587 research outputs found
Nested Sequential Monte Carlo Methods
We propose nested sequential Monte Carlo (NSMC), a methodology to sample from
sequences of probability distributions, even where the random variables are
high-dimensional. NSMC generalises the SMC framework by requiring only
approximate, properly weighted, samples from the SMC proposal distribution,
while still resulting in a correct SMC algorithm. Furthermore, NSMC can in
itself be used to produce such properly weighted samples. Consequently, one
NSMC sampler can be used to construct an efficient high-dimensional proposal
distribution for another NSMC sampler, and this nesting of the algorithm can be
done to an arbitrary degree. This allows us to consider complex and
high-dimensional models using SMC. We show results that motivate the efficacy
of our approach on several filtering problems with dimensions in the order of
100 to 1 000.Comment: Extended version of paper published in Proceedings of the 32nd
International Conference on Machine Learning (ICML), Lille, France, 201
Capacity estimation of two-dimensional channels using Sequential Monte Carlo
We derive a new Sequential-Monte-Carlo-based algorithm to estimate the
capacity of two-dimensional channel models. The focus is on computing the
noiseless capacity of the 2-D one-infinity run-length limited constrained
channel, but the underlying idea is generally applicable. The proposed
algorithm is profiled against a state-of-the-art method, yielding more than an
order of magnitude improvement in estimation accuracy for a given computation
time
Sequential Monte Carlo for Graphical Models
We propose a new framework for how to use sequential Monte Carlo (SMC)
algorithms for inference in probabilistic graphical models (PGM). Via a
sequential decomposition of the PGM we find a sequence of auxiliary
distributions defined on a monotonically increasing sequence of probability
spaces. By targeting these auxiliary distributions using SMC we are able to
approximate the full joint distribution defined by the PGM. One of the key
merits of the SMC sampler is that it provides an unbiased estimate of the
partition function of the model. We also show how it can be used within a
particle Markov chain Monte Carlo framework in order to construct
high-dimensional block-sampling algorithms for general PGMs
Sequential Monte Carlo Methods for System Identification
One of the key challenges in identifying nonlinear and possibly non-Gaussian
state space models (SSMs) is the intractability of estimating the system state.
Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced
more than two decades ago), provide numerical solutions to the nonlinear state
estimation problems arising in SSMs. When combined with additional
identification techniques, these algorithms provide solid solutions to the
nonlinear system identification problem. We describe two general strategies for
creating such combinations and discuss why SMC is a natural tool for
implementing these strategies.Comment: In proceedings of the 17th IFAC Symposium on System Identification
(SYSID). Added cover pag
Fast and Scalable Score-Based Kernel Calibration Tests
We introduce the Kernel Calibration Conditional Stein Discrepancy test (KCCSD test), a nonparametric, kernel-based test for assessing the calibration of probabilistic models with well-defined scores. In contrast to previous methods, our test avoids the need for possibly expensive expectation approximations while providing control over its type-I error. We achieve these improvements by using a new family of kernels for score-based probabilities that can be estimated without probability density samples, and by using a conditional goodness-of-fit criterion for the KCCSD test's U-statistic. We demonstrate the properties of our test on various synthetic settings
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