Marc Pouly

Computational aspects of attack---defense trees

Attack---defense trees extend attack trees with defense nodes. This richer formalism allows for a more precise modeling of a systems vulnerabilities, by representing interactions between possible attacks and corresponding defensive measures. In this paper we compare the computational complexity of both formalisms. We identify semantics for which extending attack trees with defense nodes does not increase the computational complexity. This implies that, for these semantics, every query that can be solved efficiently on attack trees can also be solved efficiently on attack---defense trees. Furthermore, every algorithm for attack trees can directly be used to process attack---defense trees.

Generic Inference: A Unifying Theory for Automated Reasoning

This book provides a rigorous algebraic study of the most popular inference formalisms with a special focus on their wide application area, showing that all these tasks can be performed by a single generic inference algorithm. Written by the leading international authority on the topic, it includes an algebraic perspective (study of the valuation algebra framework), an algorithmic perspective (study of the generic inference schemes) and a practical perspective (formalisms and applications). Researchers in a number of fields including artificial intelligence, operational research, databases and other areas of computer science; graduate students; and professional programmers of inference methods will benefit from this work.

A Probabilistic Framework for Security Scenarios with Dependent Actions

This work addresses the growing need of performing meaningful probabilistic analysis of security. We propose a framework that integrates the graphical security modeling technique of attack–defense trees with probabilistic information expressed in terms of Bayesian networks. This allows us to perform probabilistic evaluation of attack–defense scenarios involving dependent actions. To improve the efficiency of our computations, we make use of inference algorithms from Bayesian networks and encoding techniques from constraint reasoning. We discuss the algebraic theory underlying our framework and point out several generalizations which are possible thanks to the use of semiring theory.

Generic local computation

Many problems of artificial intelligence, or more generally, many problems of information processing, have a generic solution based on local computation on join trees or acyclic hypertrees. There are several variants of this method all based on the algebraic structure of valuation algebras. A strong requirement underlying this approach is that the elements of a problem decomposition form a join tree. Although it is always possible to construct covering join trees, if the requirement is originally not satisfied, it is not always possible or not efficient to extend the elements of the decomposition to the covering join tree. Therefore in this paper different variants of an axiomatic framework of valuation algebras are introduced which prove sufficient for local computation without the need of an extension of the factors of a decomposition. This framework covers the axiomatic system proposed by Shenoy and Shafer (1990) [1]. A particular emphasis is laid on the important special cases of idempotent algebras and algebras with some notion of division. It is shown that all well-known architectures for local computation like the Shenoy-Shafer architecture, Lauritzen-Spiegelhalter and HUGIN architectures may be adapted to this new framework. Further a new architecture for idempotent algebras is presented. As examples, in addition to the classical instances of valuation algebras, semiring-based valuation algebras, Gaussian potentials and the relational algebra are presented.

Probabilistic reasoning with graphical security models

We develop a framework for probabilistic analysis of security scenarios with dependencies.We combine the security model of attack-defense trees (ADTrees) with Bayesian networks.We prove that propositionally equivalent ADTrees yield the same probability value.We compare our computational method with the standard bottom-up algorithm for ADTrees.We use semiring theory to improve the efficiency of our computations. This work provides a computational framework for meaningful probabilistic evaluation of attack-defense scenarios involving dependent actions. We combine the graphical security modeling technique of attack-defense trees with probabilistic information expressed in terms of Bayesian networks. In order to improve the efficiency of probability computations on attack-defense trees, we make use of inference algorithms and encoding techniques from constraint reasoning. The proposed approach is illustrated on a running example and the computations are automated with the help of suitable software tools. We show that the computational routines developed in this paper form a conservative generalization of the attack-defense tree formalism defined previously. We discuss the algebraic theory underlying our framework and point out several generalizations which are possible thanks to the use of semiring theory. Finally, our results apply directly to the analysis of the industrially recognized model of attack trees.

Generalized information theory for hints

This paper develops a new uncertainty measure for the theory of hints that complies with the established semantics of statistical information theory and further satisfies all classical requirements for such a measure imposed in the literature. The proposed functional decomposes into conversant uncertainty measures and therefore discloses a new interpretation of the latters as well. By abstracting to equivalence classes of hints we transport the new measure to mass functions in Dempster-Shafer theory and analyse its relationship with the aggregate uncertainty, which currently is the only known functional for the Dempster-Shafer theory of evidence that satisfies the same set of properties. Moreover, the perspective of hints reveals that the standard independence notion in Dempster-Shafer theory called non-interactivity corresponds to an amalgamation of probabilistic independence and qualitative independence between frames of discernment. All results in this paper are developed for arbitrary families of compatible frames generalizing the very specialized multi-variate systems that are usually studied in information theory.

Detection and quantification of hand eczema by visible spectrum skin pattern analysis

Hand eczema is a frequent dermatosis with severe health and financial consequences to patients and society. It follows a chronic course and persists up to 15 years after onset. Early detection of an exacerbation followed by the application of specific drugs for a few days can considerably reduce disease activity and avoid temporary disability. However, dermatitis patients usually rely on their own perception in assessing their skin condition and therefore often miss the time point for effective treatment. In this paper we present a prototype-based feasibility study of automated detection and quantification of hand eczema using texton-based imaging and machine-learning techniques.

Generalized information theory based on the theory of hints

The aggregate uncertainty is the only known functional for Dempster-Shafer theory that generalizes the Shannon and Hartley measures and satisfies all classical requirements for uncertainty measures, including subadditivity. Although being posed several times in the literature, it is still an open problem whether the aggregate uncertainty is unique under these properties. This paper derives an uncertainty measure based on the theory of hints and shows its equivalence to the pignistic entropy. It does not satisfy subadditivity, but the viewpoint of hints uncovers a weaker version of subadditivity. On the other hand, the pignistic entropy has some crucial advantages over the aggregate uncertainty. i.e. explicitness of the formula and sensitivity to changes in evidence. We observe that neither of the two measures captures the full uncertainty of hints and propose an extension of the pignistic entropy called hints entropy that satisfies all axiomatic requirements, including subadditivity, while preserving the above advantages over the aggregate uncertainty.

Generic solution construction in valuation-based systems

Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notions of solutions. Typical examples are satisfying assignments in constraint systems, models in logics or solutions to linear equation systems. Contrary to inference, there is no general algorithm to compute solutions in arbitrary valuation algebras. This paper states formal requirements for the presence of solutions and proposes a generic algorithm for solution construction based on the results of a previously executed inference scheme. We study the application of generic solution construction to semiring constraint systems, sparse linear systems and algebraic path problems and show that the proposed method generalizes various existing approaches for specific formalisms in the literature.

On using Support Vector Machines for the Detection and Quantification of Hand Eczema.

Hand eczema is one of the most frequent skin diseases affecting up to 14% of the population. Early detection and continuous observation of eczemas allows for efficient treatment and can therefore relieve symptoms. However, purely manual skin control is tedious and often error prone. Thus, an automatic approach that can assist the dermatologist with his work is desirable. Together with our industry partner swiss4ward, we devised an image processing method for hand eczema segmentation based on support vector machines and conducted several experiments with different feature sets. Our implementation is planned to be integrated into a clinical information system for operational use at the University Hospital Zurich. Instead of focusing on a high accuracy like most existing state-of-the-art approaches, we selected F1 score as our primary measure. This decision had several implications regarding the design of our segmentation method, since all popular implementations of support vector machines aim for optimizing accuracy. Finally, we evaluated our system and achieved an F1 score of 58.6% for front sides of hands and 43.8% for back sides, which outperforms several state-of-the-art methods that were tested on our gold standard data set as well.