arXiv subjects

Jim Q. Smith

Publications and source records attributed to Jim Q. Smith.

53 records · Page 3Linked to original sources

arXiv2016

Sensitivity analysis, multilinearity and beyond

Sensitivity methods for the analysis of the outputs of discrete Bayesian networks have been extensively studied and implemented in different software packages. These methods usually focus on the study of sensitivity functions and on the impact of a parameter change to the Chan-Darwiche distance. Although not fully recognized, the majority of these results heavily rely on the multilinear structure of atomic probabilities in terms of the conditional probability parameters associated with this type of network. By defining a statistical model through the polynomial expression of its associated defining conditional probabilities, we develop a unifying approach to sensitivity methods applicable to a large suite of models including extensions of Bayesian networks, for instance context-specific and dynamic ones, and chain event graphs. By then focusing on models whose defining polynomial is multilinear, our algebraic approach enables us to prove that the Chan-Darwiche distance is minimized for a certain class of multi-parameter contemporaneous variations when parameters are proportionally covaried.

cs.AI↗

arXiv2016

The correlation space of Gaussian latent tree models and model selection without fitting

We provide a complete description of possible covariance matrices consistent with a Gaussian latent tree model for any tree. We then present techniques for utilising these constraints to assess whether observed data is compatible with that Gaussian latent tree model. Our method does not require us first to fit such a tree. We demonstrate the usefulness of the inverse-Wishart distribution for performing preliminary assessments of tree-compatibility using semialgebraic constraints. Using results from Drton et al. (2008) we then provide the appropriate moments required for test statistics for assessing adherence to these equality constraints. These are shown to be effective even for small sample sizes and can be easily adjusted to test either the entire model or only certain macrostructures hypothesized within the tree. We illustrate our exploratory tetrad analysis using a linguistic application and our confirmatory tetrad analysis using a biological application.

stat.ME↗

arXiv2015

Coherent Frameworks for Statistical Inference serving Integrating Decision Support Systems

A subjective expected utility policy making centre, managing complex, dynamic systems, needs to draw on the expertise of a variety of disparate panels of experts and integrate this information coherently. To achieve this, diverse supporting probabilistic models need to be networked together, the output of one model providing the input to the next. In this paper we provide a technology for designing an integrating decision support system and to enable the centre to explore and compare the efficiency of different candidate policies. We develop a formal statistical methodology to underpin this tool. In particular, we derive sufficient conditions that ensure inference remains coherent before and after relevant evidence is accommodated into the system. The methodology is illustrated throughout using examples drawn from two decision support systems: one designed for nuclear emergency crisis management and the other to support policy makers in addressing the complex challenges of food poverty in the UK.

stat.ME↗

arXiv2015

A New Method for tackling Asymmetric Decision Problems

Chain Event Graphs are probabilistic graphical models designed especially for the analysis of discrete statistical problems which do not admit a natural product space structure. We show here how they can be used for decision analysis, and describe an optimal decision strategy based on an efficient local computation message passing scheme. We briefly describe a method for producing a parsimonious decision CEG, analogous to the parsimonious ID, and touch upon the CEG-analogues of Shachter's barren node deletion and arc reversal for ID-based solution.

stat.ME↗

arXiv2015

A Separation Theorem for Chain Event Graphs

Bayesian Networks (BNs) are popular graphical models for the representation of statistical problems embodying dependence relationships between a number of variables. Much of this popularity is due to the d-separation theorem of Pearl and Lauritzen, which allows an analyst to identify the conditional independence statements that a model of the problem embodies using only the topology of the graph. However for many problems the complete model dependence structure cannot be depicted by a BN. The Chain Event Graph (CEG) was introduced for these types of problem. In this paper we introduce a separation theorem for CEGs, analogous to the d-separation theorem for BNs, which likewise allows an analyst to identify the conditional independence structure of their model from the topology of the graph.

stat.ME↗

arXiv2014

Exact Estimation of Multiple Directed Acyclic Graphs

This paper considers the problem of estimating the structure of multiple related directed acyclic graph (DAG) models. Building on recent developments in exact estimation of DAGs using integer linear programming (ILP), we present an ILP approach for joint estimation over multiple DAGs, that does not require that the vertices in each DAG share a common ordering. Furthermore, we allow also for (potentially unknown) dependency structure between the DAGs. Results are presented on both simulated data and fMRI data obtained from multiple subjects.

