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Title: Higher order parametric inverse regression Authors:  Daniel Kapla - TU Wien (Austria) [presenting]
Abstract: A method is proposed for sufficient dimension reduction of tensor-valued predictors (multi-dimensional arrays) for regression or classification. We assume the predictors conditional on the response follow a quadratic exponential family in a generalized linear model, where the relation via a link is multi-linear. Using a multi-linear relation allows us to perform per-axis reductions that drastically reduce the total number of parameters in regressions with higher-order tensor-valued predictors. We derive maximum likelihood estimates for the multi-linear sufficient dimension reduction of the tensor-valued predictors. Furthermore, we provide an estimation algorithm which utilizes the tensor structure allowing efficient implementations. The performance of the method is illustrated via simulations and real-world examples.