论文标题
KLLR：一个依赖比例的多元模型类，用于回归分析
KLLR: A scale-dependent, multivariate model class for regression analysis
论文作者
论文摘要
天文系统的潜在物理学控制了其可测量特性之间的关系。因此，量化人群的系统级可观察性特性之间的统计关系提供了对该类别系统的天体物理驱动因素的见解。尽管纯线性模型在有限的系统尺度上捕获行为，但天体物理学最终取决于尺度依赖性的事实意味着需要采用更灵活的方法来描述在广泛的动态范围内的人口统计数据。对于此类应用，我们介绍并实施了一类内核 - 定位的线性回归（KLLR）模型。 KLLR是对常用的线性模型的自然扩展，该模型允许线性模型的参数 - 归一化，斜率和协方差矩阵 - 依赖于尺度。 KLLR分为两个步骤进行推断：（1）它估计一组自变量和因变量之间的平均关系和； （2）它估计给定一组自变量的因变量的条件协方差。我们在模拟设置中演示了该模型的性能，并展示了所提出的模型在分析暗物质光晕的重量含量时的应用。作为这项工作的一部分，我们公开发布了KLLR方法的Python实施。
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.
