The task of causal structure discovery from empirical data is a fundamental problem in many areas. Experimental data is crucial for accomplishing this task. However, experiments are typically expensive, and must be selected with great care. This paper

We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n2 n) time, where n is the number of attributes; the number of parents per attribute is bounded by a constant. In this paper we show that the posterior probabilities for all the n(n−1) potential edges can be computed in O(n2 n) total time. This result is achieved by a forward–backward technique and fast Möbius transform algorithms, which are of independent interest. The resulting speedup by a factor of about n 2 allows us to experimentally study the statistical power of learning moderate-size networks. We report results from a simulation study that covers data sets with 20 to 10,000 records over 5 to 25 discrete attributes. 1

The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuous-valued data linear acyclic causal models with additive noise are often used because these models are well understood and there are well-known methods to fit them to data. In reality, of course, many causal relationships are more or less nonlinear, raising some doubts as to the applicability and usefulness of purely linear methods. In this contribution we show that in fact the basic linear framework can be generalized to nonlinear models. In this extended framework, nonlinearities in the data-generating process are in fact a blessing rather than a curse, as they typically provide information on the underlying causal system and allow more aspects of the true data-generating mechanisms to be identified. In addition to theoretical results we show simulations and some simple real data experiments illustrating the identification power provided by nonlinearities. 1

I propose a common framework that combines three different paradigms in machine learning: generative, discriminative and imitative learning. A generative probabilistic distribution is a principled way to model many machine learning and machine perception problems. Therein, one provides domain specific knowledge in terms of structure and parameter priors over the joint space of variables. Bayesian networks and Bayesian statistics provide a rich and flexible language for specifying this knowledge and subsequently refining it with data and observations. The final result is a distribution that is a good generator of novel exemplars.

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High-throughput proteomic data can be used to reveal the connectivity of signaling networks and the influences between signaling molecules. We present a primer on the use of Bayesian networks for this task. Bayesian networks have been successfully used to derive causal influences among biological signaling molecules (for example, in the analysis of intracellular multicolor flow cytometry). We discuss ways to automatically derive a Bayesian network model from proteomic data and to interpret the resulting model.

In the context of learning Bayesian networks from data, very little work has been published on methods for assessing the quality of an induced model. This issue, however, has received a great deal of attention in the statistics literature. In this paper, we take a well-known method from statistics, Efron's Bootstrap, and examine its applicability for assessing a confidence measure on features of the learned network structure. We also compare this method to assessments based on a practical realization of the Bayesian methodology.

Many different Bayesian network models have been suggested...

computation. In preparation. Address for correspondence:

We propose a new method of discovering causal structures, based on the detection of local, spontaneous changes in the underlying data-generating model. We derive expressions for the Bayesian score that a causal structure should obtain from streams of data produced by locally changing distributions. Simulation experiments indicate that dynamic information may improve the power of discovery up to the theoretical limits set by statistical indistinguishability. 1