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On Undirected Representations of Bayesian Networks
 ACM SIGIR Workshop on Mathematical/Formal Models in Information Retrieval
, 2001
"... Empirical studies clearly demonstrate the effectiveness of the nested jointree (NJT) representation in probabilistic inference. A NJT is a traditional Markov network (MN) together with a possible local MN nested in each clique. These nested MNs can themselves contain other nested MNs in a recu ..."
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Cited by 7 (6 self)
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Empirical studies clearly demonstrate the effectiveness of the nested jointree (NJT) representation in probabilistic inference. A NJT is a traditional Markov network (MN) together with a possible local MN nested in each clique. These nested MNs can themselves contain other nested MNs in a recursive manner. However, the NJT representation is not necessarily a faithful representation of a given Bayesian network (BN).
Towards Automated Synthesis of Data Mining Programs
 Proc. 5th Intl. Conf. Knowledge Discovery and Data Mining
, 1999
"... Code synthesis is routinely used in industry to generate GUIs, form lling applications, and database support code and is even used with COBOL. In this paper we consider the question of whether code synthesis could also be applied to the data mining phase of knowledge discovery. We view this as a rap ..."
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Cited by 6 (4 self)
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Code synthesis is routinely used in industry to generate GUIs, form lling applications, and database support code and is even used with COBOL. In this paper we consider the question of whether code synthesis could also be applied to the data mining phase of knowledge discovery. We view this as a rapid prototyping method. Rapid prototyping of statistical data analysis algorithms would allow experienced analysts to experiment with di erent statistical models before choosing one, but without requiring prohibitively expensive programming e orts. It would also smooth the steep learning curve often faced by novice users of data mining tools and libraries. Finally, it would accelerate dissemination of essential research results and the development of applications. In this paper, we present a framework and the basic software for the automated synthesis of data analysis programs. We use a speci cation language that generalizes Bayesian networks, a popular notation used in many communities. Using decomposition methods and algorithm templates, our system transforms the network through several levels of representation and then nally into pseudocode which can be translated into the implementation language of choice. Here, we explain the framework on a mixture of Gaussians model, a core data mining algorithm at the heart of many commercial clustering tools. We mention the e ectiveness of our framework by generating pseudocode for some more sophisticated algorithms from recent literature.
Conditional Independence Structures Examined via Minors
, 1997
"... this paper is a study of wellknown classes of CIrelations from the viewpoint of minors with a special emphasis on graphical visualization. After some preliminaries in Section 2 we characterize the classes of semigraphoids, pseudographoids and graphoids by means of their forbidden or compulsory 3m ..."
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Cited by 3 (1 self)
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this paper is a study of wellknown classes of CIrelations from the viewpoint of minors with a special emphasis on graphical visualization. After some preliminaries in Section 2 we characterize the classes of semigraphoids, pseudographoids and graphoids by means of their forbidden or compulsory 3minors in Section 3. Then we provide in the next section a succint minor characterization of separation graphoids and an axiomatic characterization of boundary semigraphoids which originate from simple graphs according to the global and local Markov assumptions, respectively. Further we mention dseparation graphoids and their minors. In the second part of the paper we concentrate on semimatroids and especially on a new class of semimatroids called simple semimatroids. This class is of special interest for us because it is relatively easy to handle and, at the same time, the presented results have strong consequences for the structure of the classes of all semimatroids and probabilistically (p) representable semimatroids. Let us recall that the prepresentable semimatroids originate from systems of random variables ¸ = (¸ i ) i2N : a relation M is prepresentable if there exists ¸ such that a triple (I; J; K)
Bayesian Data Analysis for Data Mining
 In Handbook of Data Mining
, 2002
"... Introduction The Bayesian approach to data analysis computes conditional probability distribu tions of quantities of interest (such as future observables) given the observed data. Bayesian analyses usually begin with a .full probability model  a joint probability dis tribution for all the observ ..."
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Introduction The Bayesian approach to data analysis computes conditional probability distribu tions of quantities of interest (such as future observables) given the observed data. Bayesian analyses usually begin with a .full probability model  a joint probability dis tribution for all the observable and unobservable quantities under study  and then use Bayes' theorem (Bayes, 1763) to compute the requisite conditional probability distributions (called poster'Joy distributions). The theorem itself is innocuous enough. In its simplest form, if Q denotes a quantity of interest and D denotes data, the theorem states: P(ql D) P(;lq) X P(q)/P(). This theorem prescribes the basis for statistical learning in the probabilistic frame work. With p(Q) regarded as a probabilistic statement of prior knowledge about Q before obtaining the data D, p(QI D) becomes a revised probabilistic statement of our knowledge about Q in the light of the data (Bernardo and Smith, 1994, p.2). The marginal lik
Research Note Characterizations of Decomposable Dependency Models
"... Decomposable dependency models possess a numberofinteresting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to the wellknown set characterizing dependency models that are iso ..."
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Decomposable dependency models possess a numberofinteresting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to the wellknown set characterizing dependency models that are isomorphic to undirected graphs. We also brie y discuss a potential application of our results to the problem of learning graphical models from data. 1.