We describe scoring metrics for learning Bayesian networks from a combination of user knowledge and statistical data. We identify two important properties of metrics, which we call event equivalence and parameter modularity. These properties have been mostly ignored, but when combined, greatly simplify the encoding of a user's prior knowledge. In particular, a user can express his knowledge-for the most part-as a single prior Bayesian network for the domain.

We describe scoring metrics for learning Bayesian networks from a combination of user knowledge and statistical data. We identify two important properties of metrics, which we call event equivalence and parameter modularity. These properties have been mostly ignored, but when combined, greatly simplify the encoding of a user's prior knowledge. In particular, a user can express his knowledge-for the most part-as a single prior Bayesian network for the domain.

Abstract. Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier with strong assumptions of independence among features, called naive Bayes, is competitive with state-of-the-art classifiers such as C4.5. This fact raises the question of whether a classifier with less restrictive assumptions can perform even better. In this paper we evaluate approaches for inducing classifiers from data, based on the theory of learning Bayesian networks. These networks are factored representations of probability distributions that generalize the naive Bayesian classifier and explicitly represent statements about independence. Among these approaches we single out a method we call Tree Augmented Naive Bayes (TAN), which outperforms naive Bayes, yet at the same time maintains the computational simplicity (no search involved) and robustness that characterize naive Bayes. We experimentally tested these approaches, using problems from the University of California at Irvine repository, and compared them to C4.5, naive Bayes, and wrapper methods for feature selection.

We describe scoring metrics for learning Bayesian networks from a combination of user knowledge and statistical data. Previous work has concentrated on metrics for domains containing only discrete variables, under the assumption that data represents a multinomial sample. In this paper, we extend this work, developing scoring metrics for domains containing only continuous variables under the assumption that continuous data is sampled from a multivariate normal distribution. Our work extends traditional statistical approaches for identifying vanishing regression coefficients in that we identify two important assumptions, called event equivalence and parameter modularity, that when combined allow the construction of prior distributions for multivariate normal parameters from a single prior Bayesian network specified by a user.

An important feature of Bayesian networks is that they facilitate explicit encoding of information about independencies in the domain, information that is indispensable for efficient inferencing. This article characterizes all independence assertions that logically follow from the topology of a network and develops a linear time algorithm that identifies these assertions. The algorithm's correctness is based on the soundness of a graphical criterion, called d-separation, and its optimality stems from the completeness of dseparation. An enhanced version of d-separation, called D-separation, is defined, extending the algorithm to networks that encode functional dependencies. Finally, the algorithm is shown to work for a broad class of nonprobabilistic independencies.

We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let W be an n × n, n ≥ 3, positive-definite symmetric matrix of random variables and f (W ) be a pdf of W . Then, f(W ) is a Wishart distribution if and only if W 11 − W 12 W −1 22 W 12 is independent of {W 12 , W 22 } for every block partitioning W 11 , W 12 , W 12 , W 22 of W . Similar characterizations of the normal and normal-Wishart distributions are provided as well. We also show how to construct a prior for every DAG model over X from the prior of a single regression model.

Neurocutaneous syndromes represent a vast, largely heterogeneous group of disorders characterized by neurological and dermatological manifestations, reflecting the common embryonic origin of epidermal and neural tissues. In the present report, we describe a novel neurocutaneous syndrome characterized by cerebral dysgenesis, neuropathy, ichthyosis, and keratoderma (CEDNIK syndrome). Using homozygosity mapping in two large families, we localized the disease gene to 22q11.2 and identified, in all patients, a 1-bp deletion in SNAP29, which codes for a SNARE protein involved in vesicle fusion. SNAP29 expression was decreased in the skin of the patients, resulting in abnormal maturation of lamellar granules and, as a consequence, in mislocation of epidermal lipids and proteases. These data underscore the importance of vesicle trafficking regulatory mechanisms for proper neuroectodermal differentiation.

We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. For decomposable graphical models these conditions are equivalent to a set of conditional independence statements similar to the Hammersley--Clifford theorem; however, we show that for nondecomposable graphical models they are not. We also show that nondecomposable models can have nonrational maximum likelihood estimates. These results are used to give several novel characterizations of decomposable graphical models.Comment: Published at http://dx.doi.org/10.1214/009053606000000263 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org