Title: Covariance and precision matrix estimation, and dimension reduction in regression problems
Abstract: Many problems in data analysis can be formulated as learning the structure or a function of the data in a high-dimensional ambient space. To mitigate the effects of high-dimensionality, a number of recent advances are based on the observation that real-world data has an underlying low-dimensional structure. In this talk we present finite sample concentration inequalities, for the estimation of covariance and precision matrices for high-dimensional random vectors, which exploit the low-dimensional complexity of data. We discuss the learning of high dimensional functions where the relationship between the features and the responses is of a lower dimensional nature. Our focus is on the monotonic single-index model, and a novel nonlinear generalization thereof.
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