Optimal subsampling for softmax regression
WebThis method was named as optimal subsampling methods motivated 4 fromtheA-optimalitycriterion(OSMAC),andwasimprovedinWang(2024b)byadopt-5 ing unweighted target functions for subsamples and Poisson subsampling. In addition 6 to logistic regression, OSMAC was investigated to include softmax regression (Yao and Websubsampling least squares regression. On the other hand, several scholars have developed optimal subsampling methods for parametric regression problems. For example, Wang et al. (2024a) proposed an inverse weighted subsampling method for logistic regression based on the A- or L-optimality criterion. Subsequently, a more efficient estimation
Optimal subsampling for softmax regression
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WebThe increasing volumes of data bring new challenges for parameter estimation in softmax regression, and the optimal subsampling method is an effective way to solve them. … WebJan 28, 2024 · The optimal subsampling methods have been investigated to include logistic regression models, softmax regression models, generalized linear models, quantile …
WebFeb 1, 2024 · Furthermore, the optimal subsampling probabilities are derived according to the A-optimality criterion. It is shown that the estimator based on the optimal subsampling asymptotically achieves a smaller variance than that by the uniform random subsampling. WebDec 1, 2024 · Wang H Ma Y Optimal subsampling for quantile regression in big data Biometrika 2024 108 1 99 112 4226192 10.1093/biomet/asaa043 1462.62248 Google Scholar; Wang H Zhu R Ma P Optimal subsampling for large sample logistic regression J. Am. Stat. Assoc. 2024 113 522 829 844 3832230 10.1080/01621459.2024.1292914 …
For the softmax regression model with massive data, we have established the asymptotic normality of the general subsampling estimator, and then derived optimal subsampling probabilities under the A-optimality criterion and the L-optimality with a specific L. See more As N\rightarrow \infty , {\mathbf {M}}_N=N^{-1}\sum _{i=1}^{N}{\varvec{\phi }}_i({\hat{\varvec{\beta }}}_{{\mathrm {full}}})\otimes ({\mathbf {x}}_i{\mathbf {x}}_i^\mathrm{T}) goes to a positive-definite matrix in … See more In this theorem, both n and N go to infinity, but there are no restrictions on their relative orders. Even if n is larger than N, the theorem is still … See more For k=2, 4, N^{-2}\sum _{i=1}^{N}\pi _i^{-1}\Vert {\mathbf {x}}_i\Vert ^k=O_P(1); and there exists some \delta >0 such that N^{-(2+\delta )}\sum … See more Under Assumptions 1 and 2, given the full data {\mathcal {D}}_N in probability, as n\rightarrow \infty and N\rightarrow \infty , the approximation error {\hat{\varvec{\beta … See more Weboped 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 …
WebThis paper fills the gap by studying the subsampling method for a widely used missing data estimator, the augmented inverse probability weighting (AIPW) estimator. The response mean estimation problem with missing responses is discussed for illustration. A two-stage subsampling method is proposed via Poisson sampling framework.
WebJul 21, 2024 · We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions … green bay packers waiting list season ticketsWebMar 25, 2024 · We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling … Expand. 59. PDF. Save. Alert. Optimal Sampling for Generalized Linear Models Under Measurement Constraints. Tao Zhang, Y. Ning, D. Ruppert; flower shops in oak hill ohioWebThis idea was generalized in [11] to softmax regression. An optimal subsampling method under the A-optimality criterion (OSMAC) for logistic re-gression inspired by the idea of … green bay packers vs seattle seahawksWeb844, 2024b) 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 … green bay packers vs washingtonWebApr 25, 2024 · Softmax Regression Model; Image by Author. First, we have flattened our 28x28 image into a vector of length 784, represented by x in the above image. Second, we calculate the linear part for each class → zc = wc.X + bc where, zc is the linear part of the c’th class and wc is the set of weights of the c’th class. bc is the bias for the c ... green bay packers vs washington redskinsWebApr 21, 2009 · The model is an extension of the clustered ordinal regression approach of Hedeker and Gibbons that includes the continuous outcome. To handle subsampling, we then derive a partial likelihood (PL) that is based on the bivariate model, and we give an expression for the PL score in Section 3. We show that consistent estimates can be … green bay packers vs seahawksWebApr 1, 2024 · Abstract: The information-based optimal subdata selection (IBOSS) is a computationally efficient method to select informative data points from large data sets … green bay packers vs titans game stream live