arXiv Machine Learning
Jul 15
Learning and Testing Convex Functions
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.
Smoothed Analysis for Learning Concepts with Low Intrinsic Dimension
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.
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arXiv Machine Learning
Sep 17
Efficient Robust Learning at the Information-Theoretic Limit
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 Machine Learning
Jun 26
Fast algorithms for learning a Gaussian under halfspace truncation with optimal sample complexity
arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
arXiv Machine Learning
Oct 8
Oracle-Efficient and Parameter-Free Agnostic Smoothed Online Learning
arXiv:2610. 10499v1 Announce Type: new Abstract: Online learning is an attractive framework in many domains because it permits well-defined learning even when data are dependent or chosen adversarially.
arXiv Machine Learning
Jun 16
Can Neural Networks Achieve Optimal Computational-statistical Tradeoff? An Analysis on Single-Index Model
arXiv:2606. 15219v1 Announce Type: new Abstract: In this work, we tackle the following question: Can neural networks trained with gradient-based methods achieve the optimal computational-statistical tradeoff in learning Gaussian single-index models?
arXiv Machine Learning
Sep 11
Relatively Smart II: Tractable or Semi-Supervised Instance-Optimal Learning
The paper extends the study of relatively smart learning, showing that ERM and any proper consistent learner are relatively smart for binary classification in the distribution‑free setting, achieving a quadratic sample‑complexity blowup. It further demonstrates that semi‑supervised relatively smart learning is possible with only a quadratic blowup in unlabeled data and no blowup in labeled data, though this requires a leave‑most‑out transductive approach and incurs intractability when only an agnostic ERM oracle is available. The results clarify the trade‑offs between sample efficiency, label efficiency, and computational tractability in relatively smart learning.
arXiv Machine Learning
Jun 30
Actively Learning Halfspaces without Synthetic Data
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 Machine Learning
Jun 17
Tight $L_\infty$ Sample Complexity for Low-Degree and Sparse Boolean Polynomials
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.
arXiv Machine Learning
Sep 4
A Closed-Form Formula for Consistent Lipschitz Regression on Metric Spaces with Sparse Neural Network Realizations
arXiv:2609. 03129v1 Announce Type: cross Abstract: Several classical machine-learning methods, such as KRRs and SVRs, are both computationally and analytically tractable since their estimators either admit closed-form expressions or are obtained by minimizing convex training objectives; neither feature is generally available for deep neural networks.
arXiv Machine Learning
Jun 15
On Rate-Optimal Partitioning Classification from Observable and from Privatised Data
arXiv:2312. 14889v4 Announce Type: replace-cross Abstract: In this paper we revisit the classical method of partitioning classification and prove novel convergence rates under relaxed conditions, both for observable (non-privatised) and for privatised data.
arXiv Machine Learning
Jul 13
A Fourier analytique approach to Gaussian mixture learning
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 Machine Learning
Jul 28
Learning Distributions from Multiple Data Providers
arXiv:2607. 24732v1 Announce Type: cross Abstract: Motivated by learning from heterogeneous and overlapping data providers, we study a stylized model of distribution learning from restricted conditional samples.