KLLR: A scale-dependent, multivariate model class for regression analysis

TL;DR

The paper introduces KLLR, a flexible, scale-dependent multivariate regression model for astrophysical data analysis, capable of capturing complex relationships across a wide dynamic range.

Contribution

It presents KLLR, a novel extension of linear regression that models scale-dependent parameters, with demonstrated applications and a publicly available Python implementation.

Findings

KLLR accurately models scale-dependent relationships in simulated data.

Application to dark matter halos reveals new insights into baryonic content.

The method outperforms traditional linear models in capturing astrophysical variability.

Abstract

The underlying physics of astronomical systems governs the relation between their measurable properties. Consequently, quantifying the statistical relationships between system-level observable properties of a population offers insights into the astrophysical drivers of that class of systems. While purely linear models capture behavior over a limited range of system scale, the fact that astrophysics is ultimately scale-dependent implies the need for a more flexible approach to describing population statistics over a wide dynamic range. For such applications, we introduce and implement a class of Kernel-Localized Linear Regression (KLLR) models. KLLR is a natural extension to the commonly-used linear models that allows the parameters of the linear model -- normalization, slope, and covariance matrix -- to be scale-dependent. KLLR performs inference in two steps: (1) it estimates the mean relation between a set of independent variables and a dependent variable and; (2) it estimates the conditional covariance of the dependent variables given a set of independent variables. We demonstrate the model's performance in a simulated setting and showcase an application of the proposed model in analyzing the baryonic content of dark matter halos. As a part of this work, we publicly release a Python implementation of the KLLR method.