Archive for anytime algorithm

anytime algorithm

Posted in Books, Statistics with tags , , , , , , , , , on January 11, 2017 by xi'an

Lawrence Murray, Sumeet Singh, Pierre Jacob, and Anthony Lee (Warwick) recently arXived a paper on Anytime Monte Carlo. (The earlier post on this topic is no coincidence, as Lawrence had told me about this problem when he visited Paris last Spring. Including a forced extension when his passport got stolen.) The difficulty with anytime algorithms for MCMC is the lack of exchangeability of the MCMC sequence (except for formal settings where regeneration can be used).

When accounting for duration of computation between steps of an MCMC generation, the Markov chain turns into a Markov jump process, whose stationary distribution α is biased by the average delivery time. Unless it is constant. The authors manage this difficulty by interlocking the original chain with a secondary chain so that even- and odd-index chains are independent. The secondary chain is then discarded. This provides a way to run an anytime MCMC. The principle can be extended to K+1 chains, run one after the other, since only one of those chains need be discarded. It also applies to SMC and SMC². The appeal of anytime simulation in this particle setting is that resampling is no longer a bottleneck. Hence easily distributed among processors. One aspect I do not fully understand is how the computing budget is handled, since allocating the same real time to each iteration of SMC seems to envision each target in the sequence as requiring the same amount of time. (An interesting side remark made in this paper is the lack of exchangeability resulting from elaborate resampling mechanisms, lack I had not thought of before.)

anytime!

Posted in Books, Mountains, pictures, Statistics, Travel with tags , , , , , on December 22, 2016 by xi'an

“An anytime algorithm is an algorithm that can be run continuously, generating progressively better solutions when afforded additional computation time. Traditional particle-based inference algorithms are not anytime in nature; all particles need to be propagated in lock-step to completion in order to compute expectations.”

Following a discussion with Lawrence Murray last week, I read Paige et al.  NIPS 2014 paper on their anytime sequential Monte Carlo algorithm. As explained above, an anytime algorithm is interruptible, meaning it can be stopped at any time without biasing the outcome of the algorithm. While MCMC algorithms can qualify as anytime (provided they are in stationary regime), it is not the case with sequential and particle Monte Carlo algorithms, which do not have an inbred growing mechanism preserving the target. In the case of Paige et al.’s proposal, the interruptible solution returns an unbiased estimator of the marginal likelihood at time n for any number of particles, even when this number is set or increased during the computation. The idea behind the solution is to create a particle cascade by going one particle at a time and creating children of this particle in proportion to the current average weight. An approach that can be run indefinitely. And since memory is not infinite, the authors explain how to cap the number of alive particles without putting the running distribution in jeopardy…