14,742 research outputs found
Particle Efficient Importance Sampling
The efficient importance sampling (EIS) method is a general principle for the
numerical evaluation of high-dimensional integrals that uses the sequential
structure of target integrands to build variance minimising importance
samplers. Despite a number of successful applications in high dimensions, it is
well known that importance sampling strategies are subject to an exponential
growth in variance as the dimension of the integration increases. We solve this
problem by recognising that the EIS framework has an offline sequential Monte
Carlo interpretation. The particle EIS method is based on non-standard
resampling weights that take into account the look-ahead construction of the
importance sampler. We apply the method for a range of univariate and bivariate
stochastic volatility specifications. We also develop a new application of the
EIS approach to state space models with Student's t state innovations. Our
results show that the particle EIS method strongly outperforms both the
standard EIS method and particle filters for likelihood evaluation in high
dimensions. Moreover, the ratio between the variances of the particle EIS and
particle filter methods remains stable as the time series dimension increases.
We illustrate the efficiency of the method for Bayesian inference using the
particle marginal Metropolis-Hastings and importance sampling squared
algorithms
Bibliographic Review on Distributed Kalman Filtering
In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud
The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area
Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models
We propose a new class of filtering and smoothing methods for inference in
high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models.
The main idea is to combine the ensemble Kalman filter and smoother, developed
in the geophysics literature, with state-space algorithms from the statistics
literature. Our algorithms address a variety of estimation scenarios, including
on-line and off-line state and parameter estimation. We take a Bayesian
perspective, for which the goal is to generate samples from the joint posterior
distribution of states and parameters. The key benefit of our approach is the
use of ensemble Kalman methods for dimension reduction, which allows inference
for high-dimensional state vectors. We compare our methods to existing ones,
including ensemble Kalman filters, particle filters, and particle MCMC. Using a
real data example of cloud motion and data simulated under a number of
nonlinear and non-Gaussian scenarios, we show that our approaches outperform
these existing methods
Learning Sparse High Dimensional Filters: Image Filtering, Dense CRFs and Bilateral Neural Networks
Bilateral filters have wide spread use due to their edge-preserving
properties. The common use case is to manually choose a parametric filter type,
usually a Gaussian filter. In this paper, we will generalize the
parametrization and in particular derive a gradient descent algorithm so the
filter parameters can be learned from data. This derivation allows to learn
high dimensional linear filters that operate in sparsely populated feature
spaces. We build on the permutohedral lattice construction for efficient
filtering. The ability to learn more general forms of high-dimensional filters
can be used in several diverse applications. First, we demonstrate the use in
applications where single filter applications are desired for runtime reasons.
Further, we show how this algorithm can be used to learn the pairwise
potentials in densely connected conditional random fields and apply these to
different image segmentation tasks. Finally, we introduce layers of bilateral
filters in CNNs and propose bilateral neural networks for the use of
high-dimensional sparse data. This view provides new ways to encode model
structure into network architectures. A diverse set of experiments empirically
validates the usage of general forms of filters
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