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  • 1.
    Bendtsen, Marcus
    et al.
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, Faculty of Science & Engineering.
    Peña, Jose M.
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, Faculty of Science & Engineering.
    Gated Bayesian Networks for Algorithmic Trading2016In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 69, p. 58-80Article in journal (Refereed)
    Abstract [en]

    Gated Bayesian networks (GBNs) are a recently introduced extension of Bayesian networks that aims to model dynamical systems consisting of several distinct phases. In this paper, we present an algorithm for semi-automatic learning of GBNs. We use the algorithm to learn GBNs that output buy and sell decisions for use in algorithmic trading systems. We show how using the learnt GBNs can substantially lower risks towards invested capital, while at the same time generating similar or better rewards, compared to the benchmark investment strategy buy-and-hold.

  • 2.
    Dunin-Keplicz, Barbara
    et al.
    University of Warsaw.
    Anh Nguyen, Linh
    University of Warsaw.
    Szalas, Andrzej
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    Tractable approximate knowledge fusion using the Horn fragment of serial propositional dynamic logic2010In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 51, no 3, p. 346-362Article in journal (Refereed)
    Abstract [en]

    In this paper we investigate a technique for fusing approximate knowledge obtained from distributed, heterogeneous information sources. This issue is substantial, e.g., in modeling multiagent systems, where a group of loosely coupled heterogeneous agents cooperate in achieving a common goal. Information exchange, leading ultimately to knowledge fusion, is a natural and vital ingredient of this process. We use a generalization of rough sets and relations [30], which depends on allowing arbitrary similarity relations. The starting point of this research is [6], where a framework for knowledge fusion in multiagent systems is introduced. Agents individual perceptual capabilities are represented by similarity relations, further aggregated to express joint capabilities of teams, This aggregation, expressing a shift from individual to social level of agents activity, has been formalized by means of dynamic logic. The approach of Doherty et al. (2007) [6] uses the full propositional dynamic logic, which does not guarantee tractability of reasoning. Our idea is to adapt the techniques of Nguyen [26-28] to provide an engine for tractable approximate database querying restricted to a Horn fragment of serial dynamic logic. We also show that the obtained formalism is quite powerful in applications.

  • 3.
    Etminani, Kobra
    et al.
    Ferdowsi University of Mashhad, Iran.
    Naghibzadeh, Mahmoud
    Ferdowsi University of Mashhad, Iran.
    Peña, Jose M.
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, The Institute of Technology.
    DemocraticOP: A Democratic way of aggregating Bayesian network parameters2013In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 54, no 5, p. 602-614Article in journal (Refereed)
    Abstract [en]

    When there are several experts in a specific domain, each may believe in a different Bayesian network (BN) representation of the domain. In order to avoid having to work with several BNs, it is desirable to aggregate them into a single BN. One way of finding the aggregated BN is to start by finding the structure, and then find the parameters. In this paper, we focus on the second step, assuming that the structure has been found by some previous method.

    DemocraticOP is a new way of combining experts’ parameters in a model. The logic behind this approach is borrowed from the concept of democracy in the real world. We assume that there is a ground truth and that each expert represents a deviation from it - the goal is to try to find the ground truth based on the experts’ opinions. If the experts do not agree, then taking a simple average of their opinions (as occurs in classical aggregation functions such as LinOP and LogOP) is flawed. Instead, we believe it is better to identify similar opinions through clustering, and then apply averaging, or any other aggregation function, over the cluster with the highest number of members to obtain the aggregated parameters that are closest to the ground truth. In other words, respect the majority as is done in democratic societies instead of averaging over all experts’ parameters. The new approach is implemented and tested over several BNs with different numbers of variables and parameters, and with different numbers of experts. The results show that DemocraticOP outperforms two commonly used methods, LinOP and LogOP, in three key metrics: the average of absolute value of the difference between the true probability distribution and the one corresponding to the aggregated parameters, Kullback-Leibler divergence, and running time.

  • 4.
    Pena, Jose M
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, Faculty of Science & Engineering.
    Correction: Marginal AMP chain graphs (vol 55, pg 1185, 2014)2015In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 66, p. 139-140Article in journal (Other academic)
    Abstract [en]

    n/a

  • 5.
    Pena, Jose M
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, The Institute of Technology.
    Learning AMP chain graphs and some marginal models thereof under faithfulness2014In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 55, no 4, p. 1011-1021Article in journal (Refereed)
    Abstract [en]

    This paper deals with chain graphs under the Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. Moreover, we show that the extension of Meeks conjecture to AMP chain graphs does not hold, which compromises the development of efficient and correct score + search learning algorithms under assumptions weaker than faithfulness. We also study the problem of how to represent the result of marginalizing out some nodes in an AMP CG. We introduce a new family of graphical models that solves this problem partially. We name this new family maximal covariance-concentration graphs because it includes both covariance and concentration graphs as subfamilies.

