Séance Séminaire

Colloquium de Mathématiques

Error control for variable selection in high-dimensional models

Variable selection is a fundamental problem encountered in diverse fields where practitioners have to assess the importance of input variables with regards to an outcome of interest. Statistically controlled variable selection has been shown to limit the proportion of selected variables that are independent of the outcome. Yet this problem is much harder than usual variable selection since guarantees on False Positives have to be provided. In this talks we address two core questions:   First we question the selection criterion used for selection: while the False Discovery Rate is popular, we illustrate its limitations and propose an approach to control instead the False discovery Proportion with high probability   Second, we show how to perform such statistically valid selection for complex non-linear models, such as those obtained from deep learning techniques. We illustrate these contributions with applications to brain mapping.