21,605 research outputs found
Neural adaptive sequential Monte Carlo
Sequential Monte Carlo (SMC), or particle filtering, is a popular class of
methods for sampling from an intractable target distribution using a sequence
of simpler intermediate distributions. Like other importance sampling-based
methods, performance is critically dependent on the proposal distribution: a
bad proposal can lead to arbitrarily inaccurate estimates of the target
distribution. This paper presents a new method for automatically adapting the
proposal using an approximation of the Kullback-Leibler divergence between the
true posterior and the proposal distribution. The method is very flexible,
applicable to any parameterized proposal distribution and it supports online
and batch variants. We use the new framework to adapt powerful proposal
distributions with rich parameterizations based upon neural networks leading to
Neural Adaptive Sequential Monte Carlo (NASMC). Experiments indicate that NASMC
significantly improves inference in a non-linear state space model
outperforming adaptive proposal methods including the Extended Kalman and
Unscented Particle Filters. Experiments also indicate that improved inference
translates into improved parameter learning when NASMC is used as a subroutine
of Particle Marginal Metropolis Hastings. Finally we show that NASMC is able to
train a latent variable recurrent neural network (LV-RNN) achieving results
that compete with the state-of-the-art for polymorphic music modelling. NASMC
can be seen as bridging the gap between adaptive SMC methods and the recent
work in scalable, black-box variational inference
Sequential Monte Carlo samplers for semilinear inverse problems and application to magnetoencephalography
We discuss the use of a recent class of sequential Monte Carlo methods for
solving inverse problems characterized by a semi-linear structure, i.e. where
the data depend linearly on a subset of variables and nonlinearly on the
remaining ones. In this type of problems, under proper Gaussian assumptions one
can marginalize the linear variables. This means that the Monte Carlo procedure
needs only to be applied to the nonlinear variables, while the linear ones can
be treated analytically; as a result, the Monte Carlo variance and/or the
computational cost decrease. We use this approach to solve the inverse problem
of magnetoencephalography, with a multi-dipole model for the sources. Here,
data depend nonlinearly on the number of sources and their locations, and
depend linearly on their current vectors. The semi-analytic approach enables us
to estimate the number of dipoles and their location from a whole time-series,
rather than a single time point, while keeping a low computational cost.Comment: 26 pages, 6 figure
Variational Sequential Monte Carlo
Many recent advances in large scale probabilistic inference rely on
variational methods. The success of variational approaches depends on (i)
formulating a flexible parametric family of distributions, and (ii) optimizing
the parameters to find the member of this family that most closely approximates
the exact posterior. In this paper we present a new approximating family of
distributions, the variational sequential Monte Carlo (VSMC) family, and show
how to optimize it in variational inference. VSMC melds variational inference
(VI) and sequential Monte Carlo (SMC), providing practitioners with flexible,
accurate, and powerful Bayesian inference. The VSMC family is a variational
family that can approximate the posterior arbitrarily well, while still
allowing for efficient optimization of its parameters. We demonstrate its
utility on state space models, stochastic volatility models for financial data,
and deep Markov models of brain neural circuits
Sequential Design for Optimal Stopping Problems
We propose a new approach to solve optimal stopping problems via simulation.
Working within the backward dynamic programming/Snell envelope framework, we
augment the methodology of Longstaff-Schwartz that focuses on approximating the
stopping strategy. Namely, we introduce adaptive generation of the stochastic
grids anchoring the simulated sample paths of the underlying state process.
This allows for active learning of the classifiers partitioning the state space
into the continuation and stopping regions. To this end, we examine sequential
design schemes that adaptively place new design points close to the stopping
boundaries. We then discuss dynamic regression algorithms that can implement
such recursive estimation and local refinement of the classifiers. The new
algorithm is illustrated with a variety of numerical experiments, showing that
an order of magnitude savings in terms of design size can be achieved. We also
compare with existing benchmarks in the context of pricing multi-dimensional
Bermudan options.Comment: 24 page
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