CS294-2 Markov Chain Monte Carlo: Project Suggestions
Below is a list of suggestions for project topics. Please read the
detailed guidelines here first.
Once you have made your selections, please email me your first choice
plus at least one, and preferably two, alternatives.
Projects marked XXX have already been selected by someone.
-
Detailed analysis of card shuffles. [Bayer & Diaconis,
Annals of Applied Probability, 1992; Diaconis, Fill & Pitman,
Combinatorics, Probability & Computing, 1992.]
-
More on strong stationary times. [Aldous & Diaconis,
Advances in Applied Math., 1987; Diaconis & Fill,
Annals of Probability, 1990.]
-
XXX More on stopping rules. [Lovasz & Winkler, London Math. Soc.
Lecture Note Series 218, 1995, and references therein.]
-
Group representations and mixing times. [Diaconis & Shashahani,
Zeitschrift fuer Wahrscheinlichkeitstheorie, 1981;
Diaconis, Group Representations in Probability & Statistics,
1988.
-
XXX Generating a Random Spanning Tree. [Aldous, SIAM Journal of Discrete
Math, 1990; Broder, IEEE FOCS, 1989; Wilson, ACM STOC, 1996.]
-
Fancier coupling arguments for independent sets and colorings.
[Vigoda, IEEE FOCS, 1999;
Cooper, Dyer & Frieze, IEEE FOCS, 2001.]
-
More on coupling for colorings.
[Dyer/Frieze, Random Structures & Algorithms, 2003; Hayes/Vigoda,
ACM-SIAM SODA, 2005.]
-
More on Coupling from the Past - Further Applications. [Haggstrom & Nelander,
Statistica Neerlandica, 1998; Huber, ACM STOC, 1998.
These and many other articles on the topic can be
pulled off David Wilson's annotated bibliography at
www.dimacs.rutgers.edu/~dbwilson/exact.]
-
XXX Yet more on Coupling from the Past - An interruptible algorithm. [Fill,
Annals of Applied Prob., 1998; Fill, Machida, Murdoch & Rosenthal,
Random Structures & Algorithms, 2000. Also available from the above
web page of Wilson.]
-
XXX Markovian couplings are ineffective for Markov chains on matchings.
[Kumar & Ramesh, IEEE FOCS, 1999.]
-
Flows for the Ising model. [Jerrum & Sinclair, SIAM Journal on
Computing, 1993.]
-
XXX Flows for truncated cubes and the knapsack problem. [Morris & Sinclair,
SIAM Journal on Computing, 2004.]
-
XXX The mixing time of the Thorp shuffle. [Morris, ACM STOC, 2004.]
-
XXX An alternative bound on mixing times: Evolving sets. [Morris & Peres,
ACM STOC, 2003.]
-
Another alternative bound on mixing times: the log-Sobolev inequality. [Diaconis
& Saloff-Coste, Annals of Applied Prob., 1996; Frieze & Kannan,
Annals of Applied Prob., 1999.]
-
Yet another alternative bound: Nash inequalities. [Diaconis
& Saloff-Coste, Journal of Theoretical Probability, 1996.]
-
State of the art on volume computation. [Lovasz & Vempala, IEEE FOCS,
2003.]
-
Sampling problems associated with matroids. [Feder & Mihail, ACM
STOC, 1992; Azar, Broder & Frieze, Information Processing
Letters, 1994; Jerrum & Son, IEEE FOCS, 2002.]
-
Negative results on simulated annealing for maximum matching. [Sasaki
& Hajek, Journal of the ACM, 1988.]
-
XXX Simulated tempering: a twist on simulated annealing. [Geyer
& Thompson, Journal of the American Statistical Association,
1995; Madras & Piccioni, Annals of Applied Probability, 1999.]
-
The Dobrushin uniqueness condition: a ``rapid mixing'' condition from
statistical physics. [Weitz, Random Structures & Algorithms, 2005;
Hayes, IEEE FOCS, 2006.]
- Slow mixing in Markov chains. [Gore & Jerrum, ACM STOC, 1997;
Borgs et al., IEEE FOCS, 1999.]
-
XXX The Ising model on trees. [Kenyon, Mossel and Peres, IEEE FOCS, 2001;
Martinelli, Sinclair and Weitz, IEEE FOCS, 2003.]
-
Computing the surface area of a convex body. [Belkin, Narayanan & Niyogi,
IEEE FOCS, 2006.]