Sufficient dimension reduction is a rapidly developing research field that has wide
applications in regression diagnostics, data visualization, machine learning, genomics …

We study sparse principal components analysis in high dimensions, where p (the number of
variables) can be much larger than n (the number of observations), and analyze the problem …

We review probabilistic principal components, principal fitted components, sufficient
dimension reduction, and envelopes, arguing that at their core they are all based on …

We propose a new parsimonious version of the classical multivariate normal linear model,
yielding a maximum likelihood estimator (MLE) that is asymptotically less variable than the …

Modern technology often generates data with complex structures in which both response
and explanatory variables are matrix valued. Existing methods in the literature can tackle …

We propose a new and simple framework for dimension reduction in the large p, small n
setting. The framework decomposes the data into pieces, thereby enabling existing …

Let (X, Y) be a random pair taking values in Rp× R. In the so-called single-index model, one
has Y= f⋆(θ⋆ TX)+ W, where f⋆ is an unknown univariate measurable function, θ⋆ is an …

Sufficient dimension reduction (SDR) methods target finding lower-dimensional
representations of a multivariate predictor to preserve all the information about the …

The envelope model was first introduced as a parsimonious version of multivariate linear
regression. It uses dimension reduction techniques to remove immaterial variation in the …

The sparse generalized eigenvalue problem (GEP) plays a pivotal role in a large family of
high dimensional statistical models, including sparse Fisher's discriminant analysis …