Langevin and Hamiltonian based Sequential MCMC for Efficient Bayesian Filtering in High-dimensional Spaces

Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm, also known as particle filtering. Nevertheless, this method tends to be inefficient when applied to high dimensional problems. In this paper, we focus on another class of sequential inference methods, namely the Sequential Markov Chain Monte Carlo (SMCMC) techniques, which represent a promising alternative to SMC methods. After providing a unifying framework for the class of SMCMC approaches, we propose novel efficient strategies based on the principle of Langevin diffusion and Hamiltonian dynamics in order to cope with the increasing number of high-dimensional applications. Simulation results show that the proposed algorithms achieve significantly better performance compared to existing algorithms

Efficient Sequential Monte-Carlo Samplers for Bayesian Inference

In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such inference problems. However, in the presence of a high-dimensional and/or multimodal posterior distribution, it is widely documented that standard Monte-Carlo techniques could lead to poor performance. In this paper, the study is focused on a Sequential Monte-Carlo (SMC) sampler framework, a more robust and efficient Monte Carlo algorithm. Although this approach presents many advantages over traditional Monte-Carlo methods, the potential of this emergent technique is however largely underexploited in signal processing. In this work, we aim at proposing some novel strategies that will improve the efficiency and facilitate practical implementation of the SMC sampler specifically for signal processing applications. Firstly, we propose an automatic and adaptive strategy that selects the sequence of distributions within the SMC sampler that minimizes the asymptotic variance of the estimator of the posterior normalization constant. This is critical for performing model selection in modelling applications in Bayesian signal processing. The second original contribution we present improves the global efficiency of the SMC sampler by introducing a novel correction mechanism that allows the use of the particles generated through all the iterations of the algorithm (instead of only particles from the last iteration). This is a significant contribution as it removes the need to discard a large portion of the samples obtained, as is standard in standard SMC methods. This will improve estimation performance in practical settings where computational budget is important to consider.Comment: arXiv admin note: text overlap with arXiv:1303.3123 by other author

An Overview of Recent Advances in Monte-Carlo Methods for Bayesian Filtering in High-Dimensional Spaces

International audienc

Dynamic speech emotion recognition with state-space models

International audienceAutomatic emotion recognition from speech has been focused mainly on identifying categorical or static affect states, but the spectrum of human emotion is continuous and time-varying. In this paper, we present a recognition system for dynamic speech emotion based on state-space models (SSMs). The prediction of the unknown emotion trajectory in the affect space spanned by Arousal, Valence, and Dominance (A-V-D) descriptors is cast as a time series filtering task. The state- space models we investigated include a standard linear model (Kalman filter) as well as novel non-linear, non-parametric Gaussian Processes (GP) based SSM. We use the AVEC 2014 database for evaluation, which provides ground truth A-V-D labels which allows state and measurement functions to be learned separately simplifying the model training. For the filtering with GP SSM, we used two approximation methods: a recently proposed analytic method and Particle filter. All models were evaluated in terms of average Pearson correla- tion R and root mean square error (RMSE). The results show that using the same feature vectors, the GP SSMs achieve twice higher correlation and twice smaller RMSE than a Kalman filter

Distributional upper bound on the interference in spatial wireless multiuser ultrawideband communication systems

We develop a novel distributional upper bound on the interference created in an ultra-wideband wireless communication systems under two general assumptions: the first is that there is an unknown number of interferers who are distributed according to a homogeneous Poisson point process randomly in space; and the second is that the frequency bands occupied by the unknown number of interferers is also a random variable in an ultra-wideband setting. Then given these two general assumptions, we derive a distributional upper bound representation of the total interference

VS-LTGARCHX: A Flexible Subset Selection Approach for Estimation of log-TGARCHX Models and Its Application to BTC Markets

The log-TGARCHX model is less restrictive in terms of inclusion of exogenous variables and asymmetry lags compared to the GARCHX model. However, adding less (more) covariates than necessary may lead to underfitting (overfitting), respectively. In this context, we propose a new algorithm, called VS-LTGARCHX, which incorporates a variable selection procedure into the log-TGARCHX estimation process. Furthermore, the VS-LTGARCHX algorithm is applied to extremely volatile BTC markets using 42 conditioning variables. Interestingly, our results show that the VS-LTGARCHX models outperform the specified benchmark models in one-step-ahead forecasting