2,405 research outputs found
Active Classification for POMDPs: a Kalman-like State Estimator
The problem of state tracking with active observation control is considered
for a system modeled by a discrete-time, finite-state Markov chain observed
through conditionally Gaussian measurement vectors. The measurement model
statistics are shaped by the underlying state and an exogenous control input,
which influence the observations' quality. Exploiting an innovations approach,
an approximate minimum mean-squared error (MMSE) filter is derived to estimate
the Markov chain system state. To optimize the control strategy, the associated
mean-squared error is used as an optimization criterion in a partially
observable Markov decision process formulation. A stochastic dynamic
programming algorithm is proposed to solve for the optimal solution. To enhance
the quality of system state estimates, approximate MMSE smoothing estimators
are also derived. Finally, the performance of the proposed framework is
illustrated on the problem of physical activity detection in wireless body
sensing networks. The power of the proposed framework lies within its ability
to accommodate a broad spectrum of active classification applications including
sensor management for object classification and tracking, estimation of sparse
signals and radar scheduling.Comment: 38 pages, 6 figure
Particle-based likelihood inference in partially observed diffusion processes using generalised Poisson estimators
This paper concerns the use of the expectation-maximisation (EM) algorithm
for inference in partially observed diffusion processes. In this context, a
well known problem is that all except a few diffusion processes lack
closed-form expressions of the transition densities. Thus, in order to estimate
efficiently the EM intermediate quantity we construct, using novel techniques
for unbiased estimation of diffusion transition densities, a random weight
fixed-lag auxiliary particle smoother, which avoids the well known problem of
particle trajectory degeneracy in the smoothing mode. The estimator is
justified theoretically and demonstrated on a simulated example
Newton-based maximum likelihood estimation in nonlinear state space models
Maximum likelihood (ML) estimation using Newton's method in nonlinear state
space models (SSMs) is a challenging problem due to the analytical
intractability of the log-likelihood and its gradient and Hessian. We estimate
the gradient and Hessian using Fisher's identity in combination with a
smoothing algorithm. We explore two approximations of the log-likelihood and of
the solution of the smoothing problem. The first is a linearization
approximation which is computationally cheap, but the accuracy typically varies
between models. The second is a sampling approximation which is asymptotically
valid for any SSM but is more computationally costly. We demonstrate our
approach for ML parameter estimation on simulated data from two different SSMs
with encouraging results.Comment: 17 pages, 2 figures. Accepted for the 17th IFAC Symposium on System
Identification (SYSID), Beijing, China, October 201
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
Inference via low-dimensional couplings
We investigate the low-dimensional structure of deterministic transformations
between random variables, i.e., transport maps between probability measures. In
the context of statistics and machine learning, these transformations can be
used to couple a tractable "reference" measure (e.g., a standard Gaussian) with
a target measure of interest. Direct simulation from the desired measure can
then be achieved by pushing forward reference samples through the map. Yet
characterizing such a map---e.g., representing and evaluating it---grows
challenging in high dimensions. The central contribution of this paper is to
establish a link between the Markov properties of the target measure and the
existence of low-dimensional couplings, induced by transport maps that are
sparse and/or decomposable. Our analysis not only facilitates the construction
of transformations in high-dimensional settings, but also suggests new
inference methodologies for continuous non-Gaussian graphical models. For
instance, in the context of nonlinear state-space models, we describe new
variational algorithms for filtering, smoothing, and sequential parameter
inference. These algorithms can be understood as the natural
generalization---to the non-Gaussian case---of the square-root
Rauch-Tung-Striebel Gaussian smoother.Comment: 78 pages, 25 figure
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