The principal investigator will work in three areas of probability theory and statistics. The first is the area of probability inequalities and their statistical applications, including models of positive and negative dependence, correlation inequalities, prophet inequalities for dependent variables and certain combinatorial inequalities. The second area is that of limit theorems for graph-related, dependent random variables, with motivation from neural network models and statistics. The last area involves statistical problems in neural networks, e.g., the problem of choice of network size (dimension) allowing for both efficient learning and generalization, which appears to be related to the problem of model selection and overfitting for statistical data.
