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多元分类响应回归的条件概率张量分解AI 解读

In many modern regression applications, the response consists of multiple categorical random variables whose probability mass is a function of a common set of predictors. In this article, we propose a new method for modeling such a probability mass function in settings where the number of response variables, the number of categories per response, and the dimension of the predictor are large. Our method relies on a functional probability tensor decomposition: a decomposition…

高维多变量类别响应回归的似然方法AI 解读

We propose a penalized likelihood method to fit the bivariate categorical response regression model. Our method allows practitioners to estimate which predictors are irrelevant, which predictors only affect the marginal distributions of the bivariate response, and which predictors affect both the marginal distributions and log odds ratios. To compute our estimator, we propose an efficient first order algorithm which we extend to settings where some subjects have only one…

间接多元响应线性回归AI 解读

We propose a class of estimators of the multivariate response linear regression coefficient matrix that exploits the assumption that the response and predictors have a joint multivariate normal distribution. This allows us to indirectly estimate the regression coefficient matrix through shrinkage estimation of the parameters of the inverse regression, or the conditional distribution of the predictors given the responses. We establish a convergence rate bound for estimators…