This talk first gives an overview on how mathematical and computational methods have evolved with growing  dimensionality and sample sizes and become the foundation of modern machine learning and AI. It will also outline how ideas of trading modeling biases and variances have been developed into high-dimensional statistics and machine learning, with focus on deep learning models.  We will outline the challenges of mathematical sciences at this crossroad and offer some prospects. We will offer a general robustification principle and show how to use factor adjustments to deal with dependent measurements.  In particular, Factor Adjusted Robust Multiple testing (FarmTest) and Model selection (FarmSelect) will be introduced for high-dimensional statistical inference and model selection. The effectiveness of these methods will be revealed with an application to predicting bond risk premia using macroeconomic time series.  Further insights on the prospects of machine learning and AI will be offered.

海报