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
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
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
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
1d ago
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.
arXiv Machine Learning
Jun 10
Efficiently Learning Drifting Halfspaces with Massart Noise
arXiv:2606. 11149v1 Announce Type: new Abstract: We study the problem of learning a drifting concept in the presence of Massart noise.
arXiv Machine Learning
Jul 31
Tight Bounds for Learning Polyhedra with a Margin
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 Machine Learning
Aug 11
Optimal Learning Under Tsybakov Noise
arXiv:2608. 08416v1 Announce Type: new Abstract: Probably Approximately Correct (PAC) learning [Val84] is a fundamental learning model that has been extensively investigated.