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. 1

In this paper, we consider the problem of compressing graphs of the link structure of the World Wide Web. We provide efficient algorithms for such compression that are motivated by recently proposed random graph models for describing the Web.

Comparative genome hybridization (CGH) is a laboratory method to measure gains and losses of chromosomal regions in tumor cells. It is believed that DNA gains and losses in tumor cells do not occur entirely at random, but partly through some flow of causality. Models that relate tumor progression to the occurrence of DNA gains and losses could be very useful in hunting cancer genes and in cancer diagnosis. We lay some mathematical foundations for inferring a model of tumor progression from a CGH data set. We consider a class of tree models that are more general than a path model that has been developed for colorectal cancer. We derive a tree model inference algorithm based on the idea of a maximum-weight branching in a graph, and we show that under plausible assumptions our algorithm infers the correct tree. We have implemented our methods in software, and we illustrate with a CGH data set for renal cancer.

The direct application of statistics to stochastic optimization in evolutionary computation has become more important and present over the last few years. With the introduction of the notion of the Estimation of Distribution Algorithm (EDA), a new line of research has been named. The application area so far has mostly been the same as for the classic genetic algorithms, being the binary vector encoded problems. The most important aspect in the new algorithms is the part where probability densities are estimated. In probability theory, a distinction is made between discrete and continuous distributions and methods. Using the rationale for density estimation based evolutionary algorithms, we present an algorithmic framework for them, named IDEA. This allows us to define such algorithms for vectors of both continuous and discrete random variables, combining techniques from existing EDAs as well as density estimation theory. The emphasis is on techniques for vectors of continuous random variables, for which we present new algorithms in the field of density estimation based evolutionary algorithms, using two different density estimation models.

Abstract. We consider a general class of optimization problems regarding spanning trees in directed graphs (arborescences). We present an algorithm for solving such problems, which can be considered as a generalization of Edmonds ’ algorithm for the solution of the minimum-cost arborescence problem. The considered class of optimization problems includes as special cases the standard minimum-cost arborescence problem, the bottleneck and the lexicographically optimal arborescence problem.

Renal cell carcinoma is characterized by an accumulation of complex chromosomal alterations during tumor progression. Chromosome 3p deletions are known to occur early in the carcinogenesis, but the nature of subsequent events, their interrelationships, and their sequence is poorly understood, as one usually only obtains a single “view ” of the dynamic process of tumor development in a particular cancer patient. To address this limitation, we used comparative genomic hybridization analysis in combination with a distance-based and a branching-tree method to search for tree models of the oncogenesis process of 116 conventional (clear cell) renal carcinomas. This provides a means to analyze and model cancer development processes based on a more dynamic model, including the presence of multiple pathways, as compared with the fixed linear model first proposed by Vogelstein et al. (N. Engl. J. Med., 319: 525–532, 1988) for colorectal cancer. The most common DNA losses involved 3p (61%),

Abstract. We consider minimum equivalent digraph problem, its maximum optimization variant and some non-trivial extensions of these two types of problems motivated by biological and social network applications. We provide 3-approximation algorithms for all the minimiza-2 tion problems and 2-approximation algorithms for all the maximization problems using appropriate primal-dual polytopes. We also show lower bounds on the integrality gap of the polytope to provide some intuition on the final limit of such approaches. Furthermore, we provide APXhardness result for all those problems even if the length of all simple cycles is bounded by 5. 1

Suppose your city is planning to construct a rapid rail system. They want to construct the most economical system possible that will meet the needs of the city. Certainly, a minimum requirement is that passengers must be able to ride from any station in the system to any other station. In addition, several alternate routes are under consideration between some of the stations. Some of these routes are more expensive to construct than others. How can the city select the most inexpensive design that still connects all the proposed stations? The model for this problem associates vertices with the proposed stations and edges with all the proposed routes that could be constructed. The edges are labeled (weighted) with their proposed costs. To solve the rapid rail problem, we must find a connected graph (so that all stations can be reached from all other stations) with the minimum possible sum of the edge weights. Note that to construct a graph with minimum edge weight sum, we must avoid cycles, since otherwise we could remove the most expensive edge (largest weight) on the cycle, obtaining a new connected graph with smaller weight sum. What we desire is a

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We prove that maximum weight branchings in directed graphs can be approximated in time O(m) up to a factor of 1 − ǫ, where ǫ> 0 is an arbitrary constant. Key words: approximation algorithm, graph algorithm, branching 1