stat.ML↗

arXiv2014

Estimating causal structure using conditional DAG models

This paper considers inference of causal structure in a class of graphical models called "conditional DAGs". These are directed acyclic graph (DAG) models with two kinds of variables, primary and secondary. The secondary variables are used to aid in estimation of causal relationships between the primary variables. We give causal semantics for this model class and prove that, under certain assumptions, the direction of causal influence is identifiable from the joint observational distribution of the primary and secondary variables. A score-based approach is developed for estimation of causal structure using these models and consistency results are established. Empirical results demonstrate gains compared with formulations that treat all variables on an equal footing, or that ignore secondary variables. The methodology is motivated by applications in molecular biology and is illustrated here using simulated data and in an analysis of proteomic data from the Cancer Genome Atlas.

stat.ME↗

arXiv2014

Gaussian Tree Constraints Applied to Acoustic Linguistic Functional Data

Evolutionary models of languages are usually considered to take the form of trees. With the development of so-called tree constraints the plausibility of the tree model assumptions can be addressed by checking whether the moments of observed variables lie within regions consistent with trees. In our linguistic application, the data set comprises acoustic samples (audio recordings) from speakers of five Romance languages or dialects. We wish to assess these functional data for compatibility with a hereditary tree model at the language level. A novel combination of canonical function analysis (CFA) with a separable covariance structure provides a method for generating a representative basis for the data. This resulting basis is formed of components which emphasize language differences whilst maintaining the integrity of the observational language-groupings. A previously unexploited Gaussian tree constraint is then applied to component-by-component projections of the data to investigate adherence to an evolutionary tree. The results indicate that while a tree model is unlikely to be suitable for modeling all aspects of the acoustic linguistic data, certain features of the spoken Romance languages highlighted by the separable-CFA basis may indeed be suitably modeled as a tree.

stat.AP↗

arXiv2013

On the Geometry of Bayesian Graphical Models with Hidden Variables

In this paper we investigate the geometry of the likelihood of the unknown parameters in a simple class of Bayesian directed graphs with hidden variables. This enables us, before any numerical algorithms are employed, to obtain certain insights in the nature of the unidentifiability inherent in such models, the way posterior densities will be sensitive to prior densities and the typical geometrical form these posterior densities might take. Many of these insights carry over into more complicated Bayesian networks with systematic missing data.

cs.LG↗

arXiv2013

Approximate Learning in Complex Dynamic Bayesian Networks

In this paper we extend the work of Smith and Papamichail (1999) and present fast approximate Bayesian algorithms for learning in complex scenarios where at any time frame, the relationships between explanatory state space variables can be described by a Bayesian network that evolve dynamically over time and the observations taken are not necessarily Gaussian. It uses recent developments in approximate Bayesian forecasting methods in combination with more familiar Gaussian propagation algorithms on junction trees. The procedure for learning state parameters from data is given explicitly for common sampling distributions and the methodology is illustrated through a real application. The efficiency of the dynamic approximation is explored by using the Hellinger divergence measure and theoretical bounds for the efficacy of such a procedure are discussed.

cs.LG↗

arXiv2012

The Dependence of Routine Bayesian Model Selection Methods on Irrelevant Alternatives

Bayesian methods - either based on Bayes Factors or BIC - are now widely used for model selection. One property that might reasonably be demanded of any model selection method is that if a model ${M}_{1}$ is preferred to a model ${M}_{0}$, when these two models are expressed as members of one model class $\mathbb{M}$, this preference is preserved when they are embedded in a different class $\mathbb{M}'$. However, we illustrate in this paper that with the usual implementation of these common Bayesian procedures this property does not hold true even approximately. We therefore contend that to use these methods it is first necessary for there to exist a "natural" embedding class. We argue that in any context like the one illustrated in our running example of Bayesian model selection of binary phylogenetic trees there is no such embedding.

