One of the intuitions underlying many graph-based methods for clustering and semi-supervised learning, is that class or cluster boundaries pass through areas of low probability density. In this paper… (More)

Let K be a polytope in R<sup>n</sup> defined by m linear inequalities. We give a new Markov Chain algorithm to draw a nearly uniform sample from K. The underlying Markov Chain is the first to have a… (More)

We consider the problem of optimizing an approximately convex function over a bounded convex set in Rn using only function evaluations. The problem is reduced to sampling from an approximately… (More)

We propose a computationally efficient random walk on a convex body which rapidly mixes to a time-varying Gibbs distribution. In the setting of online convex optimization and repeated games, the… (More)

We present a Markov Chain, “Dikin walk”, for sampling from a convex body equipped with a self-concordant barrier. This Markov Chain corresponds to a natural random walk with respect to a Riemannian… (More)

We study the task of uniformly minimizing all the `p norms of the vector of edge loads in an undirected graph while obliviously routing a multicommodity flow. Let G be an undirected graph having m… (More)

The hypothesis that high dimensional data tends to lie in the vicinity of a low dimensional manifold is the basis of a collection of methodologies termed Manifold Learning. In this paper, we study… (More)

Kostka numbers and Littlewood-Richardson coefficients appear in combinatorics and representation theory. Interest in their computation stems from the fact that they are present in quantum mechanical… (More)

We point out that the positivity of a Littlewood–Richardson coefficient c γ α,β for sln can be decided in strongly polynomial time. This means that the number of arithmetic operations is polynomial… (More)

The underlying hypothesis of this field is that due to constraints that limit the degrees of freedom of the generative process, data tend to lie near a low dimensional submanifold. This has been… (More)