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Abstract:
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This talk first gives a brief overview on how nonparametric methods have evolved with growing dimensionality and sample sizes. It will also outline how these methods of trading modeling biases and variances have been developed into high-dimensional statistics and machine learning, including high-dimensional regression using kernel tricks and deep learning models. Now, nonparametric methods have been widely fused into contemporary statistics and machine learning. We will illustrate the applications of nonparametric techniques in high-dimensional robust covariance estimation, high-dimensional conditional dependence graph construction, and projected principal component analysis. The first technique will be applied to Factor Adjusted Robust Multiple testing (FARM-test) and Model selection (FARM-select) while the latter two will be used to do high-dimensional regression, using nonparametric smoothing as a starting point. The effectiveness of these methods will be revealed with both biological and financial data.
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