The posterior-Viterbi: a new decoding algorithm for hidden Markov models

Background: Hidden Markov models (HMM) are powerful machine learning tools successfully applied to problems of computational Molecular Biology. In a predictive task, the HMM is endowed with a decoding algorithm in order to assign the most probable state path, and in turn the class labeling, to an unknown sequence. The Viterbi and the posterior decoding algorithms are the most common. The former is very efficient when one path dominates, while the latter, even though does not guarantee to preserve the automaton grammar, is more effective when several concurring paths have similar probabilities. A third good alternative is 1-best, which was shown to perform equal or better than Viterbi. Results: In this paper we introduce the posterior-Viterbi (PV) a new decoding which combines the posterior and Viterbi algorithms. PV is a two step process: first the posterior probability of each state is computed and then the best posterior allowed path through the model is evaluated by a Viterbi algorithm. Conclusions: We show that PV decoding performs better than other algorithms first on toy models and then on the computational biological problem of the prediction of the topology of beta-barrel membrane proteins.Comment: 23 pages, 3 figure

Hidden-Markov Program Algebra with iteration

We use Hidden Markov Models to motivate a quantitative compositional semantics for noninterference-based security with iteration, including a refinement- or "implements" relation that compares two programs with respect to their information leakage; and we propose a program algebra for source-level reasoning about such programs, in particular as a means of establishing that an "implementation" program leaks no more than its "specification" program. This joins two themes: we extend our earlier work, having iteration but only qualitative, by making it quantitative; and we extend our earlier quantitative work by including iteration. We advocate stepwise refinement and source-level program algebra, both as conceptual reasoning tools and as targets for automated assistance. A selection of algebraic laws is given to support this view in the case of quantitative noninterference; and it is demonstrated on a simple iterated password-guessing attack

The impact of mutation and gene conversion on the local diversification of antigen genes in African trypanosomes

Patterns of genetic diversity in parasite antigen gene families hold important information about their potential to generate antigenic variation within and between hosts. The evolution of such gene families is typically driven by gene duplication, followed by point mutation and gene conversion. There is great interest in estimating the rates of these processes from molecular sequences for understanding the evolution of the pathogen and its significance for infection processes. In this study, a series of models are constructed to investigate hypotheses about the nucleotide diversity patterns between closely related gene sequences from the antigen gene archive of the African trypanosome, the protozoan parasite causative of human sleeping sickness in Equatorial Africa. We use a hidden Markov model approach to identify two scales of diversification: clustering of sequence mismatches, a putative indicator of gene conversion events with other lower-identity donor genes in the archive, and at a sparser scale, isolated mismatches, likely arising from independent point mutations. In addition to quantifying the respective probabilities of occurrence of these two processes, our approach yields estimates for the gene conversion tract length distribution and the average diversity contributed locally by conversion events. Model fitting is conducted using a Bayesian framework. We find that diversifying gene conversion events with lower-identity partners occur at least five times less frequently than point mutations on variant surface glycoprotein (VSG) pairs, and the average imported conversion tract is between 14 and 25 nucleotides long. However, because of the high diversity introduced by gene conversion, the two processes have almost equal impact on the per-nucleotide rate of sequence diversification between VSG subfamily members. We are able to disentangle the most likely locations of point mutations and conversions on each aligned gene pair

Robot introspection through learned hidden Markov models

In this paper we describe a machine learning approach for acquiring a model of a robot behaviour from raw sensor data. We are interested in automating the acquisition of behavioural models to provide a robot with an introspective capability. We assume that the behaviour of a robot in achieving a task can be modelled as a finite stochastic state transition system. Beginning with data recorded by a robot in the execution of a task, we use unsupervised learning techniques to estimate a hidden Markov model (HMM) that can be used both for predicting and explaining the behaviour of the robot in subsequent executions of the task. We demonstrate that it is feasible to automate the entire process of learning a high quality HMM from the data recorded by the robot during execution of its task.The learned HMM can be used both for monitoring and controlling the behaviour of the robot. The ultimate purpose of our work is to learn models for the full set of tasks associated with a given problem domain, and to integrate these models with a generative task planner. We want to show that these models can be used successfully in controlling the execution of a plan. However, this paper does not develop the planning and control aspects of our work, focussing instead on the learning methodology and the evaluation of a learned model. The essential property of the models we seek to construct is that the most probable trajectory through a model, given the observations made by the robot, accurately diagnoses, or explains, the behaviour that the robot actually performed when making these observations. In the work reported here we consider a navigation task. We explain the learning process, the experimental setup and the structure of the resulting learned behavioural models. We then evaluate the extent to which explanations proposed by the learned models accord with a human observer's interpretation of the behaviour exhibited by the robot in its execution of the task

S-estimation of hidden Markov models

A method for robust estimation of dynamic mixtures of multivariate distributions is proposed. The EM algorithm is modified by replacing the classical M-step with high breakdown S-estimation of location and scatter, performed by using the bisquare multivariate S-estimator. Estimates are obtained by solving a system of estimating equations that are characterized by component specific sets of weights, based on robust Mahalanobis-type distances. Convergence of the resulting algorithm is proved and its finite sample behavior is investigated by means of a brief simulation study and n application to a multivariate time series of daily returns for seven stock markets