  • 6.
    Pena, Jose M
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, The Institute of Technology.
    Marginal AMP chain graphs2014In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 55, no 5, p. 1185-1206Article in journal (Refereed)
    Abstract [en]

    We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph under marginalization of some of its nodes. However, MAMP chain graphs do not only subsume AMP chain graphs but also multivariate regression chain graphs. We describe global and pairwise Markov properties for MAMP chain graphs and prove their equivalence for compositional graphoids. We also characterize when two MAMP chain graphs are Markov equivalent. For Gaussian probability distributions, we also show that every MAMP chain graph is Markov equivalent to some directed and acyclic graph with deterministic nodes under marginalization and conditioning on some of its nodes. This is important because it implies that the independence model represented by a MAMP chain graph can be accounted for by some data generating process that is partially observed and has selection bias. Finally, we modify MAMP chain graphs so that they are closed under marginalization for Gaussian probability distributions. This is a desirable feature because it guarantees parsimonious models under marginalization.

  • 7.
    Pena, Jose M
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Representing independence models with elementary triplets2017In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 88, p. 587-601Article in journal (Refereed)
    Abstract [en]

    In an independence model, the triplets that represent conditional independences between singletons are called elementary. It is known that the elementary triplets represent the independence model unambiguously under some conditions. In this paper, we show how this representation helps performing some operations with independence models, such as finding the dominant triplets or a minimal independence map of an independence model, or computing the union or intersection of a pair of independence models, or performing causal reasoning. For the latter, we rephrase in terms of conditional independences some of Pearls results for computing causal effects. (C) 2016 Elsevier Inc. All rights reserved.

  • 8.
    Pena, Jose M
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Bendtsen, Marcus
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, Faculty of Science & Engineering.
    Causal effect identification in acyclic directed mixed graphs and gated models2017In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 90, p. 56-75Article in journal (Refereed)
    Abstract [en]

    We introduce a new family of graphical models that consists of graphs with possibly directed, undirected and bidirected edges but without directed cycles. We show that these models are suitable for representing causal models with additive error terms. We provide a set of sufficient graphical criteria for the identification of arbitrary causal effects when the new models contain directed and undirected edges but no bidirected edge. We also provide a necessary and sufficient graphical criterion for the identification of the causal effect of a single variable on the rest of the variables. Moreover, we develop an exact algorithm for learning the new models from observational and interventional data via answer set programming. Finally, we introduce gated models for causal effect identification, a new family of graphical models that exploits context specific independences to identify additional causal effects. (C) 2017 Elsevier Inc. All rights reserved.

  • 9.
    Pena, Jose M
    et al.
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, Faculty of Science & Engineering.
    Gomez-Olmedo, Manuel
    University of Granada, Spain.
    Learning marginal AMP chain graphs under faithfulness revisited2016In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 68, p. 108-126Article in journal (Refereed)
    Abstract [en]

    Marginal AMP chain graphs are a recently introduced family of models that is based on graphs that may have undirected, directed and bidirected edges. They unify and generalize the AMP and the multivariate regression interpretations of chain graphs. In this paper, we present a constraint based algorithm for learning a marginal AMP chain graph from a probability distribution which is faithful to it. We show that the marginal AMP chain graph returned by our algorithm is a distinguished member of its Markov equivalence class. We also show that our algorithm performs well in practice. Finally, we show that the extension of Meeks conjecture to marginal AMP chain graphs does not hold, which compromises the development of efficient and correct score+search learning algorithms under assumptions weaker than faithfulness. (C) 2015 Elsevier Inc. All rights reserved.

  • 10.
    Pernestål, Anna
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Nyberg, Mattias
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Bayesian Inference by Combining Training Data and Background Knowledge Expressed as Likelihood Constraints2009In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731Article in journal (Other academic)
    Abstract [en]

    Bayesian inference, or classification, from data is a powerful method for determining states of process when no detailed physical model of the process exists. However, the performance of Bayesian inference from data is dependent on the amount of training data available. In many real applications the amount of training data is limited, and inference results become insufficient. Thus it is important to take other kinds of information into account in the inference as well. In this paper, we consider a general type of background knowledge that appears in many real applications, for example medical diagnosis, technical diagnosis, and econometrics. We show how it can be expressed as constraints on the likelihoods, and provide detailed description of the computations. The method is applied to a diagnosis example, where it is clearly shown how the integration of background knowledge improves diagnosis when training data is limited.

  • 11.
    Pernestål, Anna
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Nyberg, Mattias
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Non-stationary Dynamic Bayesian Networks in Modeling of Troubleshooting Process2009In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731Article in journal (Other academic)
    Abstract [en]

    In research and industry, decision theoretic troubleshooting of complex automotive systems has recently gained increased interest. With suitable troubleshooting, uptime can be increased and repair times shortened. To perform decision theoretic troubleshooting, probability computations are needed. In this work we consider computation of these probabilities under external interventions, which changes dependency relations. We apply a non-stationary dynamic Bayesian network (nsDBN), where the interventions so called events. The events change dependency relations, and drive the nsDBN forward. In the paper, we present how to build models using event driven nsDBN, how to perform inference, and how to use the method in troubleshooting. Event driven nsDBN can be used to model any process subject to interventions, and in particular it opens for solving more general troubleshooting problems than previously presented in literature.

