Abstract
Particle methods, also known as Sequential Monte Carlo, have been ubiquitous for Bayesian inference for state-space models, particulary when dealing with nonlinear non-Gaussian scenarios. However, in many practical situations, the state-space model contains unknown model parameters that need to be estimated simultaneously with the state. In this paper, We discuss a sequential analysis for combined parameter and state estimation. An online learning method is proposed to approach the distribution of the model parameter by tuning a flexible proposal mixture distribution to minimize their Kullback-Leibler divergence. We derive the sequential learning method by using a truncated Dirichlet processes normal mixture and present a general algorithm under a framework of the auxiliary particle filtering. The proposed algorithm is verified in a blind deconvolution problem, which is a typical state-space model with unknown model parameters. Furthermore, in a more challenging application that we call meta-modulation, which is a more complex blind deconvolution problem with sophisticated system evolution equations, the proposed method performs satisfactorily and achieves an exciting result for high efficiency communication.
Highlights
State-space model, a class of probabilistic graphical model (Koller and Friedman, 2009) that describes the dependence between the unobserved state variable and the observed measurement, is a fundamental model for statistical inference with diversely applications in fields like statistics, econometrics, and information engineering (West and Harrison, 1997; Cappeet al., 2005)
An online learning method is proposed to approach the distribution of the model parameter by tuning a flexible proposal mixture distribution to minimize their Kullback-Leibler divergence
The maximum likelihood approach generally converges rather slowly, but it may be a good choice for large data sets because of its low complexity; Bayesian methods apply directly to the augmented states and Markov chain Monte Carlo steps are utilized to improve the inference/estimation of the model parameter ( Gilks and Berzuini, 2001; Fearnhead, 2002; Andrieu et al, 2010)
Summary
State-space model, a class of probabilistic graphical model (Koller and Friedman, 2009) that describes the dependence between the unobserved state variable and the observed measurement, is a fundamental model for statistical inference with diversely applications in fields like statistics, econometrics, and information engineering (West and Harrison, 1997; Cappeet al., 2005). One early and straightforward way to deal with this problem is to extend the original state to an augmented state that includes the state and the parameter together, and to apply a standard particle filter to perform inference for both of them. This naive approach has been recognized not to be efficient, because the parameter space is not well explored (Kitagawa, 1998; Liu and West, 2001).
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