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High dimensional graphs and variable selection with the Lasso
 ANNALS OF STATISTICS
, 2006
"... The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso is a ..."
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Cited by 751 (23 self)
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The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso is a computationally attractive alternative to standard covariance selection for sparse highdimensional graphs. Neighborhood selection estimates the conditional independence restrictions separately for each node in the graph and is hence equivalent to variable selection for Gaussian linear models. We show that the proposed neighborhood selection scheme is consistent for sparse highdimensional graphs. Consistency hinges on the choice of the penalty parameter. The oracle value for optimal prediction does not lead to a consistent neighborhood estimate. Controlling instead the probability of falsely joining some distinct connectivity components of the graph, consistent estimation for sparse graphs is achieved (with exponential rates), even when the number of variables grows as the number of observations raised to an arbitrary power.
A SINful approach to Gaussian graphical model selection
 Journal of Statistical Planning and Inference
"... Abstract. Multivariate Gaussian graphical models are defined in terms of Markov properties, i.e., conditional independences associated with the underlying graph. Thus, model selection can be performed by testing these conditional independences, which are equivalent to specified zeroes among certain ..."
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Cited by 36 (5 self)
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Abstract. Multivariate Gaussian graphical models are defined in terms of Markov properties, i.e., conditional independences associated with the underlying graph. Thus, model selection can be performed by testing these conditional independences, which are equivalent to specified zeroes among certain (partial) correlation coefficients. For concentration graphs, covariance graphs, acyclic directed graphs, and chain graphs (both LWF and AMP), we apply Fisher’s ztransformation, ˇ Sidák’s correlation inequality, and Holm’s stepdown procedure, to simultaneously test the multiple hypotheses obtained from the Markov properties. This leads to a simple method for model selection that controls the overall error rate for incorrect edge inclusion. In practice, we advocate partitioning the simultaneous pvalues into three disjoint sets, a significant set S, an indeterminate set I, and a nonsignificant set N. Then our SIN model selection method selects two graphs, a graph whose edges correspond to the union of S and I, and a more conservative graph whose edges correspond to S only. Prior information about the presence and/or absence of particular edges can be incorporated readily. 1.
Multiple testing and error control in Gaussian graphical model selection
 Statistical Science
"... Abstract. Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the pattern of edges in the graph into a pattern of cond ..."
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Cited by 30 (4 self)
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Abstract. Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the pattern of edges in the graph into a pattern of conditional independences that is imposed on the variables ’ joint distribution. Focusing on Gaussian models, we review classical graphical models. For these models the defining conditional independences are equivalent to vanishing of certain (partial) correlation coefficients associated with individual edges that are absent from the graph. Hence, Gaussian graphical model selection can be performed by multiple testing of hypotheses about vanishing (partial) correlation coefficients. We show and exemplify how this approach allows one to perform model selection while controlling error rates for incorrect edge inclusion. Key words and phrases: Acyclic directed graph, Bayesian network, bidirected graph, chain graph, concentration graph, covariance graph, DAG, graphical model, multiple testing, undirected graph. 1.
Graphical models for marked point processes based on local independence
 J.R Statist. Soc. B
"... A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so–called local independencies, meaning that the intensities of certain types of events are independent of some (but not necessarilly all) events in the past. This dynami ..."
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Cited by 28 (4 self)
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A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so–called local independencies, meaning that the intensities of certain types of events are independent of some (but not necessarilly all) events in the past. This dynamic concept of independence is asymmetric, similar to Granger non–causality, so that the corresponding local independence graphs differ considerably from classical graphical models. Hence a new notion of graph separation, called δ–separation, is introduced and implications for the underlying model as well as for likelihood inference are explored. Benefits regarding facilitation of reasoning about and understanding of dynamic dependencies as well as computational simplifications are discussed.
An Estimation of Distribution Algorithm for Nurse Scheduling
 Annals of Operations Research, in print
, 2006
"... Abstract Schedules can be built in a similar way to a human scheduler by using a set of rules that involve domain knowledge. This paper presents an Estimation of Distribution Algorithm (EDA) for the nurse scheduling problem, which involves choosing a suitable scheduling rule from a set for the assig ..."
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Cited by 25 (8 self)
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Abstract Schedules can be built in a similar way to a human scheduler by using a set of rules that involve domain knowledge. This paper presents an Estimation of Distribution Algorithm (EDA) for the nurse scheduling problem, which involves choosing a suitable scheduling rule from a set for the assignment of each nurse. Unlike previous work that used Genetic Algorithms (GAs) to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The EDA is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.
The TM Algorithm for Maximising a Conditional Likelihood Function
 Biometrika
, 2001
"... This article describes an algorithm for maximising a conditional likelihood function when the corresponding unconditional likelihood function is more easily maximised. The algorithm is similar to the EM algorithm but dierent as the parameters rather than the data are augmented and the conditional ra ..."
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Cited by 14 (0 self)
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This article describes an algorithm for maximising a conditional likelihood function when the corresponding unconditional likelihood function is more easily maximised. The algorithm is similar to the EM algorithm but dierent as the parameters rather than the data are augmented and the conditional rather than the marginal likelihood function is maximised. In exponential families the algorithm takes a particular simple form which is computationally very close to the EM algorithm. The algorithm alternates between a Tstep which calculates a tilted version of the unconditional likelihood function and an Mstep which maximises it. The algorithm applies to mixed graphical chain models (Lauritzen & Wermuth, 1989) and their generalisations (Edwards, 1990), and was developed with these in mind, but it may have applications beyond these. The algorithm has been implemented in the most recent version of the MIM software (Edwards, 2000), where it was named the ME algorithm. The name has been chang
A Bayesian optimization algorithm for the nurse scheduling problem
 In Proceedings of 2003 congress on evolutionary computation (CEC2003
, 2003
"... Copyright and reuse: The Nottingham ePrints service makes this work by researchers of the University of Nottingham available open access under the following conditions. This article is made available under the University of Nottingham End User licence and may be reused according to the conditions of ..."
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Cited by 11 (1 self)
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Copyright and reuse: The Nottingham ePrints service makes this work by researchers of the University of Nottingham available open access under the following conditions. This article is made available under the University of Nottingham End User licence and may be reused according to the conditions of the licence. For more details see:
Wishart distributions for decomposable covariance graph models, Ann. Statist
, 2010
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Exploiting parameter domain knowledge for learning in Bayesian networks
 Carnegie Mellon University
, 2005
"... implied, of any sponsoring institution, the U.S. government or any other entity. ..."
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Cited by 9 (1 self)
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implied, of any sponsoring institution, the U.S. government or any other entity.