Poyiadjis et al. (2011) show how particle methods can be used to estimate both the score and the observed information matrix for state space models. These methods either suffer from a computational cost that is quadratic in the number of particles, or produce estimates whose variance increases quadratically with the amount of data. This paper introduces an alternative approach for estimating these terms at a computational cost that is linear in the number of particles. The method is derived using a combination of kernel density estimation, to avoid the particle degeneracy that causes the quadratically increasing variance, and Rao-Blackwellisation. Crucially, we show the method is robust to the choice of bandwidth within the kernel density estimation, as it has good asymptotic properties regardless of this choice. Our estimates of the score and observed information matrix can be used within both online and batch procedures for estimating parameters for state space models. Empirical results show improved parameter estimates compared to existing methods at a significantly reduced computational cost. Supplementary materials including code are available.
Joint state and parameter estimation is a core problem for dynamic Bayesian networks. Although modern probabilistic inference toolkits make it relatively easy to specify large and practically relevant probabilistic models, the silver bullet---an efficient and general online inference algorithm for such problems---remains elusive, forcing users to write special-purpose code for each application. We propose a novel blackbox algorithm -- a hybrid of particle filtering for state variables and assumed density filtering for parameter variables. It has following advantages: (a) it is efficient due to its online nature, and (b) it is applicable to both discrete and continuous parameter spaces . On a variety of toy and real models, our system is able to generate more accurate results within a fixed computation budget. This preliminary evidence indicates that the proposed approach is likely to be of practical use.
Particle physicists began fiddling with artificial intelligence (AI) in the late 1980s, just as the term "neural network" captured the public's imagination. Their field lends itself to AI and machine-learning algorithms because nearly every experiment centers on finding subtle spatial patterns in the countless, similar readouts of complex particle detectors--just the sort of thing at which AI excels. Particle physicists strive to understand the inner workings of the universe by smashing subatomic particles together with enormous energies to blast out exotic new bits of matter, such as the the long-predicted Higgs boson, which was discovered in 2012 at the world's largest proton collider, the Large Hadron Collider (LHC) in Switzerland. Such exotic particles don't come with labels, however. In a fraction of a nanosecond, they decay into other particles, and physicists must spot all those more-common particles and see whether they fit together in a way that's consistent with them coming from the same parent--a job made far harder by the hordes of extraneous particles in a typical collision.
Particle MCMC is a class of algorithms that can be used to analyse state-space models. They use MCMC moves to update the parameters of the models, and particle filters to propose values for the path of the state-space model. Currently the default is to use random walk Metropolis to update the parameter values. We show that it is possible to use information from the output of the particle filter to obtain better proposal distributions for the parameters. In particular it is possible to obtain estimates of the gradient of the log posterior from each run of the particle filter, and use these estimates within a Langevin-type proposal. We propose using the recent computationally efficient approach of Nemeth et al. (2013) for obtaining such estimates. We show empirically that for a variety of state-space models this proposal is more efficient than the standard random walk Metropolis proposal in terms of: reducing autocorrelation of the posterior samples, reducing the burn-in time of the MCMC sampler and increasing the squared jump distance between posterior samples.
As one of Bayesian analysis tools, Hidden Markov Model (HMM) has been used to in extensive applications. Most HMMs are solved by Baum-Welch algorithm (BWHMM) to predict the model parameters, which is difficult to find global optimal solutions. This paper proposes an optimized Hidden Markov Model with Particle Swarm Optimization (PSO) algorithm and so is called PSOHMM. In order to overcome the statistical constraints in HMM, the paper develops re-normalization and re-mapping mechanisms to ensure the constraints in HMM. The experiments have shown that PSOHMM can search better solution than BWHMM, and has faster convergence speed.