arXiv subjects

Tomas Gonzalez

Publications and source records attributed to Tomas Gonzalez.

4 recordsLinked to original sources

arXiv2026

Statistical Rates for Entropic Optimal Transport in the Discrete to SubGaussian Regime

We study statistical rates in entropic optimal transport in the semi-discrete regime where one measure has finite support and the other is subGaussian. Our main result establishes parametric convergence rates for the empirical dual potentials to their population counterparts, with no dimension dependence in the leading term. Our result relies on tailored strong concavity analysis of the semi-dual objective, coupled with specialized bounds for the semi-discrete potentials. As a consequence, we obtain fast rates for downstream quantities derived from the optimal coupling. Chiefly, the empirical barycentric projection achieves a squared-error rate $n^{-1}$, matching the fully compact case and improving over the less favorable $n^{-1/2}$ rate known for fully subGaussian settings. Altogether, these results may indicate a lower complexity adaptation phenomenon whereby the statistical complexity of the barycentric projection is governed by the discrete measure. As an application, we analyze Sinkhorn-EM, an EM-type algorithm in which the E-step is replaced by an entropic optimal transport problem. In a well-specified and balanced two-component Gaussian mixture model, we prove $\sqrt{n}$-consistency of the empirical iterates to their population counterparts for any fixed number of iterations, matching classical EM rates up to a $\sqrt{\log n}$ factor. Simulations support the theory.

math.ST↗

arXiv2026

FoggyTrust: Robust Federated Learning with Hierarchical Trust Networks

Byzantine-robust federated learning seeks to protect distributed model training from malicious or corrupted clients without requiring access to their private data. FLTrust addresses this challenge by introducing a trusted server-side root dataset that assigns trust scores to client updates for more robust aggregation. In this work, we propose FOGGYTRUST, a hierarchical extension of FLTrust that localizes trust computation to fog nodes, allowing the framework to better handle globally heterogeneous data while preserving robustness within locally homogeneous client groups. We further show that this two-level architecture can simultaneously address distribution mismatch in trust estimation and client drift across groups by combining local trust-based aggregation with heterogeneity-aware global optimizers such as FedAdam and SCAFFOLD. Across benchmark datasets, FOGGYTRUST achieves its strongest gains on more challenging heterogeneous settings, particularly on CIFAR-10 under Krum and Trim attacks, where it achieves an over 50% improvement over FLTrust. We also test FOGGYTRUST in a real-world safari dataset to show the promise of hierarchical trust networks for robust federated learning in socially impactful, safety-critical settings such as distributed wildlife monitoring.

cs.LG↗

arXiv2026

Optimal Rates for Differentially Private Hypothesis Testing with E-values

E-values have attracted considerable interest in recent years as flexible tools for enabling anytime-valid and adaptive data analysis. Hypothesis testing is at the core of many of these applications, which can often involve private or sensitive data. In this work, we answer a simple but important question: given two distributions $\mathbb{P}$ and $\mathbb{Q}$, what is the maximum achievable e-power when testing $X\sim \mathbb{P}^n$ against $X\sim\mathbb{Q}^n$ with e-values that satisfy $\varepsilon$-differential privacy? We characterize the optimal rate for this problem and provide an algorithm which matches it exactly. In the sequential setting, when observations arrive one-by-one and the analyst chooses when to halt, we give matching upper and lower bounds on the stopping times of any private e-process. Numerical experiments confirm the practicality of our algorithms, which require less data than the recently proposed DP-SPRT across a range of sequential testing problems and privacy levels.

cs.CR↗

arXiv2026

Vector-valued self-normalized concentration inequalities beyond sub-Gaussianity

The study of self-normalized processes plays a crucial role in a wide range of applications, from sequential decision-making to econometrics. While the behavior of self-normalized concentration has been widely investigated for scalar-valued processes, vector-valued processes remain comparatively underexplored, especially outside of the sub-Gaussian framework. In this contribution, we provide concentration bounds for self-normalized processes with light tails beyond sub-Gaussianity (such as Bennett or Bernstein bounds). We illustrate the relevance of our results in the context of online linear regression, with applications in (kernelized) linear bandits.

stat.ML↗