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张量预测变量充分降维的广义多线性模型AI 解读

We consider supervised learning problems with tensor-valued input. We derive multilinear sufficient reductions for the regression or classification problem by modeling the conditional distribution of the predictors given the response as a member of the quadratic exponential family. We develop estimation procedures of sufficient reductions for both continuous and binary tensor-valued predictors. We prove the consistency and asymptotic normality of the estimated sufficient…

指数族逆向预测变量回归中的充分降维AI 解读

We develop methodology for identifying and estimating sufficient reductions in regressions with predictors that, given the response, follow a multivariate exponential family distribution. This setup includes regressions where predictors are all continuous, all categorical, or mixtures of categorical and continuous. We derive the minimal sufficient reduction of the predictors and its maximum likelihood estimator by modeling the conditional distribution of the predictors given…

椭圆轮廓逆向预测变量下的回归充分降维AI 解读

There are two general approaches based on inverse regression for estimating the linear sufficient reductions for the regression of Y on X: the moment-based approach such as SIR, PIR, SAVE, and DR, and the likelihood-based approach such as principal fitted components (PFC) and likelihood acquired directions (LAD) when the inverse predictors, X|Y, are normal. By construction, these methods extract information from the first two conditional moments of X|Y; they can only…

切片逆回归的扩展AI 解读

Sliced inverse regression (SIR) and an associated chi-squared test for dimension have been introduced as a method for reducing the dimension of regression problems whose predictor variables are normal. In this article the assumptions on the predictor distribution, under which the chi-squared test was proved to apply, are relaxed, and the result is extended. A general weighted chi-squared test that does not require normal regressors for the dimension of a regression is given.…

通过参数逆回归估计回归的结构维数AI 解读

Summary A new estimation method for the dimension of a regression at the outset of an analysis is proposed. A linear subspace spanned by projections of the regressor vector X, which contains part or all of the modelling information for the regression of a vector Y on X, and its dimension are estimated via the means of parametric inverse regression. Smooth parametric curves are fitted to the p inverse regressions via a multivariate linear model. No restrictions are placed on…