arXiv subjects

Kota Kurihara

Publications and source records attributed to Kota Kurihara.

2 recordsLinked to original sources

arXiv2026

An Axiomatic Analysis of Distributionally Robust Optimization with $q$-Norm Ambiguity Sets for Probability Smoothing

We analyze the axiomatic properties of a class of probability estimators derived from Distributionally Robust Optimization (DRO) with $q$-norm ambiguity sets ($q$-DRO), a principled approach to the zero-frequency problem. While classical estimators such as Laplace smoothing are characterized by strong linearity axioms like Ratio Preservation, we show that $q$-DRO provides a flexible alternative that satisfies other desirable properties. We first prove that for any $q \in [1, \infty]$, the $q$-DRO estimator satisfies the fundamental axioms of Positivity and Symmetry. For the case of $q \in (1, \infty)$, we then prove that it also satisfies Order Preservation. Our analysis of the optimality conditions also reveals that the $q$-DRO formulation is equivalent to the regularized empirical loss minimization.

math.OC↗

arXiv2025

A scalable mixed-integer conic optimization approach to cardinality-constrained Poisson regression with safe screening

This paper introduces a novel approach for cardinality-constrained Poisson regression to address feature selection challenges in high-dimensional count data. We formulate the problem as a mixed-integer conic optimization, enabling the use of modern solvers for optimal solutions. To enhance computational efficiency, we develop a safe screening based on Fenchel conjugates, thereby effectively removing irrelevant features before optimization. Experiments on synthetic datasets demonstrate that our safe screening significantly reduces the problem size, leading to substantial improvements in computational time. Our approach can solve Poisson regression problems with tens of thousands of features, exceeding the scale of previous studies. This work provides a valuable tool for interpretable feature selection in high-dimensional Poisson regression.

math.OC↗