Topological data analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. These methods include clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation and persistent homology. This paper reviews some...

We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to a forest; rather, we form kernel density estimates of...

type="main" xml:id="rssb12021-abs-0001" <title type="main">Summary</title> <p>We study distribution-free, non-parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band by combining the...</p>

Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data. In this paper we study a variant of this problem where the original n input variables are compressed by a...