Sequential inference methods for non-homogeneous poisson processes with state-space prior

© 2018 IEEE. The Non-homogeneous Poisson process is a point process with time-varying intensity across its domain, the use of which arises in numerous areas in signal processing and machine learning. However, applications are largely limited by the intractable likelihood function and the high computational cost of existing inference schemes. We present a sequential inference framework that utilises generative Poisson data and sequential Markov Chain Monte Carlo (SMCMC) algorithm to enable online inference in various applications. The proposed model is compared to competing methods on synthetic datasets and tested with real-world financial data

Efficient alternatives to the Ephraim and Malah suppression rule for audio signal enhancement

Audio signal enhancement often involves the application of a time-varying filter, or suppression rule, to the frequency-domain transform of a corrupted signal. Here we address suppression rules derived under a Gaussian model and interpret them as spectral estimators in a Bayesian statistical framework. With regard to the optimal spectral amplitude estimator of Ephraim and Malah, we show that under the same modelling assumptions, alternative methods of Bayesian estimation lead to much simpler suppression rules exhibiting similarly effective behaviour. We derive three of such rules and demonstrate that, in addition to permitting a more straightforward implementation, they yield a more intuitive interpretation of the Ephraim and Malah solution

Fully Bayesian inference for α-stable distributions using a Poisson series representation

In this paper we develop an approach to Bayesian Monte Carlo inference for skewed α-stable distributions. Based on a series representation of the stable law in terms of infinite summations of random Poisson process arrival times, our framework leads to a simple representation in terms of conditionally Gaussian distributions for certain latent variables. Inference can therefore be carried out straightforwardly using techniques such as auxiliary variables versions of Markov chain Monte Carlo (MCMC) methods. The Poisson series representation (PSR) is further extended to practical application by introducing an approximation of the series residual terms based on exact moment calculations. Simulations illustrate the proposed framework applied to skewed α-stable simulated and real-world data, successfully estimating the distribution parameter values and being consistent with other (non-Bayesian) approaches. The methods are highly suitable for incorporation into hierarchical Bayesian models, and in this case the conditionally Gaussian structure of our model will lead to very efficient computations compared to other approaches.Godsill acknowledges partial funding for the work from the EPSRC BTaRoT project EP/K020153/1, and Tatjana Lemke acknowledges PhD funding from Fraunhofer ITWM, Kaiserslautern.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.dsp.2015.08.01

Sequential Dynamic Leadership Inference Using Bayesian Monte Carlo Methods

Hierarchy and leadership interactions commonly occur in animal groups, crowds of people and in vehicle motions. Such interactions are often affected by one or more individuals who possess key domain information (e.g. final destination, environmental constraints and best routes) or pertinent traits (e.g. better navigation, sensing and decision making capabilities) compared with the rest of the group. This paper presents a framework for the automatic identification of group structure and leadership from noisy sensory observations of tracked groups. Accordingly, a new leader-follower model is developed which assumes the dynamics of the group to be a multivariate Ornstein–Uhlenbeck process with the designated leader(s) drifting to the destination and followers reverting to the leaders’ state. Sequential Monte Carlo (SMC) approaches, and specifically the sequential Markov chain Monte Carlo (SMCMC) approach, are adopted to infer, probabilistically, the evolving leadership structure. A Rao-Blackwellisation scheme is employed such that the kinematic state of the objects in the group is inferred in closed form by Kalman filtering. Experiments show that the proposed techniques can successfully determine the leadership structures in challenging scenarios with a corresponding enhancement in tracking accuracy through direct consideration of the leadership interactions of the group

Bayesian Intent Prediction in Object Tracking Using Bridging Distributions.

In several application areas, such as human computer interaction, surveillance and defence, determining the intent of a tracked object enables systems to aid the user/operator and facilitate effective, possibly automated, decision making. In this paper, we propose a probabilistic inference approach that permits the prediction, well in advance, of the intended destination of a tracked object and its future trajectory. Within the framework introduced here, the observed partial track of the object is modeled as being part of a Markov bridge terminating at its destination, since the target path, albeit random, must end at the intended endpoint. This captures the underlying long term dependencies in the trajectory, as dictated by the object intent. By determining the likelihood of the partial track being drawn from a particular constructed bridge, the probability of each of a number of possible destinations is evaluated. These bridges can also be employed to produce refined estimates of the latent system state (e.g., object position, velocity, etc.), predict its future values (up until reaching the designated endpoint) and estimate the time of arrival. This is shown to lead to a low complexity Kalman-filter-based implementation of the inference routine, where any linear Gaussian motion model, including the destination reverting ones, can be applied. Free hand pointing gestures data collected in an instrumented vehicle and synthetic trajectories of a vessel heading toward multiple possible harbors are utilized to demonstrate the effectiveness of the proposed approach

