1047 papers
This collection explores the fascinating intersection of mathematics and statistics, a field dedicated to making sense of data, uncertainty, and patterns in the world around us. From refining the algorithms that power modern technology to modeling complex biological systems, these studies provide the rigorous tools needed to turn raw numbers into reliable knowledge.
Here at Gist.Science, we process every new preprint in this category as it appears on arXiv. Our team transforms these dense academic papers into both plain-language overviews for general readers and detailed technical summaries for specialists, ensuring the latest breakthroughs are accessible to everyone. Below are the latest papers in this dynamic field, curated to help you stay ahead of the curve.
This paper extends the theoretical understanding of two-sample tests based on nearest neighbor graphs by establishing detection thresholds for cases where the number of neighbors grows with sample size, proposing a 2-sided test to close an exponent gap, and demonstrating that increasing graph density enhances statistical power.
This paper establishes that a relaxed variant of Ollivier's coarse Ricci curvature, characterized by a defective Wasserstein bound, implies local concentration and entropy-transport regularization effects, which are then applied to derive cutoff criteria for Markov processes in negatively curved settings such as Langevin dynamics and Proximal Samplers.
This paper introduces a projective maximum-entropy framework on the space of nonnegative measures that unifies various generalized entropy formulations, characterizes the resulting optimizer as a -exponential density, and provides a principled method to uniquely determine its deformation parameter based on a prescribed Mahalanobis acceptance region, thereby enabling the construction of bounded-support reference distributions without additional constraints.
This paper establishes a Kesten-Stigum dichotomy for node classification on sparse graphs, proving that the value of depth in message passing is determined by the ratio : below the threshold (), additional layers yield diminishing returns, while above it (), depth geometrically reduces error toward a branching-process floor, with optimal finite depths identified via belief propagation simulations.
This paper proposes a framework for honest physical-support inference after latent dictionary learning that accounts for dictionary uncertainty and collision singularities by profiling test representations over robust training-moment regions, thereby achieving minimax-optimal resolution rates and providing resolution-adaptive confidence statements that distinguish between group and fine-support ambiguity.
This paper establishes tight sample complexity bounds for estimating min-entropy and Rényi entropy, proving that min-entropy requires samples—correcting a previous characterization—and that Rényi entropy of order requires samples, utilizing novel estimators and lower-bound constructions to resolve the dependence on both alphabet size and order.
This paper demonstrates that mirror and knockoff+ thresholds can fail to control the false discovery rate under dependence, even when p-values are uniform and satisfy positive regression dependence, because their validity relies on the specific joint behavior of null signs rather than just marginal symmetry or standard distributional assumptions.
This paper investigates the information-theoretic and algorithmic limits of detecting arbitrary planted subgraphs in random graphs under restricted access via non-adaptive edge queries, establishing matching query complexity bounds for diverse graph families by leveraging structural mechanisms such as dense motifs, high-degree vertices, and global edge density.
This paper proposes a softmax-based query-value model for multiple instance regression that decouples concept and labeling mechanisms, deriving EM-like iterations and proving that a single random initialization of the value vector suffices for the algorithm to converge in constant steps with high probability given a polynomial number of bags.
This paper introduces a "semantic map" framework that bridges the gap between a language model's word-level probabilities and meaningful state-level uncertainties, enabling the derivation of auditable, paraphrase-stable posterior estimates for professional decision-making through semiparametric calibration.