stat.ME↗

arXiv2012

Propagation using Chain Event Graphs

A Chain Event Graph (CEG) is a graphial model which designed to embody conditional independencies in problems whose state spaces are highly asymmetric and do not admit a natural product structure. In this paer we present a probability propagation algorithm which uses the topology of the CEG to build a transporter CEG. Intriungly,the transporter CEG is directly analogous to the triangulated Bayesian Network (BN) in the more conventional junction tree propagation algorithms used with BNs. The propagation method uses factorization formulae also analogous to (but different from) the ones using potentials on cliques and separators of the BN. It appears that the methods will be typically more efficient than the BN algorithms when applied to contexts where there is significant asymmetry present.

cs.AI↗

arXiv2012

Tree cumulants and the geometry of binary tree models

In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on the theory of partially ordered sets allows us to obtain a convenient parametrization of this model class. The construction of the proposed coordinate system mirrors the combinatorial definition of cumulants. A simple product-like form of the resulting parametrization gives insight into identifiability issues associated with this model class. In particular, we provide necessary and sufficient conditions for such a model to be identified up to the switching of labels of the inner nodes. When these conditions hold, we give explicit formulas for the parameters of the model. Whenever the model fails to be identified, we use the new parametrization to describe the geometry of the unidentified parameter space. We illustrate these results using a simple example.

math.ST↗

arXiv2011

Implicit inequality constraints in a binary tree model

In this paper we investigate the geometry of a discrete Bayesian network whose graph is a tree all of whose variables are binary and the only observed variables are those labeling its leaves. We provide the full geometric description of these models which is given by a set of polynomial equations together with a set of complementary implied inequalities induced by the positivity of probabilities on hidden variables. The phylogenetic invariants given by the equations can be useful in the construction of simple diagnostic tests. However, in this paper we point out the importance of also incorporating the associated inequalities into any statistical analysis. The full characterization of these inequality constraints derived in this paper helps us determine how and why routine statistical methods can break down for this model class.

math.ST↗

arXiv2010

Semi-parametric dynamic time series modelling with applications to detecting neural dynamics

This paper illustrates novel methods for nonstationary time series modeling along with their applications to selected problems in neuroscience. These methods are semi-parametric in that inferences are derived by combining sequential Bayesian updating with a non-parametric change-point test. As a test statistic, we propose a Kullback--Leibler (KL) divergence between posterior distributions arising from different sets of data. A closed form expression of this statistic is derived for exponential family models, whereas standard Markov chain Monte Carlo output is used to approximate its value and its critical region for more general models. The behavior of one-step ahead predictive distributions under our semi-parametric framework is described analytically for a dynamic linear time series model. Conditions under which our approach reduces to fully parametric state-space modeling are also illustrated. We apply our methods to estimating the functional dynamics of a wide range of neural data, including multi-channel electroencephalogram recordings, longitudinal behavioral experiments and in-vivo multiple spike trains recordings. The estimated dynamics are related to the presentation of visual stimuli, to the evaluation of a learning performance and to changes in the functional connections between neurons over a sequence of experiments.

stat.AP↗

arXiv2009

Bayesian MAP Model Selection of Chain Event Graphs

The class of chain event graph models is a generalisation of the class of discrete Bayesian networks, retaining most of the structural advantages of the Bayesian network for model interrogation, propagation and learning, while more naturally encoding asymmetric state spaces and the order in which events happen. In this paper we demonstrate how with complete sampling, conjugate closed form model selection based on product Dirichlet priors is possible, and prove that suitable homogeneity assumptions characterise the product Dirichlet prior on this class of models. We demonstrate our techniques using two educational examples.

stat.ME↗

arXiv2007

The causal manipulation of chain event graphs

Discrete Bayesian Networks have been very successful as a framework both for inference and for expressing certain causal hypotheses. In this paper we present a class of graphical models called the chain event graph (CEG) models, that generalises the class of discrete BN models. It provides a flexible and expressive framework for representing and analysing the implications of causal hypotheses, expressed in terms of the effects of a manipulation of the generating underlying system. We prove that, as for a BN, identifiability analyses of causal effects can be performed through examining the topology of the CEG graph, leading to theorems analogous to the back-door theorem for the BN.

stat.ME↗