395 research outputs found
Uniform random generation of large acyclic digraphs
Directed acyclic graphs are the basic representation of the structure
underlying Bayesian networks, which represent multivariate probability
distributions. In many practical applications, such as the reverse engineering
of gene regulatory networks, not only the estimation of model parameters but
the reconstruction of the structure itself is of great interest. As well as for
the assessment of different structure learning algorithms in simulation
studies, a uniform sample from the space of directed acyclic graphs is required
to evaluate the prevalence of certain structural features. Here we analyse how
to sample acyclic digraphs uniformly at random through recursive enumeration,
an approach previously thought too computationally involved. Based on
complexity considerations, we discuss in particular how the enumeration
directly provides an exact method, which avoids the convergence issues of the
alternative Markov chain methods and is actually computationally much faster.
The limiting behaviour of the distribution of acyclic digraphs then allows us
to sample arbitrarily large graphs. Building on the ideas of recursive
enumeration based sampling we also introduce a novel hybrid Markov chain with
much faster convergence than current alternatives while still being easy to
adapt to various restrictions. Finally we discuss how to include such
restrictions in the combinatorial enumeration and the new hybrid Markov chain
method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin
Hierarchical Models in the Brain
This paper describes a general model that subsumes many parametric models for
continuous data. The model comprises hidden layers of state-space or dynamic
causal models, arranged so that the output of one provides input to another. The
ensuing hierarchy furnishes a model for many types of data, of arbitrary
complexity. Special cases range from the general linear model for static data to
generalised convolution models, with system noise, for nonlinear time-series
analysis. Crucially, all of these models can be inverted using exactly the same
scheme, namely, dynamic expectation maximization. This means that a single model
and optimisation scheme can be used to invert a wide range of models. We present
the model and a brief review of its inversion to disclose the relationships
among, apparently, diverse generative models of empirical data. We then show
that this inversion can be formulated as a simple neural network and may provide
a useful metaphor for inference and learning in the brain
Computational neuroimaging strategies for single patient predictions
AbstractNeuroimaging increasingly exploits machine learning techniques in an attempt to achieve clinically relevant single-subject predictions. An alternative to machine learning, which tries to establish predictive links between features of the observed data and clinical variables, is the deployment of computational models for inferring on the (patho)physiological and cognitive mechanisms that generate behavioural and neuroimaging responses. This paper discusses the rationale behind a computational approach to neuroimaging-based single-subject inference, focusing on its potential for characterising disease mechanisms in individual subjects and mapping these characterisations to clinical predictions. Following an overview of two main approaches – Bayesian model selection and generative embedding – which can link computational models to individual predictions, we review how these methods accommodate heterogeneity in psychiatric and neurological spectrum disorders, help avoid erroneous interpretations of neuroimaging data, and establish a link between a mechanistic, model-based approach and the statistical perspectives afforded by machine learning
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Combining heterogeneous sources of data for the reverse-engineering of gene regulatory networks
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Gene Regulatory Networks (GRNs) represent how genes interact in various cellular processes by describing how the expression level, or activity, of genes can affect the expression of the other genes. Reverse-engineering GRN models can help biologists understand and gain insight into genetic conditions and diseases. Recently, the increasingly widespread use of DNA microarrays, a high-throughput technology that allows the expression of thousands of genes to be measured simultaneously in biological experiments, has led to many datasets of gene expression measurements becoming publicly available and a subsequent explosion of research in the reverse-engineering of GRN models. However, microarray technology has a number of limitations as a data source for the modelling of GRNs, due to concerns over its reliability and the reproducibility of experimental results. The underlying theme of the research presented in this thesis is the incorporation of multiple sources and different types of data into techniques for reverse-engineering or learning GRNs from data. By drawing on many data sources, the resulting network models should be more robust, accurate and reliable than models that have been learnt using a single data source. This is achieved by focusing on two main strands of research. First, the thesis presents some of the earliest work in the incorporation of prior knowledge that has been generated from a large body of scientific papers, for Bayesian network based GRN models. Second, novel methods for the use of multiple microarray datasets to produce Bayesian network based GRN models are introduced. Empirical evaluations are used to show that the incorporation of literature-based prior knowledge and combining multiple microarray datasets can provide an improvement, when compared to the use of a single microarray dataset, for the reverse-engineering of Bayesian network based GRN models
Expert judgement for dependence in probabilistic modelling : a systematic literature review and future research directions
Many applications in decision making under uncertainty and probabilistic risk assessment require the assessment of mul- tiple, dependent uncertain quantities, so that in addition to marginal distributions, interdependence needs to be modelled in order to properly understand the overall risk. Nevertheless, relevant historical data on dependence information are often not available or simply too costly to obtain. In this case, the only sensible option is to elicit this uncertainty through the use of expert judgements. In expert judgement studies, a structured approach to eliciting variables of interest is desirable so that their assessment is methodologically robust. One of the key decisions during the elicitation process is the form in which the uncertainties are elicited. This choice is subject to various, potentially con icting, desiderata related to e.g. modelling convenience, coherence between elicitation parameters and the model, combining judgements, and the assessment burden for the experts. While extensive and systematic guidance to address these considerations exists for single variable uncertainty elicitation, for higher dimensions very little such guidance is available. Therefore this paper o ers a systematic review of the current literature on eliciting dependence. The literature on the elicitation of dependence parameters such as correlations is presented alongside commonly used dependence models and experience from case studies. From this, guidance about the strategy for dependence assessment is given and gaps in the existing research are identi ed to determine future directions for structured methods to elicit dependence
Dynamic models of brain imaging data and their Bayesian inversion
This work is about understanding the dynamics of neuronal systems, in particular with
respect to brain connectivity. It addresses complex neuronal systems by looking at
neuronal interactions and their causal relations. These systems are characterized using
a generic approach to dynamical system analysis of brain signals - dynamic causal
modelling (DCM). DCM is a technique for inferring directed connectivity among
brain regions, which distinguishes between a neuronal and an observation level. DCM
is a natural extension of the convolution models used in the standard analysis of
neuroimaging data. This thesis develops biologically constrained and plausible
models, informed by anatomic and physiological principles. Within this framework, it
uses mathematical formalisms of neural mass, mean-field and ensemble dynamic
causal models as generative models for observed neuronal activity. These models
allow for the evaluation of intrinsic neuronal connections and high-order statistics of
neuronal states, using Bayesian estimation and inference. Critically it employs
Bayesian model selection (BMS) to discover the best among several equally plausible
models. In the first part of this thesis, a two-state DCM for functional magnetic
resonance imaging (fMRI) is described, where each region can model selective
changes in both extrinsic and intrinsic connectivity. The second part is concerned with
how the sigmoid activation function of neural-mass models (NMM) can be
understood in terms of the variance or dispersion of neuronal states. The third part
presents a mean-field model (MFM) for neuronal dynamics as observed with
magneto- and electroencephalographic data (M/EEG). In the final part, the MFM is
used as a generative model in a DCM for M/EEG and compared to the NMM using
Bayesian model selection
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