  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.
