arXiv subjects

Eugene Han

Publications and source records attributed to Eugene Han.

3 recordsLinked to original sources

arXiv2026

Rectified Fisher-Bingham Model for Compositional Data with Zeros

This paper introduces a rectified and renormalized Fisher-Bingham model for compositional data with zeros, motivated in part by the presence of zeros in microbiota studies. The approach represents compositions through a square-root transformation that maps data to the positive orthant of the unit sphere, and models them via a latent Fisher-Bingham followed by a deterministic transformation that induces exact zeros. This construction yields a coherent likelihood without requiring zero imputation or separate modeling of zero and nonzero components. Parameter estimation is performed using a Monte Carlo expectation-maximization algorithm that accommodates the latent structure. We further develop a score test for detecting structured differences in composition across groups, providing a parametric alternative to commonly used distance-based methods. Simulation studies demonstrate that the proposed method closely approximates the induced distribution and achieves higher power for detecting structured compositional changes, particularly when observations include many zero-valued components. An application to a dietary intervention study illustrates that the method identifies meaningful microbiota shifts not detected by standard approaches.

stat.ME↗

arXiv2025

Reinforcement Learning with Continuous Actions Under Unmeasured Confounding

This paper addresses the challenge of offline policy learning in reinforcement learning with continuous action spaces when unmeasured confounders are present. While most existing research focuses on policy evaluation within partially observable Markov decision processes (POMDPs) and assumes discrete action spaces, we advance this field by establishing a novel identification result to enable the nonparametric estimation of policy value for a given target policy under an infinite-horizon framework. Leveraging this identification, we develop a minimax estimator and introduce a policy-gradient-based algorithm to identify the in-class optimal policy that maximizes the estimated policy value. Furthermore, we provide theoretical results regarding the consistency, finite-sample error bound, and regret bound of the resulting optimal policy. Extensive simulations and a real-world application using the German Family Panel data demonstrate the effectiveness of our proposed methodology.

stat.ML↗

arXiv2017

Linear $d$-polychromatic $Q_{d-1}$-colorings of the Hypercube

Let $n \ge d \ge \ell \ge 1$ be integers, and denote the $n$-dimensional hypercube by $Q_n$. A coloring of the $\ell$-dimensional subcubes $Q_\ell$ in $Q_n$ is called a $Q_\ell$-coloring. Such a coloring is $d$-polychromatic if every $Q_d$ in the $Q_n$ contains a $Q_\ell$ of every color. In this paper we consider a specific class of $Q_\ell$-colorings that are called linear. Given $\ell$ and $d$, let $p_{lin}^\ell(d)$ be the largest number of colors such that there is a $d$-polychromatic linear $Q_\ell$-coloring of $Q_n$ for all $n \ge d$. We prove that for all $d \ge 3$, $p_{lin}^{d-1}(d) = 2$. In addition, using a computer search, we determine $p_{lin}^\ell(d)$ for some specific values of $\ell$ and $d$, in some cases improving on previously known lower bounds.

math.CO↗