Posts Tagged invited talk
I am speaking in the statistics seminar at The Ohio State University next week. The title of my talk is “Fast approximation algorithms for partition functions of Gibbs distributions”. It will be held in the Eighteenth Avenue Building, Room 170 on Thursday, May 24th from 3:30 to 4:30 pm. More details can be found here.
Abstract: Finding the partition function of Gibbs distributions has applications in model selection and building estimators for parameters of spatial models. This talk will present a new algorithm for estimating these partition functions. The method combines a well balanced cooling schedule created through a technique called TPA and a product importance sampler. One advantage of the algorithm over existing methods is the standard deviation of the estimate can be bounded theoretically. That is to say, unlike most algorithms where the standard deviation must itself be estimated, the standard deviation of this algorithm is fixed ahead of time by the use. The number of samples necessary to build a close estimate grows almost linearly in the logarithm of the partition function, making the approach suitable for high dimensional problems. The samples needed for the estimate can be generated rapidly by methods such as parallel tempering.
This Tuesday I’m starting off the talks for the Spring in the Algebra/Number Theory/Combinatorics Seminar here in Claremont. It will be at 12:15 on 24 Jan 2012 in Millikan 134. Complete details can be found here. The title is “A gadget for reducing the Ising model to matchings”, and it is joint work that I did with my first graduate student, Jenny Law.
Abstract: In my talk last semester in the seminar, I presented a classic result: the problem of counting the number of solutions to a logic formula can be turned into a problem of summing weighted perfect matchings in a graph. The key idea was the use of a combinatorial “gadget”. In this talk I’ll present a gadget developed with my first graduate student, Jenny Law, that allows for what is called a simulation reduction. The reduction works as follows: if you are able to sample randomly from a weighted distribution on perfect matchings in a graph, then you can also simulate from the Ising model, a classical model from statistical physics that has been heavily studied since its inception in the 1920’s. (http://arxiv.org/abs/0907.0477)
Today I am giving the Algebra/Number Theory/Combinatorics Seminar at the Claremont Colleges. This talk, “What is a #P complete problem” is a prequel in a sense to an earlier talk I gave in the Seminar last year. In the earlier talk, I discussed new methods for approximating the permanent of a matrix. In this talk, I will argue that finding the permanent is a hard problem. One way to characterize hardness of a numerical problem is the notion of number P problems, or #P for short. I will define #P problems and give Ben-Dor and Halevi’s 1993 proof that finding the permanent of a matrix is a #P hard problem, so if we could solve it quickly, any problem in #P could also be solved quickly.