标题： 选择性推断与学习混合图模型 显示英文标题

标题： Selective Inference and Learning Mixed Graphical Models

摘要： 本文研究了现代统计学中的两个问题。 首先，我们研究选择性推断，即针对通过对数据进行观察后选择的假设进行推断的问题。 动机应用是通过套索（lasso）选择回归系数的推断。 我们提出了条件选择方法，该方法允许有效的选择性推断，并研究了其在套索以及几种其他选择算法中的应用。 在第二部分，我们考虑了连续和离散变量的配对图模型结构学习问题。 我们提出了一种新的配对模型，适用于具有连续和离散变量的图形模型的结构学习。 在之前的研究中，作者们考虑了高斯图模型结构的学习和离散模型结构的学习。 我们的方法自然地将这两种工作推广到了混合情况。 正则化方案涉及一种新型的对称组套索范数的使用，并且自然地来源于模型的特定参数化。 我们提供了在高维情况下我们的估计器是模型选择一致的条件。 显示英文摘要

摘要： This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by the lasso. We present the Condition-on-Selection method that allows for valid selective inference, and study its application to the lasso, and several other selection algorithms. In the second part, we consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to structure learning. In previous work, authors have considered structure learning of Gaussian graphical models and structure learning of discrete models. Our approach is a natural generalization of these two lines of work to the mixed case. The penalization scheme involves a novel symmetric use of the group-lasso norm and follows naturally from a particular parametrization of the model. We provide conditions under which our estimator is model selection consistent in the high-dimensional regime.