Detecting recombination in 4-taxa DNA sequence alignments with Bayesian hidden Markov models and Markov chain Monte Carlo

This article presents a statistical method for detecting recombination in DNA sequence alignments, which is based on combining two probabilistic graphical models: (1) a taxon graph (phylogenetic tree) representing the relationship between the taxa, and (2) a site graph (hidden Markov model) representing interactions between different sites in the DNA sequence alignments. We adopt a Bayesian approach and sample the parameters of the model from the posterior distribution with Markov chain Monte Carlo, using a Metropolis-Hastings and Gibbs-within-Gibbs scheme. The proposed method is tested on various synthetic and real-world DNA sequence alignments, and we compare its performance with the established detection methods RECPARS, PLATO, and TOPAL, as well as with two alternative parameter estimation schemes.

Chow–Liu trees are sufficient predictive models for reproducing key features of functional networks of periictal EEG time-series

Seizure freedom in patients suffering from pharmacoresistant epilepsies is still not achieved in 20–30% of all cases. Hence, current therapies need to be improved, based on a more complete understanding of ictogenesis. In this respect, the analysis of functional networks derived from intracranial electroencephalographic (iEEG) data has recently become a standard tool. Functional networks however are purely descriptive models and thus are conceptually unable to predict fundamental features of iEEG time-series, e.g., in the context of therapeutical brain stimulation. In this paper we present some first steps towards overcoming the limitations of functional network analysis, by showing that its results are implied by a simple predictive model of time-sliced iEEG time-series. More specifically, we learn distinct graphical models (so called Chow–Liu (CL) trees) as models for the spatial dependencies between iEEG signals. Bayesian inference is then applied to the CL trees, allowing for an analytic derivation/prediction of functional networks, based on thresholding of the absolute value Pearson correlation coefficient (CC) matrix. Using various measures, the thus obtained networks are then compared to those which were derived in the classical way from the empirical CC-matrix. In the high threshold limit we find (a) an excellent agreement between the two networks and (b) key features of periictal networks as they have previously been reported in the literature. Apart from functional networks, both matrices are also compared element-wise, showing that the CL approach leads to a sparse representation, by setting small correlations to values close to zero while preserving the larger ones. Overall, this paper shows the validity of CL-trees as simple, spatially predictive models for periictal iEEG data. Moreover, we suggest straightforward generalizations of the CL-approach for modeling also the temporal features of iEEG signals.

Graphical modelling for brain connectivity via partial coherence

Spectral and coherence methodologies are ubiquitous for the analysis of multiple time series. Partial coherence analysis may be used to try to determine graphical models for brain functional connectivity. The outcome of such an analysis may be considerably influenced by factors such as the degree of spectral smoothing, line and interference removal, matrix inversion stabilization and the suppression of effects caused by side-lobe leakage, the combination of results from different epochs and people, and multiple hypothesis testing. This paper examines each of these steps in turn and provides a possible path which produces relatively ‘clean’ connectivity plots. In particular we show how spectral matrix diagonal up-weighting can simultaneously stabilize spectral matrix inversion and reduce effects caused by side-lobe leakage, and use the stepdown multiple hypothesis test procedure to help formulate an interaction strength.

Approximate algorithms for credal networks with binary variables

This paper presents a family of algorithms for approximate inference in credal networks (that is, models based on directed acyclic graphs and set-valued probabilities) that contain only binary variables. Such networks can represent incomplete or vague beliefs, lack of data, and disagreements among experts; they can also encode models based on belief functions and possibilistic measures. All algorithms for approximate inference in this paper rely on exact inferences in credal networks based on polytrees with binary variables, as these inferences have polynomial complexity. We are inspired by approximate algorithms for Bayesian networks; thus the Loopy 2U algorithm resembles Loopy Belief Propagation, while the Iterated Partial Evaluation and Structured Variational 2U algorithms are, respectively, based on Localized Partial Evaluation and variational techniques. (C) 2007 Elsevier Inc. All rights reserved.

Inference about the number of contributors to a DNA mixture: Comparative analyses of a Bayesian network approach and the maximum allele count method.

