The Annals of Applied Probability

Log-Sobolev inequalities and sampling from log-concave distributions

Alan Frieze and Ravi Kannan

Full-text: Open access

Abstract

We consider the problem of sampling according to a distribution with log-concave density F over a convex body $K \subseteq \mathbf{R}^n$. The sampling is done using a biased random walk and we give improved polynomial upper bounds on the time to get a sample point with distribution close to F.

Article information

Source
Ann. Appl. Probab., Volume 9, Number 1 (1999), 14-26.

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1029962595

Digital Object Identifier
doi:10.1214/aoap/1029962595

Mathematical Reviews number (MathSciNet)
MR1682608

Zentralblatt MATH identifier
0931.68140

Subjects
Primary: 68Q20 60J15

Keywords
Log-Sobolev inequalities Markov chains random walks log-concave

Citation

Frieze, Alan; Kannan, Ravi. Log-Sobolev inequalities and sampling from log-concave distributions. Ann. Appl. Probab. 9 (1999), no. 1, 14--26. doi:10.1214/aoap/1029962595. https://projecteuclid.org/euclid.aoap/1029962595


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References

  • 1 APPLEGATE, D. and KANNAN, R. 1991. Sampling and integration of log-concave functions. In Proceedings of the 23rd Annual ACM Sy mposium on Theory of Computing 156 163.
  • ACM, New York.
  • 2 DIACONIS, P. and SALOFF-COSTE, L. 1998. Logarithmic Sobolev inequalities for finite Markov chains. Unpublished manuscript.
  • 3 FRIEZE, A. M., KANNAN, R. and POLSON, N. 1994. Sampling from log-concave distributions. Ann. Appl. Probab. 4 812 837.
  • 4 KANNAN, R., LOVASZ, L. and SIMONOVITS, M. 1998. Random walks and an O* n volume ´ algorithm for convex bodies. Random Structures Algorithms. To appear.
  • 5 LOVASZ, L. and SIMONOVITS, M. 1990. Mixing rate of Markov chains, an isoperimetric ´ inequality and computing the volume. In Proceeding of the 31st Annual IEEE Sy mposium on Foundations of Computer Science 346 355. IEEE, New York.
  • 6 LOVASZ, L. and SIMONOVITS, M. 1993. Random walks in a convex body and an improved ´ volume algorithm. Random Structures Algorithms 4 359 412.
  • 7 METROPOLIS, N., ROSENBERG, ROSENBLUTH, TELLER and TELLER 1953. Equation of state calculation by fast computing machines. J. Chemical physics 21 1087 1092.
  • 8 SINCLAIR, A. J. and JERRUM, M. R. 1989. Approximate counting, uniform generation and rapidly mixing Markov chains. Inform. and Comput. 82 93 133.
  • PITTSBURGH, PENNSy LVANIA 15213 PITTSBURGH, PENNSy LVANIA 15213