arXiv:2606. 07931v1 Announce Type: cross Abstract: We prove a variance-aware pointwise majorizing-measure theorem for centered Gaussian processes.
arXiv:2606. 23867v1 Announce Type: new Abstract: The exact computation of the Normalized Maximum Likelihood (NML) codelength for regular non-smooth estimators (e.
arXiv:2509.01809v2 Announce Type: replace-cross Abstract: We consider the problem of support recovery for sparse binary signals from noisy linear measurements. For sparse Gaussian measurement matrice...
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:2607. 10618v1 Announce Type: cross Abstract: We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated.
arXiv:2602. 16568v2 Announce Type: replace-cross Abstract: Sparse recovery is among the most well-studied problems in learning theory and high-dimensional statistics.
The paper presents a non‑asymptotic analysis of Markov chain Monte Carlo (MCMC) algorithms that learn and apply a preconditioner based on either the target covariance or the expected Hessian of the target potential. It compares the finite‑time computational costs of these preconditioned schemes with unpreconditioned counterparts, providing guarantees for algorithms such as the Unadjusted Langevin Algorithm (ULA) and the proximal sampler. The analysis relies on a contraction assumption in the Wasserstein‑2 distance to formalize approximate independence and bridge modern MCMC theory with classical effective sample size heuristics.
The paper investigates the computational and statistical challenges of the calibration distance, a key metric for measuring miscalibration in probabilistic predictors. It presents an efficient algorithm for exact computation when the distribution has a uniform marginal and noiseless labels, and shows that the problem becomes NP‑hard if either assumption is dropped. The authors also provide a polynomial‑time approximation scheme for the general case and establish tight sample complexity bounds for estimating the calibration distance from data.
The paper introduces a Bayesian approach to matrix completion that uses a nuclear norm-based prior and addresses the challenge of unknown noise variance by placing a prior on it. It presents the first sampler for this model, providing a non‑asymptotic polynomial‑time guarantee in terms of matrix dimensions and desired accuracy. The method discretizes the noise precision and employs thermodynamic integration to construct a categorical posterior, offering a feasibility result for Bayesian sampling in non‑log‑concave settings.
SelectPFN is a prior‑data‑fitted network that jointly performs Bayesian variable selection and prediction for sparse nonlinear regression. In a single forward pass it outputs posterior inclusion probabilities for each variable and makes predictions using only sampled subsets, ensuring excluded variables cannot influence the result. The method achieves exact finite‑sample false discovery rate control via column‑permutation equivariance and knockoff statistics, and outperforms lasso, BART, DART, LassoNet, and other sparse neural networks on synthetic and real data with up to 500 predictors.
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:2603.29715v2 Announce Type: replace Abstract: Nonnegative matrix factorization (NMF) approximates a nonnegative matrix, X, by the product of two nonnegative factors, WH, where W has r columns a...