Optimal subsampling for softmax regression
Optimal subsampling for softmax regression
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DOI：
10.1007/s00362-018-01068-6
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发表时间：
2018-12
影响因子：
1.3
通讯作者：
Yaqiong Yao;Haiying Wang
中科院分区：
文献类型：
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作者：
Yaqiong Yao;Haiying Wang
为了应对海量数据的挑战，Wang等人（J Am Stat Asynchronous 113（522）：829-844，2018 b）开发了一种用于逻辑回归的最佳子采样方法。本文的目的是将他们的方法扩展到softmax回归，这也被称为多项逻辑回归，通常用于对具有多个分类响应的数据进行建模。我们首先推导出一般下采样估计量的渐近分布，然后在A-最优性准则和L-最优性准则下，在特定的L矩阵下，推导出最优下采样概率。由于最佳子采样概率取决于未知数，我们采用了两阶段的自适应过程来解决这个问题，并使用数值模拟来证明其性能。
To meet the challenge of massive data, Wang et al. (J Am Stat Assoc 113(522):829–844, 2018b) developed an optimal subsampling method for logistic regression. The purpose of this paper is to extend their method to softmax regression, which is also called multinomial logistic regression and is commonly used to model data with multiple categorical responses. We first derive the asymptotic distribution of the general subsampling estimator, and then derive optimal subsampling probabilities under the A-optimality criterion and the L-optimality criterion with a specific L matrix. Since the optimal subsampling probabilities depend on the unknowns, we adopt a two-stage adaptive procedure to address this issue and use numerical simulations to demonstrate its performance.