Heckerman, D. and Geiger, D. (December, 1994). Learning Bayesian networks. Technical Report MSR-TR-95-02, Microsoft.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....learned models. Whereas previous theory refinement methods have focused on logic based and neural network representations, our learned models are represented using stochastic context free grammars. The task we address is also similar to the problem of learning the structure of Bayesian networks [Heckerman, Geiger, Chickering, 1995; Chickering, 1996] where the statistical properties of a training set are used to guide the modifications of the network structure. Again, the principal difference between our approach and this body of work is the difference in the representation language. There has also been related work in ....

Heckerman, D.; Geiger, D.; and Chickering, D. M. 1995. Learning Bayesian networks. Machine Learning 20:197--243.

....level from the parent behavior to a certain child behavior is updated after each child behavior s activation following the activation of the parent behavior. Let ) t v E i represent the expected valence of child behavior i at time t. The updated value ) 1 ( t v E i is computed as[9] 1 1 ) 1 ( a a a N v i I N N t v E i t v E i (2) after the child behavior i is activated. Here, I is the arousal level of the affect and v i is the actual valence that the creature just experienced as the result of the activation. a is the ....

Heckerman, D., Learning Bayesian Networks, In The Ninth Annual Conference on Neural Information Processing Systems, Denver CO, November 1995

....of the optimal policy in an Influence diagram: LS93] 3 Learning Acquiring Models Survey: Bun95a] Hec95b] 3.1 Learning probabilities given structure: General purpose EM techniques not listed) LPP95] Mus93] 3. 2 Learning structure Bayesian Learning Approaches: HGC94, HGC95] HG95] CGH94] Hec95b] Hec95a] GH95a] GH95b] HB94a] DL93b] CH91b] CH91a] AC94] Bad92] Bun94] CH92] Coo95b] Coo95a] SDLC93] Bou94] Bun91] Bun95b] GH94b] MDL: LB93] Suz93] Non Bayesian Learning Approaches: These usually involve statistical tests to find conditional ....

David Heckerman and Dan Geiger. Learning bayesian networks. Technical Report MSR-TR-95-02, Microsoft Research, Redmond, WA, February 1995.

....have used Bayesian networks to encode expert knowledge. More recently, AI researchers and statisticians have begun to investigate methods for learning Bayesian networks, including Bayesian methods [Cooper and Herskovits, 1991, Buntine, 1991, Spiegelhalter et al. 1993, Dawid and Lauritzen, 1993, Heckerman et al. 1994], quasi Bayesian methods [Lam and Bacchus, 1993, Suzuki, 1993] and nonBayesian methods [Pearl and Verma, 1991, Spirtes et al. 1993] In this paper, we concentrate on the Bayesian approach, which takes prior knowledge and combines it with data to produce one or more Bayesian networks. Our ....

....a possible approach for avoiding these assumptions. Second, we combined informative priors from our construction to create the likelihoodequivalent BDe metric for complete databases. We note that our metrics and methods for constructing priors may be extended to nondiscrete domains [Geiger and Heckerman, 1994, Learning Bayesian Networks, MSR TR 94 09 45 Heckerman and Geiger, 1994] Third, we described search methods for identifying network structures with high posterior probabilities. We described polynomial algorithms for finding the highest scoring network structures in the special case where every ....

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Heckerman, D. and Geiger, D. (December, 1994). Learning Bayesian networks. Technical Report MSR-TR-95-02, Microsoft.

....whenever a prior Dirichlet pdf is not sufficient to describe prior knowledge. Such a situation occurs, for example, if knowledge about I Delta is more precise than knowledge about Jji . A full discussion of the application of our characterization to directed graphical models can be found in [Heckerman et al. 1995]. In the last section of the present article we discuss the ramifications of our results for inferring decomposable graphical models in connection to the analysis given by [Dawid and Lauritzen, 1993] 2 Background The Dirichlet pdf is defined as follows. Let OE 1 ; OE l be positive random ....

....i Delta g k i=1 and f jji g n j=1 are defined in terms of f ij g and since ij = i Delta jji , there exists a one to one and onto correspondence between f ij g and f i Delta g [ f jji g. The Jacobian J k;n of this transformation is given by J kn = k Y i=1 n Gamma1 i Delta (3) [Heckerman et al. 1995]. The following lemmaprovides a known property of Dirichlet densities ( Dawid and Lauritzen, 1993] Lemma 7.2) Lemma 1 Let f ij g, 1 i k, 1 j n, where k and n are integers greater than 1, be a set of positive random variables having a Dirichlet distribution. Then, f I ( I Delta ) is ....

Heckerman, D., Geiger, D., and Chickering, D. (1995). Learning Bayesian networks. Machine Learning, to appear.

....the random sample (i.e. database) D = fC 1 ; Cm g contains no missing data that is, each case C l consists of the observation of all the variables in U (we say that D is complete) In Section 8, we consider the more difficult problem where D contains missing data. Buntine (1994) and Heckerman and Geiger (1994) discuss the case where U may contain continuous variables. When a database D is a random sample from a multivariate physical probability distribution that can be encoded in B S , we simply say that D is a random sample from B S . As an example, consider the domain U consisting of two binary ....

....(1995) Charniak (1991) provides an easy to read introduction to the Bayesian network representation. Spiegelhalter et al. 1993) and Heckerman et al. 1995b) give simple discussions of methods for learning Bayesian networks for domains containing only discrete variables. Buntine (1994) and Heckerman and Geiger (1994) provide more detailed discussions. Experimental comparisons of different learning approaches can be found in Cooper and Herskovits (1992) Aliferis and Cooper (1994) Lauritzen et al. 1994) Cowell et al. 1995) and Heckerman et al. 1995b) In addition to directed models, researchers have also ....

Heckerman, D. and Geiger, D. (December, 1994). Learning Bayesian networks. Technical Report MSR-TR-95-02, Microsoft, Redmond, WA.

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D. Heckerman, D. Geiger and D. Chickering, Learning Bayesian networks, Machine Learning, 1995, to appear.

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