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Hi everyone, I was wondering if anyone was familiar with methods for "learning" good proposal distributions for use with Particle Filters. This may be in the form of learning parameters for a proposal a ala Adaptive MCMC or perhaps something nonparametric such as laying down evenly spaced anchor points and using Gaussian Kernels. I would like if possible not to be specific to low dimensional or strictly continuous distributions, but if that's all the theory provides that's fine too. The overall feeling I get is that proposal engineering is a rather painful art, and I wanted to know what theory exists in doing away with it. For my particular problem, assume I can evaluate pointwise and sample from the transition dynamics P(x' | x) and observation model P(y | x'), and my overarching goal is to sample Pr(x' | x, y). A typical particle filter would use P(x'|x) as the proposal distribution and reweight by Pr(y | x'), but if P(y | x') is nearly deterministic, most particles will get rejected. Thanks! |
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Sampling from P(x' | x, y) is optimal. If you can't sample from that, then the next best choice would probably be some linear combination of P(x' | x) and P(x' | y). If you can't sample from P(x' | y), then any approximation to it is better than nothing; basically, if P(y | x') is nearly deterministic, you need to base your proposal on y somehow. I wonder if you could formulate this as an MDP, where the reward signal is the effective sample size (ESS) of the particle filter after each step, and then learn good proposals that way. Thanks Kevin! I'll think about it, maybe you're on to something. I could always fall back on hand-picking a q(x' | x, y), but I think it would be great if it could be done automatically.
(Dec 05 '11 at 22:38)
Daniel Duckwoth
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