dimensional geometric representations from a collection of ``anchor--positive--negativ...
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:2511. 11498v2 Announce Type: replace-cross Abstract: We consider the problems of \emph{learning} and \emph{testing} real-valued convex functions over Gaussian space.