In the forensic examination of DNA mixtures, the question of how to set the total number of contributors (N) presents a topic of ongoing interest. Part of the discussion gravitates around issues of bias, in particular when assessments of the number of contributors are not made prior to considering the genotypic configuration of potential donors. Further complication may stem from the observation that, in some cases, there may be numbers of contributors that are incompatible with the set of alleles seen in the profile of a mixed crime stain, given the genotype of a potential contributor. In such situations, procedures that take a single and fixed number contributors as their output can lead to inferential impasses. Assessing the number of contributors within a probabilistic framework can help avoiding such complication. Using elements of decision theory, this paper analyses two strategies for inference on the number of contributors. One procedure is deterministic and focuses on the minimum number of contributors required to 'explain' an observed set of alleles. The other procedure is probabilistic using Bayes' theorem and provides a probability distribution for a set of numbers of contributors, based on the set of observed alleles as well as their respective rates of occurrence. The discussion concentrates on mixed stains of varying quality (i.e., different numbers of loci for which genotyping information is available). A so-called qualitative interpretation is pursued since quantitative information such as peak area and height data are not taken into account. The competing procedures are compared using a standard scoring rule that penalizes the degree of divergence between a given agreed value for N, that is the number of contributors, and the actual value taken by N. Using only modest assumptions and a discussion with reference to a casework example, this paper reports on analyses using simulation techniques and graphical models (i.e., Bayesian networks) to point out that setting the number of contributors to a mixed crime stain in probabilistic terms is, for the conditions assumed in this study, preferable to a decision policy that uses categoric assumptions about N.

Probabilistic evidential assessment of gunshot residue particle evidence (Part II) : Bayesian parameter estimation for experimental count data.

Part I of this series of articles focused on the construction of graphical probabilistic inference procedures, at various levels of detail, for assessing the evidential value of gunshot residue (GSR) particle evidence. The proposed models - in the form of Bayesian networks - address the issues of background presence of GSR particles, analytical performance (i.e., the efficiency of evidence searching and analysis procedures) and contamination. The use and practical implementation of Bayesian networks for case pre-assessment is also discussed. This paper, Part II, concentrates on Bayesian parameter estimation. This topic complements Part I in that it offers means for producing estimates useable for the numerical specification of the proposed probabilistic graphical models. Bayesian estimation procedures are given a primary focus of attention because they allow the scientist to combine (his/her) prior knowledge about the problem of interest with newly acquired experimental data. The present paper also considers further topics such as the sensitivity of the likelihood ratio due to uncertainty in parameters and the study of likelihood ratio values obtained for members of particular populations (e.g., individuals with or without exposure to GSR).

The Individualized Genetic Barrier Predicts Treatment Response in a Large Cohort of HIV-1 Infected Patients.

The success of combination antiretroviral therapy is limited by the evolutionary escape dynamics of HIV-1. We used Isotonic Conjunctive Bayesian Networks (I-CBNs), a class of probabilistic graphical models, to describe this process. We employed partial order constraints among viral resistance mutations, which give rise to a limited set of mutational pathways, and we modeled phenotypic drug resistance as monotonically increasing along any escape pathway. Using this model, the individualized genetic barrier (IGB) to each drug is derived as the probability of the virus not acquiring additional mutations that confer resistance. Drug-specific IGBs were combined to obtain the IGB to an entire regimen, which quantifies the virus' genetic potential for developing drug resistance under combination therapy. The IGB was tested as a predictor of therapeutic outcome using between 2,185 and 2,631 treatment change episodes of subtype B infected patients from the Swiss HIV Cohort Study Database, a large observational cohort. Using logistic regression, significant univariate predictors included most of the 18 drugs and single-drug IGBs, the IGB to the entire regimen, the expert rules-based genotypic susceptibility score (GSS), several individual mutations, and the peak viral load before treatment change. In the multivariate analysis, the only genotype-derived variables that remained significantly associated with virological success were GSS and, with 10-fold stronger association, IGB to regimen. When predicting suppression of viral load below 400 cps/ml, IGB outperformed GSS and also improved GSS-containing predictors significantly, but the difference was not significant for suppression below 50 cps/ml. Thus, the IGB to regimen is a novel data-derived predictor of treatment outcome that has potential to improve the interpretation of genotypic drug resistance tests.

Semantic and fuzzy modelling for human behaviour recognition in smart spaces : a case study on ambient assisted living.

