Constant-degree graph expansions that preserve the treewidth

Many hard algorithmic problems dealing with graphs, circuits, formulas and constraints admit polynomial-time upper bounds if the underlying graph has small treewidth. The same problems often encourage reducing the maximal degree of vertices to simplify theoretical arguments or address practical concerns. Such degree reduction can be performed through a sequence of splittings of vertices, resulting in an _expansion_ of the original graph. We observe that the treewidth of a graph may increase dramatically if the splittings are not performed carefully. In this context we address the following natural question: is it possible to reduce the maximum degree to a constant without substantially increasing the treewidth? Our work answers the above question affirmatively. We prove that any simple undirected graph G=(V, E) admits an expansion G'=(V', E') with the maximum degree <= 3 and treewidth(G') <= treewidth(G)+1. Furthermore, such an expansion will have no more than 2|E|+|V| vertices and 3|E| edges; it can be computed efficiently from a tree-decomposition of G. We also construct a family of examples for which the increase by 1 in treewidth cannot be avoided.Comment: 12 pages, 6 figures, the main result used by quant-ph/051107

Probabilistic expert systems for handling artifacts in complex DNA mixtures

This paper presents a coherent probabilistic framework for taking account of allelic dropout, stutter bands and silent alleles when interpreting STR DNA profiles from a mixture sample using peak size information arising from a PCR analysis. This information can be exploited for evaluating the evidential strength for a hypothesis that DNA from a particular person is present in the mixture. It extends an earlier Bayesian network approach that ignored such artifacts. We illustrate the use of the extended network on a published casework example

Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

Accelerated Training of Max-Margin Markov Networks with Kernels

Abstract. Structured output prediction is an important machine learn-ing problem both in theory and practice, and the max-margin Markov network (M3N) is an effective approach. All state-of-the-art algorithms for optimizing M3N objectives take at least O(1/) number of iterations to find an accurate solution. [1] broke this barrier by proposing an excessive gap reduction technique (EGR) which converges in O(1/ iterations. However, it is restricted to Euclidean projections which con-sequently requires an intractable amount of computation for each iter-ation when applied to solve M3N. In this paper, we show that by ex-tending EGR to Bregman projection, this faster rate of convergence can be retained, and more importantly, the updates can be performed effi-ciently by exploiting graphical model factorization. Further, we design a kernelized procedure which allows all computations per iteration to be performed at the same cost as the state-of-the-art approaches.

A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms

Novel Loci for Adiponectin Levels and Their Influence on Type 2 Diabetes and Metabolic Traits : A Multi-Ethnic Meta-Analysis of 45,891 Individuals

J. Kaprio, S. Ripatti ja M.-L. Lokki työryhmien jäseniä.Peer reviewe

Applications of HUGIN to Diagnosis and Control of Autonomous Vehicles

Abstract. We present an application of HUGIN to solve problems related to diagnosis and control of autonomous vehicles. The application is based on a distributed architecture supporting diagnosis and control of autonomous units. The purpose of the architecture is to assist the operator or piloting system in managing fault detection, risk assessment, and recovery plans under uncertainty. To handle uncertainty, we focus on the use of probabilistic graphical models (PGMs) as implemented in the HUGIN tool. We describe the application of PGMs to three problems of diagnosis and control of autonomous vehicles. Based on the HUGIN tool, limited memory influence diagrams (LIMIDs) are used to represent and solve complex problems of diagnosis and control of autonomous ground and underwater vehicles. In particular, we describe how battery monitoring and control problems related to an underwater and a ground vehicle are solved and how to solve the problem of assessing the quality of a sonar image related to an underwater vehicle.