Posts Tagged talk
I’m speaking about some of the work that I have done on randomly generating, and counting the number of, linear extensions of a poset.
Abstract: Suppose I try to shuffle a deck of n cards by randomly transposing adjacent cards. It turns out you need to do this O(n^3 ln(n)) times to really mix up the deck. Now suppose I add some extra rules that look like: “The King of Hearts must be above the Queen of Spades” or “The Queen of Spades must be above the 9 of Diamonds” and so on. I will shuffle the same way, but if an adjacent transposition would cause me to violate one of my rules, I do not execute the transposition. The surprising fact is that it still takes O(n^3 ln(n)) steps to mix up the deck! Now these shuffles with rules is more formally known as linear extensions of a partial order. In this talk I will show where the O(n^3 ln(n)) is coming from, and show how to exactly draw uniformly from the set of linear extensions. I will also discuss recent work on this problem and why embedding this problem in a continuous context can lead to better algorithms for counting linear extensions.
See here for more details.
It is summer in an even year, which means it is time for the Eleventh World Meeting of ISBA, this time held in Kyoto, Japan. For the first time I am organizing a session here, and we have some great speakers lined up: Galin Jones, James Flegal, Alex Beskos, and yours truly. My talk is: Fast approximation algorithms for partition functions of Gibbs distributions, and has an abstract very close to my longer talk at Ohio State last month.
Abstract: A new algorithm for estimating the partition function of a Gibbs distribution is presented. The method combines a well balanced cooling schedule created through 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. 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.
The talk that I gave at UMSL can now be downloaded here. This talk describes two different protocols for perfect simulation. The first, Partially Recursive Acceptance Rejection, gives an easy way to generate perfect samples from loosely coupled Markov random fields (such as the Ising model) in linear time without building a Markov chain at all for the problem.
The second part discusses Sequential Acceptance Rejection, a method that has proved useful for problems like approximating the permanent in dense problem instances.
I will be giving the Statistics Seminar at UCLA on October 18th. The talk is titled: “Perfect simulation of repulsive point processes”.
Abstract Entities in competition for resources, such as towns in a country or trees in a forest, often are further apart from each other than would be predicted if their spatial distribution was independently uniform. Repulsive point processes are used to model such data, but rarely are these distributions given in closed form. Instead, they can be given as either an algorithmic model, or as a unnormalized density with respect to a spatial Poisson point process. In this talk I will show how to generate random samples exactly from an algorithmic setup called the Matérn Type III model, and from an unnormalized density called the Strauss model. Also, I will discuss effective ways to turn these samples into estimates using these models.
The talk that I gave at Greek Stochastics γ has now been posted to the list of talks on my website here. The talk, entitled “The Paired Product Estimator for normalizing constants of Gibbs distribution” details a method for approximation of partition functions that is markedly faster than previously known methods.