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

首席研究员将在概率论和统计学的三个领域开展工作。第一个是概率不等式及其统计应用领域，包括正、负相关性模型、相关不等式、因变量的预言不等式和某些组合不等式。第二个领域是与图相关的相依随机变量的极限定理，其动机来自神经网络模型和统计学。最后一个领域涉及神经网络中的统计问题，例如，考虑到有效学习和推广的网络规模(维度)的选择问题，这似乎与模型选择和对统计数据的过度拟合问题有关。

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.