Linearized binary regression
Linearized binary regression
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DOI：
10.1109/ciss.2018.8362200
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发表时间：
2018-02
期刊：
影响因子：
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通讯作者：
Andrew S. Lan;M. Chiang;Christoph Studer
中科院分区：
文献类型：
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作者：
Andrew S. Lan;M. Chiang;Christoph Studer
概率回归最早是由布利斯在1934年提出的，用于研究昆虫的死亡率。从那时起，大量的工作已经分析和使用probit或相关的二元回归方法（如逻辑回归）在许多应用和领域。本文提供了一个新的角度，这些行之有效的二元回归方法。具体地说，我们证明线性化probit模型与线性估计器相结合，与最先进的非线性回归方法（如后验均值或最大后验估计）相当，适用于广泛的现实世界回归问题。我们为我们的线性化估计的均方误差导出了精确的、封闭的和非渐近的表达式，这明显地将它们与通常难以分析的非线性回归方法区分开来。我们展示了我们的方法和结果对许多合成和现实世界数据集的有效性，这表明线性化二元回归在处理二值观测或测量的各种推理、估计、信号处理和机器学习应用中具有潜在的用途。
Probit regression was first proposed by Bliss in 1934 to study mortality rates of insects. Since then, an extensive body of work has analyzed and used probit or related binary regression methods (such as logistic regression) in numerous applications and fields. This paper provides a fresh angle to such well-established binary regression methods. Concretely, we demonstrate that linearizing the probit model in combination with linear estimators performs on par with state-of-the-art nonlinear regression methods, such as posterior mean or maximum aposteriori estimation, for a broad range of real-world regression problems. We derive exact, closed-form, and nonasymptotic expressions for the mean-squared error of our linearized estimators, which clearly separates them from nonlinear regression methods that are typically difficult to analyze. We showcase the efficacy of our methods and results for a number of synthetic and real-world datasets, which demonstrates that linearized binary regression finds potential use in a variety of inference, estimation, signal processing, and machine learning applications that deal with binary-valued observations or measurements.