Learning the structure of dynamic Bayesian networks from time series and steady state measurements

Lähdesmäki, Harri; Shmulevich, Ilya

doi:10.1007/s10994-008-5053-y

Cited by 33 publications

(20 citation statements)

References 37 publications

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“…The idea of Markov Chain Monte Carlo (MCMC) method [2,3] is to construct a Markov chain in which a new model * M is generated only in terms of the previous one M . It will produce a chain of models that converge to the target distribution eventually.…”

Section: Markov Chain Monte Carlo Methodsmentioning

confidence: 99%

“…In this paper, we use the approach to learn DBN based on MCMC method [2,3] to construct the structure of TQPN. Similarly, we also assume to be first order Markov and discrete model.…”

Section: Learning the Structure Of Tqpnmentioning

confidence: 99%

“…There are many kinds of networks which can be used to represent the probabilistic knowledge, such as Bayesian Networks (BNs) [1], Dynamic Bayesian Networks (DBNs) [2,3], Qualitative Probabilistic Networks (QPNs) [4] and Temporal Qualitative Probabilistic Networks (TQPNs) [5].…”

Section: Introductionmentioning

confidence: 99%

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Integration of Multiple Temporal Qualitative Probabilistic Networks in Time Series Environments

Lv¹,

Liao

2010

IJIES

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Abstract:The integration of uncertain information from different time sources is a crucial issue in various applications. In this paper, we propose an integration method of multiple Temporal Qualitative Probabilistic Networks (TQPNs) in time series environments. First, we present the method for learning TQPN from time series data. The TQPN's structure is constructed using Dynamic Bayesian Networks learning based on Markov Chain Monte Carlo. Furthermore, the corresponding qualitative influences are obtained by the conditional probabilities. Secondly, based on rough set theory, we integrate multiple TQPNs into a single QPN that preserves as much information as possible. Specifically, we take the rough-set-based dependency degree as the strength of qualitative influence, and then make the rules to solve the ambiguities reduction and cycles deletion problems which arise from the integration of different TQPNs. Finally, we verify the feasibility of the integration method by the simulation experiments.

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Section: Markov Chain Monte Carlo Methodsmentioning

confidence: 99%

“…In this paper, we use the approach to learn DBN based on MCMC method [2,3] to construct the structure of TQPN. Similarly, we also assume to be first order Markov and discrete model.…”

Section: Learning the Structure Of Tqpnmentioning

confidence: 99%

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Integration of Multiple Temporal Qualitative Probabilistic Networks in Time Series Environments

Lv¹,

Liao

2010

IJIES

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“…Husmeier (2003), Perrin et al (2003), and Rangel et al (2004) were the first to study genomic data with dynamic Bayesian networks and to propose inference procedures suitable for use with microarray data. Bayesian learning procedures are discussed in (Lähdesmäki and Shmulevich 2008). A general state-space framework that allows to model non-stationary time course data is given in Grzegorczyk and Husmeier (2009).…”

Section: Dynamic Bayesian Networkmentioning

confidence: 99%

Introduction to Graphical Modelling

Scutari

Strimmer²

2011

Handbook of Statistical Systems Biology

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The aim of this chapter is twofold. In the first part (Sections 12.1, 12.2 and 12.3) we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures. In particular we will develop Markov networks (also known as Markov random fields) and Bayesian networks, which are the subjects of most past and current literature on graphical models. In the second part (Section 12.4) we will review some applications of graphical models in systems biology. Graphical Structures and Random VariablesGraphical models are a class of statistical models which combine the rigour of a probabilistic approach with the intuitive representation of relationships given by graphs. They are composed by two parts:1. a set X = {X 1 , X 2 , . . . , X p } of random variables describing the quantities of interest. The statistical distribution of X is called the global distribution of the data, while the components it factorises into are called local distributions.2. a graph G = (V, E) in which each vertex v ∈ V, also called a node, is associated with one of the random variables in X (they are usually referred to interchangeably). Edges e ∈ E, also called links, are used to express the dependence structure of the data (the set of dependence relationships among Graph representations meet our earlier requirements of explicitness, saliency, and stability. The links in the graph permit us to express directly and quantitatively the dependence relationships, and the graph topology displays these relationships explicitly and preserves them, under any assignment of numerical parameters.The nature of the link outlined above between the dependence structure of the data and its graphical representation is given again by Pearl (1988) in terms of conditional independence (denoted with ⊥ ⊥ P ) and graphical separation (denoted with ⊥ ⊥ G ).Definition 12.1.1 A graph G is a dependency map (or D-map) of the probabilistic dependence structure P of X if there is a one-to-one correspondence between the random variables in X and the nodes V of G, such that for all disjoint subsets A, B, C of X we have Similarly, G is an independency map (or I-map) of P ifG is said to be a perfect map of P if it is both a D-map and an I-map, that is (12.3) and in this case P is said to be isomorphic to G.Note that this definition does not depend on a particular characterisation of graphical separation, and therefore on the type of graph used in the graphical model. In fact both Markov networks (Whittaker 1990) and Bayesian networks (Pearl 1988), which are by far the two most common classes of graphical models treated in literature, are defined as minimal I-maps even though the former use undirected graphs an the latter use directed acyclic graphs. Minimality requires that, if the dependence structure P of X can be expressed by multiple graphs, we must use the one with the minimum number of edges; if any further edge is removed then the graph is no longer an I-map of P...

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“…There are some complex temporal and qualitative causal relationships in these data. The causal relationships can be effectively represented by a directed graphical models, such as Bayesian Networks (BN) [1], Dynamic Bayesian Networks (DBN) [2], [3], Qualitative Probabilistic Networks (QPN) [4], and Temporal Qualitative Probabilistic Networks (TQPN) [5].…”

Section: Introductionmentioning

confidence: 99%

Learning Temporal Qualitative Probabilistic Networks from Data

Liao

2009

2009 Second International Conference on Intelligent Networks and Intelligent Systems

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Temporal Qualitative Probabilistic Networks (TQPN) have become a standard tool for modeling various qualitative and temporal causal phenomena. In this paper, we address the issue of TQPN learning from time series data. The structure of TQPN can be constructed by learning Dynamic Bayesian Networks (DBN) based on Markov Chain Monte Carlo (MCMC) method. Specifically, since the causal relationships between variables always follow the time flow, we only consider the causal relationships existing between adjacent time slices. Furthermore, we learn the corresponding relationships of both qualitative influences and qualitative synergies with the conditional probability orderings, and represent the conditional probabilities with the frequency formats. Experiment results illuminate that the method is promising.

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Learning the structure of dynamic Bayesian networks from time series and steady state measurements

Cited by 33 publications

References 37 publications

Integration of Multiple Temporal Qualitative Probabilistic Networks in Time Series Environments

Integration of Multiple Temporal Qualitative Probabilistic Networks in Time Series Environments

Introduction to Graphical Modelling

Learning Temporal Qualitative Probabilistic Networks from Data

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