Driver and Passenger Identification from Smartphone Data

The objective of this paper is twofold. First, it presents a brief overview of existing driver and passenger identification or recognition approaches which rely on smartphone data. This includes listing the typically available sensory measurements and highlighting a few key practical considerations for automotive settings. Second, a simple identification method that utilises the smartphone inertial measurements and, possibly, doors signal is proposed. It is based on analysing the user behaviour during entry, namely the direction of turning, and extracting relevant salient features, which are distinctive depending on the side of entry to the vehicle. This is followed by applying a suitable classifier and decision criterion. Experimental data is shown to demonstrate the usefulness and effectiveness of the introduced probabilistic, low-complexity, identification technique.Jaguar Land Rover under the Centre for Advanced Photonics and Electronics (CAPE) agreement

Bayesian Inference of Task-Based Functional Brain Connectivity Using Markov Chain Monte Carlo Methods

The study of functional networks in the brain is essential in order to gain a better insight into its diverse set of operations and to characterise the associated normal and abnormal behaviours. Present methods of analysing fMRI data to obtain functional connectivity are largely limited to approaches such as correlation, regression and independent component analysis, which give simple point estimates. By contrast, we propose a stochastic linear model in a Bayesian setting and employ Markov Chain Monte Carlo methods to approximate posterior distributions of full connectivity and covariance matrices. Through the use of a Bayesian probabilistic framework, distributional estimates of the linkage strengths are obtained as opposed to point estimates, and the uncertainty of the existence of such links is accounted for. We decompose the connectivity matrix as the Hadamard product of binary indicators and real-valued variables, and formulate an efficient joint-sampling scheme to infer them. The well-characterised somato-motor network is examined in a self-paced, right-handed finger opposition task based experiment, while nodes from the visual network are used for contrast during the same experiment. Unlike for the visual network, significant changes in connectivity are found in the motor network during the task. Our work provides a distributional metric for functional connectivity along with causality information, and contributes to the collection of network level descriptors of brain functions.Engineering and Physical Sciences Research Council Grant ID: EP/K020153/1; Yousef Jameel Scholarship Programm

Revisiting Synthesis Model of Sparse Audio Declipper

The state of the art in audio declipping has currently been achieved by SPADE (SParse Audio DEclipper) algorithm by Kiti\'c et al. Until now, the synthesis/sparse variant, S-SPADE, has been considered significantly slower than its analysis/cosparse counterpart, A-SPADE. It turns out that the opposite is true: by exploiting a recent projection lemma, individual iterations of both algorithms can be made equally computationally expensive, while S-SPADE tends to require considerably fewer iterations to converge. In this paper, the two algorithms are compared across a range of parameters such as the window length, window overlap and redundancy of the transform. The experiments show that although S-SPADE typically converges faster, the average performance in terms of restoration quality is not superior to A-SPADE

Extension of the bayesian alphabet for genomic selection

<p>Abstract</p> <p>Background</p> <p>Two Bayesian methods, BayesC<it>π </it>and BayesD<it>π</it>, were developed for genomic prediction to address the drawback of BayesA and BayesB regarding the impact of prior hyperparameters and treat the prior probability <it>π </it>that a SNP has zero effect as unknown. The methods were compared in terms of inference of the number of QTL and accuracy of genomic estimated breeding values (GEBVs), using simulated scenarios and real data from North American Holstein bulls.</p> <p>Results</p> <p>Estimates of <it>π </it>from BayesC<it>π</it>, in contrast to BayesD<it>π</it>, were sensitive to the number of simulated QTL and training data size, and provide information about genetic architecture. Milk yield and fat yield have QTL with larger effects than protein yield and somatic cell score. The drawback of BayesA and BayesB did not impair the accuracy of GEBVs. Accuracies of alternative Bayesian methods were similar. BayesA was a good choice for GEBV with the real data. Computing time was shorter for BayesC<it>π </it>than for BayesD<it>π</it>, and longest for our implementation of BayesA.</p> <p>Conclusions</p> <p>Collectively, accounting for computing effort, uncertainty as to the number of QTL (which affects the GEBV accuracy of alternative methods), and fundamental interest in the number of QTL underlying quantitative traits, we believe that BayesC<it>π </it>has merit for routine applications.</p

Multitrait analysis of quantitative trait loci using Bayesian composite space approach

<p>Abstract</p> <p>Background</p> <p>Multitrait analysis of quantitative trait loci can capture the maximum information of experiment. The maximum-likelihood approach and the least-square approach have been developed to jointly analyze multiple traits, but it is difficult for them to include multiple QTL simultaneously into one model.</p> <p>Results</p> <p>In this article, we have successfully extended Bayesian composite space approach, which is an efficient model selection method that can easily handle multiple QTL, to multitrait mapping of QTL. There are many statistical innovations of the proposed method compared with Bayesian single trait analysis. The first is that the parameters for all traits are updated jointly by vector or matrix; secondly, for QTL in the same interval that control different traits, the correlation between QTL genotypes is taken into account; thirdly, the information about the relationship of residual error between the traits is also made good use of. The superiority of the new method over separate analysis was demonstrated by both simulated and real data. The computing program was written in FORTRAN and it can be available for request.</p> <p>Conclusion</p> <p>The results suggest that the developed new method is more powerful than separate analysis.</p