We propose a framework for constructing goodness-of-fit tests in both low and high dimensional linear models. We advocate applying regression methods to the scaled residuals following either an ordinary least squares or ...

We study the problem of high-dimensional regression when there may be interacting variables. Approaches using sparsity-inducing penalty functions such as the Lasso (Tibshirani, 1996) can be useful for producing interpretable ...

Finding interactions between variables in large and high-dimensional datasets is often a serious computational challenge. Most approaches build up interaction sets incrementally, adding variables in a greedy fashion. The ...