  • 12.
    Peña, Jose M.
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, The Institute of Technology.
    Faithfulness in chain graphs: The discrete case2009In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 50, no 8, p. 1306-1313Article in journal (Refereed)
    Abstract [en]

    This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that the strictly positive discrete probability distributions with the prescribed sample space that factorize according to a chain graph G with dimension d have positive Lebesgue measure wrt R-d. whereas those that factorize according to G but are not faithful to it have zero Lebesgue measure wrt R-d. This means that, in the measure-theoretic sense described, almost all the strictly positive discrete probability distributions with the prescribed sample space that factorize according to G are faithful to it.

  • 13.
    Peña, Jose M.
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, The Institute of Technology.
    Reading Dependencies from Covariance Graphs2013In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 54, no 1, p. 216-227Article in journal (Refereed)
    Abstract [en]

    The covariancegraph (aka bi-directed graph) of a probability distribution p is the undirected graphG where two nodes are adjacent iff their corresponding random variables are marginally dependent in p. (It is worth mentioning that our definition of covariancegraph is somewhat non-standard. The standard definition states that the lack of an edge between two nodes of G implies that their corresponding random variables are marginally independent in p. This difference in the definition is important in this paper.) In this paper, we present a graphical criterion for readingdependencies from G, under the assumption that p satisfies the graphoid properties as well as weak transitivity and composition. We prove that the graphical criterion is sound and complete in certain sense. We argue that our assumptions are not too restrictive. For instance, all the regular Gaussian probability distributions satisfy them.

  • 14.
    Peña, Jose M.
    et al.
    Linköping University, Department of Computer and Information Science, Database and information techniques.
    Nilsson, Roland
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Computational Biology.
    Björkegren, Johan
    Computional Medicine group KI.
    Tegnér, Jesper
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Computational Biology.
    Towards scalable and data efficient learning of Markov boundaries2007In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 45, no 2, p. 211-232Article in journal (Refereed)
    Abstract [en]

    We propose algorithms for learning Markov boundaries from data without having to learn a Bayesian network first. We study their correctness, scalability and data efficiency. The last two properties are important because we aim to apply the algorithms to identify the minimal set of features that is needed for probabilistic classification in databases with thousands of features but few instances, e.g. gene expression databases. We evaluate the algorithms on synthetic and real databases, including one with 139,351 features. © 2006 Elsevier Inc. All rights reserved.

  • 15.
    Sonntag, Dag
    et al.
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, The Institute of Technology.
    Pena, Jose M
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, The Institute of Technology.
    Chain graph interpretations and their relations revisited2015In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 58, p. 39-56Article in journal (Refereed)
    Abstract [en]

    In this paper we study how different theoretical concepts of Bayesian networks have been extended to chain graphs. Today there exist mainly three different interpretations of chain graphs in the literature. These are the Lauritzen-Wermuth-Frydenberg, the Andersson-Madigan-Perlman and the multivariate regression interpretations. The different chain graph interpretations have been studied independently and over time different theoretical concepts have been extended from Bayesian networks to also work for the different chain graph interpretations. This has however led to confusion regarding what concepts exist for what interpretation. In this article we do therefore study some of these concepts and how they have been extended to chain graphs as well as what results have been achieved so far. More importantly we do also identify when the concepts have not been extended and contribute within these areas. Specifically we study the following theoretical concepts: Unique representations of independence models, the split and merging operators, the conditions for when an independence model representable by one chain graph interpretation can be represented by another chain graph interpretation and finally the extension of Meeks conjecture to chain graphs. With our new results we give a coherent overview of how each of these concepts is extended for each of the different chain graph interpretations.

  • 16.
    Sonntag, Dag
    et al.
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, Faculty of Science & Engineering.
    Pena, Jose M
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, Faculty of Science & Engineering.
    On expressiveness of the chain graph interpretations2016In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 68, p. 91-107Article in journal (Refereed)
    Abstract [en]

    In this article we study the expressiveness of the different chain graph interpretations. Chain graphs is a class of probabilistic graphical models that can contain two types of edges, representing different types of relationships between the variables in question. Chain graphs is also a superclass of directed acyclic graphs, i.e. Bayesian networks, and can thereby represent systems more accurately than this less expressive class of models. Today there do however exist several different ways of interpreting chain graphs and what conditional independences they encode, giving rise to different so-called chain graph interpretations. Previous research has approximated the number of representable independence models for the Lauritzen-Wermuth-Frydenberg and the multivariate regression chain graph interpretations using an MCMC based approach. In this article we use a similar approach to approximate the number of models representable by the latest chain graph interpretation in research, the Andersson-Madigan-Perlman interpretation. Moreover we summarize and compare the different chain graph interpretations with each other. Our results confirm previous results that directed acyclic graphs only can represent a small fraction of the models representable by chain graphs, even for a low number of nodes. The results also show that the Andersson-Madigan-Perlman and multivariate regression interpretations can represent about the same amount of models and twice the amount of models compared to the Lauritzen-Wermuth-Frydenberg interpretation. However, at the same time almost all models representable by the latter interpretation can only be represented by that interpretation while the former two have a large intersection in terms of representable models. (C) 2015 Elsevier Inc. All rights reserved.

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