Author

R. Pathak

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Preprint Aug 2026

Beyond Modern Asymptotics for Log-Likelihood Ratios in Logistic Regression

We characterize the finite sample behavior of the log-likelihood ratio statistic in binary logistic regression, uniformly over both the design and the target parameter. For $n\geq d\geq 3$, we determine, up to universal constants, its worst case $(1-\delta)$ quantile over all fixed collections of design vectors and all...

H. Chardon, R. Pathak, Nikita Zhivotovskiy · 0 citations

Preprint Jul 2026

On the metric projection onto a convex set: reverse H\"older inequalities and upper bounds

We study the $L^p(\mu)$-norm of the metric projection onto a closed, convex set $C \subset \mathbf{R}^n$ when $\mu$ is the uniform measure on the sphere or the standard Gaussian measure on $\mathbf{R}^n$. Up to universal constants, we determine the optimal reverse H\"older inequalities (i.e., $L^q-L^p$ estimates for $q...

R. Pathak · 0 citations

Preprint Jul 2026

Minimum Norm Interpolation via The Local Theory of Banach Spaces: The Role of Gaussianity

We study minimum-norm interpolation (MNI) in overparameterized linear regression with isotropic Gaussian covariates, in settings where the MNI has no closed-form formula. Whereas most prior work relied on Gaussian comparison tools such as the convex Gaussian min--max theorem (CGMT), our approach uses tools from high-di...

Gil Kur, Reese Pathak · 0 citations