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  1. ; (, ACM Symposium on Computational Geometry)
    Buchin, Kevin; Colin de Verdi\` (Ed.)
    The Gibbs Sampler is a general method for sampling high-dimensional distributions, dating back to 1971. In each step of the Gibbs Sampler, we pick a random coordinate and re-sample that coordinate from the distribution induced by fixing all the other coordinates. While it has become widely used over the past half-century, guarantees of efficient convergence have been elusive. We show that for a convex body K in ℝⁿ with diameter D, the mixing time of the Coordinate Hit-and-Run (CHAR) algorithm on K is polynomial in n and D. We also give a lower bound on the mixing rate of CHAR, showing that it is strictly worse than hit-and-run and the ball walk in the worst case. 
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  2. ; ; (, ACM Symposium on the Theory of Computing)
    Full Text Available 
  3. ; (, APPROX-RANDOM)
    Full Text Available 
  4. ; (, NeurIPS)
    Accepted Manuscript Full Text Available