arXiv Machine Learning
Jun 2
Dimension Reduction via Sum-of-Squares and Improved Clustering Algorithms for Non-Spherical Mixtures
arXiv:2411. 12438v2 Announce Type: replace-cross Abstract: We develop a new approach for clustering non-spherical (i.
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.
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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 18
How fast can you find a good hypothesis?
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 Statistics ML
3d ago
Optimal VC Dimension of Contrastive Learning with Margin
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 Machine Learning
Jun 30
Replica Symmetry Breaking and Algorithmic Thresholds in Empirical Risk Minimization under Multi-Index Model
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
arXiv Machine Learning
Sep 15
Low-Dimensional Embeddings for Gaussian Kernels on Manifolds
arXiv:2609.15179v1 Announce Type: cross Abstract: The Gaussian kernel is a widely used similarity measure underlying kernel methods such as kernel PCA and spectral clustering, but computing Gaussian...
arXiv Machine Learning
Aug 4
Improved convergence rate of kNN graph Laplacians: differentiable self-tuned affinity
arXiv:2410. 23212v3 Announce Type: replace-cross Abstract: In graph-based data analysis, $k$-nearest neighbor ($k$NN) graphs are widely used due to their adaptivity to local data densities.
arXiv Machine Learning
Jul 2
Fast Score-Based Sampling via Log-Concave Reductions
arXiv:2512. 24152v2 Announce Type: replace-cross Abstract: Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities.
arXiv Machine Learning
Aug 6
The Sample Complexity of Distributionally Robust PAC Learning under Cressie--Read Divergences
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 $\rho\geq 0$.
arXiv Machine Learning
Sep 10
Beyond Worst-Case Coreset Bounds for $k$-Clustering via Determinantal Sampling
arXiv:2609.06394v1 Announce Type: cross Abstract: Massive datasets in modern machine learning have made data reduction a central challenge, particularly for clustering tasks where memory and computat...
arXiv Machine Learning
Jul 28
Efficient Learning of Truncated Boolean Product Distributions: Influence to the Rescue
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 Machine Learning
Sep 4
Restricted Eigenvalues Beyond Gaussian Width: Threshold Occupancy under Heavy Tails
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.