TPA: A New Method for Approximate Counting

• Main Author: Schott, Sarah
• Other Authors: Huber, Mark
• Published: 2012
• Subjects: Mathematics
• Online Access: http://hdl.handle.net/10161/5429

<p>Many high dimensional integrals can be reduced to the problem of finding the relative measure of two sets. Often one set will be exponentially larger than the other. A standard method of dealing with this problem is to interpolate between the sets with a series of nested sets where neighboring nested sets have relative measures bounded above by a constant. Choosing these sets can be very difficult in practice. Here a new approach that creates a randomly drawn sequence of such sets is presented. This procedure gives faster approximation algorithms and a well-balanced set of nested sets that are essential to building effective tempering and annealing algorithms.</p> === Dissertation