Ildikó Flesch

Outlier Detection with One-Class Classifiers from ML and KDD

The problem of outlier detection is well studied in the fields of Machine Learning (ML) and Knowledge Discovery in Databases (KDD). Both fields have their own methods and evaluation procedures. In ML, Support Vector Machines and Parzen Windows are well-known methods that can be used for outlier detection. In KDD, the heuristic local-density estimation methods LOF and LOCI are generally considered to be superior outlier-detection methods. Hitherto, the performances of these ML and KDD methods have not been compared. This paper formalizes LOF and LOCI in the ML framework of one-class classification and performs a comparative evaluation of the ML and KDD outlier-detection methods on real-world datasets. Experimental results show that LOF and SVDD are the two best-performing methods. It is concluded that both fields offer outlier-detection methods that are competitive in performance and that bridging the gap between both fields may facilitate the development of outlier-detection methods.

Mondriaan sparse matrix partitioning for attacking cryptosystems by a parallel block Lanczos algorithm: a case study

A case study is presented demonstrating the application of the Mondriaan package for sparse matrix partitioning to the field of cryptology. An important step in an integer factorisation attack on the RSA public-key cryptosystem is the solution of a large sparse linear system with 0/1 coefficients, which can be done by the block Lanczos algorithm proposed by Montgomery. We parallelise this algorithm using Mondriaan partitioning and discuss the high-level components needed. A speedup of 8 is obtained on 16 processors of a Silicon Graphics Origin 3800 for the factorisation of an integer with 82 decimal digits, and a speedup of 7 for 98 decimal digits.

Using Temporal Context-Specific Independence Information in the Exploratory Analysis of Disease Processes

Disease processes in patients are temporal in nature and involve uncertainty. It is necessary to gain insight into these processes when aiming at improving the diagnosis, treatment and prognosis of disease in patients. One way to achieve these aims is by explicitly modelling disease processes; several researchers have advocated the use of dynamic Bayesian networks for this purpose because of the versatility and expressiveness of this time-oriented probabilistic formalism. In the research described in this paper, we investigate the role of context-specific independence information in modelling the evolution of disease. The hypothesis tested was that within similar populations of patients differences in the learnt structure of a dynamic Bayesian network may result, depending on whether or not patients have a particular disease. This is an example of temporal context-specific independence information. We have tested and confirmed this hypothesis using a constraint-based Bayesian network structure learning algorithm which supports incorporating background knowledge into the learning process. Clinical data of mechanically-ventilated ICU patients, some of whom developed ventilator-associated pneumonia, were used for that purpose.

Independence Decomposition in Dynamic Bayesian Networks

Dynamic Bayesian networks are a special type of Bayesian network that explicitly incorporate the dimension of time. They can be distinguished into repetitive and non-repetitive networks. Repetitiveness implies that the set of random variables of the network and their independence relations are the same at each time step. Due to their structural symmetry, repetitive networks are easier to use and are, therefore, often taken as the standard. However, repetitiveness is a very strong assumption, which normally does not hold, as particular dependences and independences may only hold at certain time steps. In this paper, we propose a new framework for independence modularisation in dynamic Bayesian networks. Our theory provides a method for separating atemporal and temporal independence relations, and offers a practical approach to building dynamic Bayesian networks that are possibly non-repetitive. A composition operator for temporal and atemporal independence relations is proposed and its properties are studied. Experimental results obtained by learning dynamic Bayesian networks from real data show that this framework offers a more accurate way for knowledge representation in dynamic Bayesian networks.

The Probabilistic Interpretation of Model-Based Diagnosis

Model-based diagnosis is the field of research concerned with the problem of finding faults in systems by reasoning with abstract models of the systems. Typically, such models offer a description of the structure of the system in terms of a collection of interacting components. For each of these components it is described how they are expected to behave when functioning normally or abnormally. The model can then be used to determine which combination of components is possibly faulty in the face of observations derived from the actual system. There have been various proposals in literature to incorporate uncertainty into the diagnostic reasoning process about the structure and behaviour of systems, since much of what goes on in a system cannot be observed. This paper proposes a method for decomposing the probability distribution underlying probabilistic model-based diagnosis in two parts: (i ) a part that offers a description of uncertain abnormal behaviour in terms of the Poisson-binomial probability distribution, and (ii ) a part describing the deterministic, normal behaviour of system components.

Simplifying Learning in Non-repetitive Dynamic Bayesian Networks

Dynamic Bayesian networks (DBNs) are increasingly adopted as tools for the modeling of dynamic domains involving uncertainty. Due to their ease of modeling, repetitive DBNs have become the standard. However, repetition does not allow the independence relations to vary over time. Non-repetitive DBNs do allow for modeling time-varying relations, but are hard to apply to dynamic domains. This paper presents a novel method that facilitates the use of non-repetitive DBNs and simplifies learning DBNs in general. This is achieved by learning disjoint sets of independence relations of separate parts of a DBN, and, subsequently, joining these relations together to obtain the complete set of independence relations of the DBN. Our simplified learning method improves previous methods by removing redundant operations which yields computational savings in the learning process of the network. Experimental results show that the simplified learning method facilitates the use of non-repetitive DNBs and enables us to build them in a seamless fashion.

Graphical Reasoning with Bayesian Networks

Nowadays, Bayesian networks are seen by many researchers as standard tools for reasoning with uncertainty. Despite the fact that Bayesian networks are graphical representations, representing dependence and independence information, normally the emphasis of the visualisation of the reasoning process is on showing changes in the associated marginal probability distributions due to entering observations, rather than on changes in the associated graph structure. In this paper, we argue that it is possible and relevant to look at Bayesian network reasoning as reasoning with a graph structure, depicting changes in the dependence and independence information. We propose a new method that is able to modify the graphical part of a Bayesian network to bring it in accordance with available observations. In this way, Bayesian network reasoning is seen as reasoning about changing dependences and independences as reflected by changes in the graph structure.