Human activity recognition in everyday environments is a critical, but challenging task in Ambient Intelligence applications to achieve proper Ambient Assisted Living, and key challenges still remain to be dealt with to realize robust methods. One of the major limitations of the Ambient Intelligence systems today is the lack of semantic models of those activities on the environment, so that the system can recognize the speci c activity being performed by the user(s) and act accordingly. In this context, this thesis addresses the general problem of knowledge representation in Smart Spaces. The main objective is to develop knowledge-based models, equipped with semantics to learn, infer and monitor human behaviours in Smart Spaces. Moreover, it is easy to recognize that some aspects of this problem have a high degree of uncertainty, and therefore, the developed models must be equipped with mechanisms to manage this type of information. A fuzzy ontology and a semantic hybrid system are presented to allow modelling and recognition of a set of complex real-life scenarios where vagueness and uncertainty are inherent to the human nature of the users that perform it. The handling of uncertain, incomplete and vague data (i.e., missing sensor readings and activity execution variations, since human behaviour is non-deterministic) is approached for the rst time through a fuzzy ontology validated on real-time settings within a hybrid data-driven and knowledgebased architecture. The semantics of activities, sub-activities and real-time object interaction are taken into consideration. The proposed framework consists of two main modules: the low-level sub-activity recognizer and the high-level activity recognizer. The rst module detects sub-activities (i.e., actions or basic activities) that take input data directly from a depth sensor (Kinect). The main contribution of this thesis tackles the second component of the hybrid system, which lays on top of the previous one, in a superior level of abstraction, and acquires the input data from the rst module's output, and executes ontological inference to provide users, activities and their in uence in the environment, with semantics. This component is thus knowledge-based, and a fuzzy ontology was designed to model the high-level activities. Since activity recognition requires context-awareness and the ability to discriminate among activities in di erent environments, the semantic framework allows for modelling common-sense knowledge in the form of a rule-based system that supports expressions close to natural language in the form of fuzzy linguistic labels. The framework advantages have been evaluated with a challenging and new public dataset, CAD-120, achieving an accuracy of 90.1% and 91.1% respectively for low and high-level activities. This entails an improvement over both, entirely data-driven approaches, and merely ontology-based approaches. As an added value, for the system to be su ciently simple and exible to be managed by non-expert users, and thus, facilitate the transfer of research to industry, a development framework composed by a programming toolbox, a hybrid crisp and fuzzy architecture, and graphical models to represent and con gure human behaviour in Smart Spaces, were developed in order to provide the framework with more usability in the nal application. As a result, human behaviour recognition can help assisting people with special needs such as in healthcare, independent elderly living, in remote rehabilitation monitoring, industrial process guideline control, and many other cases. This thesis shows use cases in these areas.

Neural Networks

We present an overview of current research on artificial neural networks, emphasizing a statistical perspective. We view neural networks as parameterized graphs that make probabilistic assumptions about data, and view learning algorithms as methods for finding parameter values that look probable in the light of the data. We discuss basic issues in representation and learning, and treat some of the practical issues that arise in fitting networks to data. We also discuss links between neural networks and the general formalism of graphical models.

Bayesian parameter estimation for latent Markov random fields and social networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.

Mapeamento de ontologias empresariais para modelos de processos de negócio em BPMN, com aplicação em processos de software

Pós-graduação em Ciência da Computação - IBILCE

The Individualized Genetic Barrier Predicts Treatment Response in a Large Cohort of HIV-1 Infected Patients

The success of combination antiretroviral therapy is limited by the evolutionary escape dynamics of HIV-1. We used Isotonic Conjunctive Bayesian Networks (I-CBNs), a class of probabilistic graphical models, to describe this process. We employed partial order constraints among viral resistance mutations, which give rise to a limited set of mutational pathways, and we modeled phenotypic drug resistance as monotonically increasing along any escape pathway. Using this model, the individualized genetic barrier (IGB) to each drug is derived as the probability of the virus not acquiring additional mutations that confer resistance. Drug-specific IGBs were combined to obtain the IGB to an entire regimen, which quantifies the virus' genetic potential for developing drug resistance under combination therapy. The IGB was tested as a predictor of therapeutic outcome using between 2,185 and 2,631 treatment change episodes of subtype B infected patients from the Swiss HIV Cohort Study Database, a large observational cohort. Using logistic regression, significant univariate predictors included most of the 18 drugs and single-drug IGBs, the IGB to the entire regimen, the expert rules-based genotypic susceptibility score (GSS), several individual mutations, and the peak viral load before treatment change. In the multivariate analysis, the only genotype-derived variables that remained significantly associated with virological success were GSS and, with 10-fold stronger association, IGB to regimen. When predicting suppression of viral load below 400 cps/ml, IGB outperformed GSS and also improved GSS-containing predictors significantly, but the difference was not significant for suppression below 50 cps/ml. Thus, the IGB to regimen is a novel data-derived predictor of treatment outcome that has potential to improve the interpretation of genotypic drug resistance tests.

