This paper proposes a comprehensive benchmarking framework for evaluating mutual information estimation methods on complex, realistic data using copula theory.

The paper proposes a novel nonparametric mutual information estimator to robustly quantify dependence between heterogeneous temporal data, specifically continuous time series and discrete event sequen…

InfoAtlas is a foundation model that estimates statistical mutual information (MI) in a single forward pass, achieving state-of-the-art accuracy with a massive speedup compared to traditional iterativ…

This paper studies the existence of polynomial measures of dependence between two random variables that satisfy the data processing inequality and vanish on independence. It proves that no such polyno…

This paper investigates the necessity of interaction for order-optimal 1-bit mean estimation in nonparametric finite-moment classes.

The paper proves a stochastic comparison for Gaussian maxima, resolving the Weak Simplex Conjecture and proving the Simplex Mean Width Conjecture.

This paper proves convergence of belief propagation algorithms for multipath data association to a unique fixed point.

The paper establishes information-theoretic lower bounds for stochastic optimization using low-bit gradients by reducing the problem to compressed Gaussian mean estimation, yielding sharp bounds on co…

This paper establishes a direct connection between Approximate Message Passing (AMP) and the Convex Gaussian Min-max Theorem (CGMT) for regularized linear regression and M-estimation.

This paper develops a framework for identifying and estimating parameters of interest in automatic debiased machine learning using a Riesz representer, which is identified when it uniquely optimizes a…

This paper analyzes the statistical and computational limits of learning bounded linear operators between Sobolev spaces from noisy data, and constructs a finite-resolution blockwise least-squares est…

The paper analyzes low-degree estimation thresholds for recovering hidden signals in planted hypergraphs and tensor PCA, establishing sharp phase transitions and providing polynomial-time recovery alg…

This paper improves the theoretical bounds for estimating discrete probability distributions using the $\ell_\infty$ norm, resolving several open questions in the field.

The paper formalizes the problem of representation identifiability in supervised learning, showing that a representation property is identifiable if and only if it is constant across all possible fact…

This paper derives deterministic limits for transfer learning performance of linear discriminant analysis in high-dimensional two-class classification under spiked covariance models.

This paper derives the Oracle Distance theorem for discrete diffusion models and proves that the negative ELBO is equal to the data entropy plus the path KL from the oracle reverse process to the lear…