Mathematical Sciences: Dependence and Inequalities, Combinatorial Limit Theorem, and Statistical Issues in Neural Networks

首席研究员将在三个领域工作， 概率论和统计学。 第一个是面积 概率不等式及其统计应用， 包括正相关和负相关的模型， 相关不等式，预言不等式 变量和某些组合不等式。 第二 面积是极限定理的图相关，依赖 随机变量，动机来自神经网络模型， 统计 最后一个领域涉及统计问题， 神经网络，例如，网络规模选择问题 （维度）允许有效的学习和 一般化，这似乎是有关的问题， 统计数据的模型选择和过拟合。

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.