Regularization for sparsity in statistical analysis and machine learning

Pragmatism is the leading motivation of regularization. We can understand regularization as a modification of the maximum-likelihood estimator so that a reasonable answer could be given in an unstable or ill-posed situation. To mention some typical examples, this happens when fitting parametric or non-parametric models with more parameters than data or when estimating large covariance matrices. Regularization is usually used, in addition, to improve the bias-variance tradeoff of an estimation. Then, the definition of regularization is quite general, and, although the introduction of a penalty is probably the most popular type, it is just one out of multiple forms of regularization. In this dissertation, we focus on the applications of regularization for obtaining sparse or parsimonious representations, where only a subset of the inputs is used. A particular form of regularization, L1-regularization, plays a key role for reaching sparsity. Most of the contributions presented here revolve around L1-regularization, although other forms of regularization are explored (also pursuing sparsity in some sense). In addition to present a compact review of L1-regularization and its applications in statistical and machine learning, we devise methodology for regression, supervised classification and structure induction of graphical models. Within the regression paradigm, we focus on kernel smoothing learning, proposing techniques for kernel design that are suitable for high dimensional settings and sparse regression functions. We also present an application of regularized regression techniques for modeling the response of biological neurons. Supervised classification advances deal, on the one hand, with the application of regularization for obtaining a na¨ıve Bayes classifier and, on the other hand, with a novel algorithm for brain-computer interface design that uses group regularization in an efficient manner. Finally, we present a heuristic for inducing structures of Gaussian Bayesian networks using L1-regularization as a filter. El pragmatismo es la principal motivación de la regularización. Podemos entender la regularización como una modificación del estimador de máxima verosimilitud, de tal manera que se pueda dar una respuesta cuando la configuración del problema es inestable. A modo de ejemplo, podemos mencionar el ajuste de modelos paramétricos o no paramétricos cuando hay más parámetros que casos en el conjunto de datos, o la estimación de grandes matrices de covarianzas. Se suele recurrir a la regularización, además, para mejorar el compromiso sesgo-varianza en una estimación. Por tanto, la definición de regularización es muy general y, aunque la introducción de una función de penalización es probablemente el método más popular, éste es sólo uno de entre varias posibilidades. En esta tesis se ha trabajado en aplicaciones de regularización para obtener representaciones dispersas, donde sólo se usa un subconjunto de las entradas. En particular, la regularización L1 juega un papel clave en la búsqueda de dicha dispersión. La mayor parte de las contribuciones presentadas en la tesis giran alrededor de la regularización L1, aunque también se exploran otras formas de regularización (que igualmente persiguen un modelo disperso). Además de presentar una revisión de la regularización L1 y sus aplicaciones en estadística y aprendizaje de máquina, se ha desarrollado metodología para regresión, clasificación supervisada y aprendizaje de estructura en modelos gráficos. Dentro de la regresión, se ha trabajado principalmente en métodos de regresión local, proponiendo técnicas de diseño del kernel que sean adecuadas a configuraciones de alta dimensionalidad y funciones de regresión dispersas. También se presenta una aplicación de las técnicas de regresión regularizada para modelar la respuesta de neuronas reales. Los avances en clasificación supervisada tratan, por una parte, con el uso de regularización para obtener un clasificador naive Bayes y, por otra parte, con el desarrollo de un algoritmo que usa regularización por grupos de una manera eficiente y que se ha aplicado al diseño de interfaces cerebromáquina. Finalmente, se presenta una heurística para inducir la estructura de redes Bayesianas Gaussianas usando regularización L1 a modo de filtro.

Markov blanket-based approach for learning multi-dimensional Bayesian network classifiers: An application to predict the European Quality of Life-5 Dimensions (EQ-5D) from the 39-item Parkinson's Disease Questionnaire (PDQ-39)

Multi-dimensional Bayesian network classifiers (MBCs) are probabilistic graphical models recently proposed to deal with multi-dimensional classification problems, where each instance in the data set has to be assigned to more than one class variable. In this paper, we propose a Markov blanket-based approach for learning MBCs from data. Basically, it consists of determining the Markov blanket around each class variable using the HITON algorithm, then specifying the directionality over the MBC subgraphs. Our approach is applied to the prediction problem of the European Quality of Life-5 Dimensions (EQ-5D) from the 39-item Parkinson’s Disease Questionnaire (PDQ-39) in order to estimate the health-related quality of life of Parkinson’s patients. Fivefold cross-validation experiments were carried out on randomly generated synthetic data sets, Yeast data set, as well as on a real-world Parkinson’s disease data set containing 488 patients. The experimental study, including comparison with additional Bayesian network-based approaches, back propagation for multi-label learning, multi-label k-nearest neighbor, multinomial logistic regression, ordinary least squares, and censored least absolute deviations, shows encouraging results in terms of predictive accuracy as well as the identification of dependence relationships among class and feature variables.