Many applications in machine learning require optimizing unknown functions defined over a
high-dimensional space from noisy samples that are expensive to obtain. We address this …

This paper addresses the problem of describing surfaces using local features and
descriptors. While methods for the detection of interest points in images and their description …

High-dimensional data analysis has been an active area, and the main focus areas have
been variable selection and dimension reduction. In practice, it occurs often that the …

Let PP be a set of nn random points in R^ d R d, generated from a probability measure on
am m-dimensional manifold M ⊂ R^ d M⊂ R d. In this paper we study the homology of U (P …

We introduce an algorithm that simultaneously estimates a classification function as well as
its gradient in the supervised learning framework. The motivation for the algorithm is to find …

The gradient learning model has been raising great attention in view of its promising
perspectives for applications in statistics, data dimensionality reducing, and other specific …

We developed localized sliced inverse regression for supervised dimension reduction. It has
the advantages of preventing degeneracy, increasing estimation accuracy, and automatic …

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The problems of dimension reduction and inference of statistical dependence are addressed
by the modeling framework of learning gradients. The models we propose hold for …

Learning function relations or understanding structures of data lying in manifolds embedded
in huge dimensional Euclidean spaces is an important topic in learning theory. In this paper …