大数据下多项式Logistic模型的最优子抽样

IF 1.5 3区数学 Q2 STATISTICS & PROBABILITY

Statistica Sinica Pub Date : 2023-01-01 DOI:10.5705/ss.202022.0277

Zhiqiang Ye, Jun Yu, Mingyao Ai

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引用次数: 0

摘要

本节给出π (β)及其导数的显式形式，π (β)及其导数是搜索极大似然估计量和理论证明的重要组成部分。可以直接计算出模型(2.1)-(2.4)的分类概率πij(β)，通过∂πij(β)∂β = πij(β)∂log πij(β)∂β， (S1.1)得到πij(β)对β的一阶导数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Optimal Subsampling for Multinomial Logistic Models With Big Data

This section is dedicated to presenting the explicit forms of πij(β)’s and their derivatives, which are important parts in searching the maximum likelihood estimator and in the theoretical proofs. The categorical probability πij(β) for Models (2.1)-(2.4) can be calculated directly, and the first derivative of πij(β) with respect to β can be gotten through ∂πij(β) ∂β = πij(β) ∂ log πij(β) ∂β , (S1.1)

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来源期刊

Statistica Sinica 数学-统计学与概率论

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

10.5 months

期刊介绍： Statistica Sinica aims to meet the needs of statisticians in a rapidly changing world. It provides a forum for the publication of innovative work of high quality in all areas of statistics, including theory, methodology and applications. The journal encourages the development and principled use of statistical methodology that is relevant for society, science and technology.