An online expectation-maximisation algorithm for nonnegative matrix factorisation models

In this paper we formulate the nonnegative matrix factorisation (NMF) problem as a maximum likelihood estimation problem for hidden Markov models and propose online expectation-maximisation (EM) algorithms to estimate the NMF and the other unknown static parameters. We also propose a sequential Monte Carlo approximation of our online EM algorithm. We show the performance of the proposed method with two numerical examples. © 2012 IFAC.

A Monte Carlo expectation maximisation algorithm for multiple target tracking

In this paper, we present an expectation-maximisation (EM) algorithm for maximum likelihood estimation in multiple target models (MTT) with Gaussian linear state-space dynamics. We show that estimation of sufficient statistics for EM in a single Gaussian linear state-space model can be extended to the MTT case along with a Monte Carlo approximation for inference of unknown associations of targets. The stochastic approximation EM algorithm that we present here can be used along with any Monte Carlo method which has been developed for tracking in MTT models, such as Markov chain Monte Carlo and sequential Monte Carlo methods. We demonstrate the performance of the algorithm with a simulation. © 2012 ISIF (Intl Society of Information Fusi).

Quantification of the effects of antibodies on the extra- and intracellular dynamics of Salmonella enterica.

Antibodies are known to be essential in controlling Salmonella infection, but their exact role remains elusive. We recently developed an in vitro model to investigate the relative efficiency of four different human immunoglobulin G (IgG) subclasses in modulating the interaction of the bacteria with human phagocytes. Our results indicated that different IgG subclasses affect the efficacy of Salmonella uptake by human phagocytes. In this study, we aim to quantify the effects of IgG on intracellular dynamics of infection by combining distributions of bacterial numbers per phagocyte observed by fluorescence microscopy with a mathematical model that simulates the in vitro dynamics. We then use maximum likelihood to estimate the model parameters and compare them across IgG subclasses. The analysis reveals heterogeneity in the division rates of the bacteria, strongly suggesting that a subpopulation of intracellular Salmonella, while visible under the microscope, is not dividing. Clear differences in the observed distributions among the four IgG subclasses are best explained by variations in phagocytosis and intracellular dynamics. We propose and compare potential factors affecting the replication and death of bacteria within phagocytes, and we discuss these results in the light of recent findings on dormancy of Salmonella.

A Stochastic Model for Electron Multiplication Charge-Coupled Devices - From Theory to Practice

Electron multiplication charge-coupled devices (EMCCD) are widely used for photon counting experiments and measurements of low intensity light sources, and are extensively employed in biological fluorescence imaging applications. These devices have a complex statistical behaviour that is often not fully considered in the analysis of EMCCD data. Robust and optimal analysis of EMCCD images requires an understanding of their noise properties, in particular to exploit fully the advantages of Bayesian and maximum-likelihood analysis techniques, whose value is increasingly recognised in biological imaging for obtaining robust quantitative measurements from challenging data. To improve our own EMCCD analysis and as an effort to aid that of the wider bioimaging community, we present, explain and discuss a detailed physical model for EMCCD noise properties, giving a likelihood function for image counts in each pixel for a given incident intensity, and we explain how to measure the parameters for this model from various calibration images. © 2013 Hirsch et al.

Occlusive Components Analysis

We study unsupervised learning in a probabilistic generative model for occlusion. The model uses two types of latent variables: one indicates which objects are present in the image, and the other how they are ordered in depth. This depth order then determines how the positions and appearances of the objects present, specified in the model parameters, combine to form the image. We show that the object parameters can be learnt from an unlabelled set of images in which objects occlude one another. Exact maximum-likelihood learning is intractable. However, we show that tractable approximations to Expectation Maximization (EM) can be found if the training images each contain only a small number of objects on average. In numerical experiments it is shown that these approximations recover the correct set of object parameters. Experiments on a novel version of the bars test using colored bars, and experiments on more realistic data, show that the algorithm performs well in extracting the generating causes. Experiments based on the standard bars benchmark test for object learning show that the algorithm performs well in comparison to other recent component extraction approaches. The model and the learning algorithm thus connect research on occlusion with the research field of multiple-causes component extraction methods.

State estimation schemes for independent component coupled hidden Markov models

Conventional Hidden Markov models generally consist of a Markov chain observed through a linear map corrupted by additive noise. This general class of model has enjoyed a huge and diverse range of applications, for example, speech processing, biomedical signal processing and more recently quantitative finance. However, a lesser known extension of this general class of model is the so-called Factorial Hidden Markov Model (FHMM). FHMMs also have diverse applications, notably in machine learning, artificial intelligence and speech recognition [13, 17]. FHMMs extend the usual class of HMMs, by supposing the partially observed state process is a finite collection of distinct Markov chains, either statistically independent or dependent. There is also considerable current activity in applying collections of partially observed Markov chains to complex action recognition problems, see, for example, [6]. In this article we consider the Maximum Likelihood (ML) parameter estimation problem for FHMMs. Much of the extant literature concerning this problem presents parameter estimation schemes based on full data log-likelihood EM algorithms. This approach can be slow to converge and often imposes heavy demands on computer memory. The latter point is particularly relevant for the class of FHMMs where state space dimensions are relatively large. The contribution in this article is to develop new recursive formulae for a filter-based EM algorithm that can be implemented online. Our new formulae are equivalent ML estimators, however, these formulae are purely recursive and so, significantly reduce numerical complexity and memory requirements. A computer simulation is included to demonstrate the performance of our results. © Taylor & Francis Group, LLC.

Gaussian process volatility model

The prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the evolution of the variance. Moreover, functional parameters are usually learned by maximum likelihood, which can lead to over-fitting. To address these problems we introduce GP-Vol, a novel non-parametric model for time-changing variances based on Gaussian Processes. This new model can capture highly flexible functional relationships for the variances. Furthermore, we introduce a new online algorithm for fast inference in GP-Vol. This method is much faster than current offline inference procedures and it avoids overfitting problems by following a fully Bayesian approach. Experiments with financial data show that GP-Vol performs significantly better than current standard alternatives.

Calibrating the Gaussian multi-target tracking model

We present novel batch and online (sequential) versions of the expectation-maximisation (EM) algorithm for inferring the static parameters of a multiple target tracking (MTT) model. Online EM is of particular interest as it is a more practical method for long data sets since in batch EM, or a full Bayesian approach, a complete browse of the data is required between successive parameter updates. Online EM is also suited to MTT applications that demand real-time processing of the data. Performance is assessed in numerical examples using simulated data for various scenarios. For batch estimation our method significantly outperforms an existing gradient based maximum likelihood technique, which we show to be significantly biased. © 2014 Springer Science+Business Media New York.

Is there a preferred classifier for operational thematic mapping?

The importance of properly exploiting a classifier's inherent geometric characteristics when developing a classification methodology is emphasized as a prerequisite to achieving near optimal performance when carrying out thematic mapping. When used properly, it is argued that the long-standing maximum likelihood approach and the more recent support vector machine can perform comparably. Both contain the flexibility to segment the spectral domain in such a manner as to match inherent class separations in the data, as do most reasonable classifiers. The choice of which classifier to use in practice is determined largely by preference and related considerations, such as ease of training, multiclass capabilities, and classification cost. © 1980-2012 IEEE.