Bayesian belief networks : from construction to inference

In het dagelijks leven is het redeneren met onzekerheden gebruikelijker dan het redeneren zonder. Bayesiaanse belief netwerken bieden een wiskundig correct formalisme om onzekerheid te representeren en op efficiëte wijze mee te redeneren. Een Bayesiaanse belief netwerk bestaat uit twee delen. Ten eerste bestaat een belief netwerk uit een een gerichte graaf zonder lussen: de netwerkstructuur. Voor elke variabele waarmee we willen redeneren is er een knoop in de graaf. We zullen de termen knoop en variabele dan ook door elkaar gebruiken. Figuur 0.1 laat een eenvoudig belief netwerk zien voor een klein medisch domein met daarin de leeftijd van een patient (a), de behoefte aan een bril (g), of het zicht beter wordt als de patient knippert (v) en of de patient klachten heeft over zijn zicht (s). Als er een directe afhankelijkheid tussen twee knopen is, dan zijn deze knopen verbonden met een pijl. Intuitief geeft de richting van de pijl een causale invloed aan. Bijvoorbeeld in Figuur 0.1 geeft de pijl van a naar g weer dat de leeftijd een indicatie is dat de patient een bril nodig heeft

IDAGs: a perfect map for any distribution

Conditional independence relations appear in many different fields of science such as probability theory, theory of belief functions, and possibility theory. Directed acyclic graphs (DAGs) are a powerful means for representing conditional independence relations. However, it is not possible for all independence relations to find a DAG that perfectly represents all conditional independencies in the relation. We present the IDAG formalism that provides for an exact representation of any independency relation. The basic idea is to enhance the formalism of DAGs with a special kind of arc for modeling induced independencies

Evaluating the replicability of significance tests for comparing learning algorithms

Abstract. Empirical research in learning algorithms for classification tasks generally requires the use of significance tests. The quality of a test is typically judged on Type I error (how often the test indicates a difference when it should not) and Type II error (how often it indicates no difference when it should). In this paper we argue that the replicability of a test is also of importance. We say that a test has low replicability if its outcome strongly depends on the particular random partitioning of the data that is used to perform it. We present empirical measures of replicability and use them to compare the performance of several popular tests in a realistic setting involving standard learning algorithms and benchmark datasets. Based on our results we give recommendations on which test to use.

Integrating Logical Reasoning and Probabilistic Chain Graphs

Abstract. Probabilistic logics have attracted a great deal of attention during the past few years. While logical languages have taken a central position in research on knowledge representation and automated reasoning, probabilistic graphical models with their probabilistic basis have taken up a similar position when it comes to reasoning with uncertainty. The formalism of chain graphs is increasingly seen as a natural probabilistic graphical formalism as it generalises both Bayesian networks and Markov networks, and has a semantics which allows any Bayesian network to have a unique graphical representation. At the same time, chain graphs do not support modelling and learning of relational aspects of a domain. In this paper, a new probabilistic logic, chain logic, is developed along the lines of probabilistic Horn logic. The chain logic leads to relational models of domains in which associational and causal knowledge are relevant and where probabilistic parameters can be learned from data.

Ontobayes approach to corporate knowledge

Abstract. In this paper, we investigate the integration of virtual knowledge communities (VKC) into an ontology-driven uncertainty model (OntoBayes). The selected overall framework for OntoBayes is the multiagent paradigm. Agents modeled with OntoBayes have two parts: knowledge and decision making parts. The former is the ontology knowledge while the latter is based upon Bayesian Networks (BN). OntoBayes is thus designed in agreement with the Agen Oriented Abstraction (AOA) paradigm. Agents modeled with OntoBayes possess a common community layer that enables to define, describe and implement corporate knowledge. This layer consists of virtual knowledge communities.