The paper develops a rigorous framework for computing the Normalized Maximum Likelihood (NML) codelength for regular path‑differentiable Lipschitz (PDL) estimators, which include non‑smooth models such as Lasso and Sparse SVMs. By leveraging geometric measure theory and a novel Propose‑and‑Project Metropolis‑Hastings sampler, the authors provide a method to exactly evaluate the stochastic complexity for these non‑smooth estimators and demonstrate its scalability to high‑dimensional settings. The study shows that the exact NML criterion can match cross‑validation performance while being more data‑efficient, offering a theoretically grounded alternative for model selection in modern machine learning.
By Trenton Lau, Gary P. T. Choi
arXiv:2602. 20376v3 Announce Type: replace-cross Abstract: We study the problem of maximizing a complex-valued quadratic form over the $K^{\text{th}}$ roots of unity.
By Ria Stevens, Fangshuo Liao, Barbara Su, Thanasis Hadjidimoulas, Jianqiang Li, Anastasios Kyrillidis
arXiv:2602. 05869v2 Announce Type: replace-cross Abstract: We introduce Wedge Sampling, a new non-adaptive sampling scheme for low-rank tensor completion.
By Hengrui Luo, Anna Ma, Ludovic Stephan, Yizhe Zhu
arXiv:2609.09211v1 Announce Type: new
Abstract: The Davis-Kahan theorem is a fundamental tool in spectral analysis, providing quantitative control over the distance between the eigenspaces of a symme...
By Huan Qing
arXiv:2609.08873v1 Announce Type: cross
Abstract: Sparsity is a powerful structural resource in optimization and statistics. We develop frameworks for leveraging sparsity in sampling problems over th...
By Syamantak Kumar, Purnamrita Sarkar, Kevin Tian, Yusong Zhu
\texttt{TensorSketch} by~\cite{pham2013fast,kar2012random} provides efficient sketching algorithms for high-dimensional polynomial kernels $\vec{x}^{\otimes p} \in \R^{d^p}$. \cite{kar2012random} uses dense Johnson-Lindenstrauss (JL)-type projections with computational cost $O(pDd)$, where $D$ denotes the sketch dimension, whereas~\cite{pham2013fast} extends the sparse \texttt{CountSketch}~\citep{count_sketch} algorithm, yielding a faster algorithm for high-dimensional sparse inputs with running time $O\big(p(\nnz{\vec{x}} + D \log D)\big)$.
arXiv:2606. 02909v1 Announce Type: cross Abstract: Gradient observations can substantially improve Gaussian process (GP) surrogates, particularly in high-dimensional settings where function evaluations are expensive.
By Hyunseok Seung, Matthias Katzfuss
arXiv:2608. 10523v1 Announce Type: cross Abstract: \texttt{TensorSketch} by~\cite{pham2013fast,kar2012random} provides efficient sketching algorithms for high-dimensional polynomial kernels $\vec{x}^{\otimes p} \in \R^{d^p}$.
By Amit Sharma, Mohammad Azhar Khan, Rameshwar Pratap, Keegan Kang
The paper introduces a Projected Riemannian Gradient Descent (RGD) algorithm for computing the Bures‑Wasserstein barycenter of positive definite matrices, achieving dimension‑independent linear convergence at unit step size. It resolves a previous dichotomy by showing that clipping eigenvalues to a fixed interval yields a closed‑form, non‑expansive projection in the BW metric, allowing the algorithm to match the empirical speed of unit‑step RGD while maintaining theoretical guarantees. The method also extends to the invariant matrix projection problem, providing a unified dimension‑independent analysis.
arXiv:2609. 03762v1 Announce Type: new Abstract: The computation of the Bures-Wasserstein (BW) barycenter of an ensemble of positive definite matrices arises throughout machine learning, optimal transport, and quantum information.
By A. Afham
arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
By Haitong Liu, Deepak Narayanan Sridharan, David Steurer, Manuel Wiedmer
arXiv:2607. 24518v1 Announce Type: new Abstract: Symmetric non-negative matrix factorization (SymNMF) recovers latent group structure from a dependence matrix, but its dense, quadratic-memory objective has confined prior work to moderate sizes.
By Lavinia Ghita, Dhruv Desai, Jake Goldberg, Roman Yokunda Enzmann