Advances in Learning Bayesian Networks of Bounded Treewidth

This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sampling $k$-trees (maximal graphs of treewidth $k$), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that $k$-tree. Some properties of these methods are discussed and proven. The approaches are empirically compared to each other and to a state-of-the-art method for learning bounded treewidth structures on a collection of public data sets with up to 100 variables. The experiments show that our exact algorithm outperforms the state of the art, and that the approximate approach is fairly accurate.Comment: 23 pages, 2 figures, 3 table

Methodological developments for probabilistic risk analyses of socio-technical systems

International audienceNowadays, the risk analysis of critical systems cannot be focused only on a technical point of view. Indeed, several major accidents have changed this initial way of thinking. As a result, there exist numerous methods that allow to study risks by considering on the main system resources: the technical process, the operator constraining this process, and the organisation conditioning human actions. However, few works propose to jointly use these different methods to study risks in a global approach. In that way, this paper presents a methodology, which is under development between CRAN, EDF and INERIS, allowing an integration of these different methods to probabilistically estimate risks. This integration is based on unification and structuring knowledge concepts; and the quantitative aspect is achieved through the use of Bayesian Networks. An application of this methodology, on an industrial case, demonstrates its feasibility and concludes on model capacities, which are about the necessary consideration of the whole causes for a system weakness treatment, and the classification of these contributors considering their criticality for this system. This tool can thus be used to help decision makers to prioritise their actions

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Stochastic Modeling and Analysis of Pathway Regulation and Dynamics

To effectively understand and treat complex diseases such as cancer, mathematical and statistical modeling is essential if one wants to represent and characterize the interactions among the different regulatory components that govern the underlying decision making process. Like in any other complex decision making networks, the regulatory power is not evenly distributed among its individual members, but rather concentrated in a few high power "commanders". In biology, such commanders are usually called masters or canalizing genes. Characterizing and detecting such genes are thus highly valuable for the treatment of cancer. Chapter II is devoted to this task, where we present a Bayesian framework to model pathway interactions and then study the behavior of master genes and canalizing genes. We also propose a hypothesis testing procedure to detect a "cut" in pathways, which is useful for discerning drugs' therapeutic effect. In Chapter III, we shift our focus to the understanding of the mechanisms of action (MOA) of cancer drugs. For a new drug, the correct understanding of its MOA is a key step for its application to cancer treatments. Using the Green Fluorescent Protein technology, researchers have been able to track various reporter genes from the same cell population for an extended period of time. Such dynamic gene expression data forms the basis for drug similarity comparisons. In Chapter III, we design an algorithm that can identify mechanistic similarities in drug responses, which leads to the characterization of their respective MOAs. Finally, in the course of drug MOA study, we observe that cells in a hypothetical homogeneous population do not respond to drug treatments in a uniform and synchronous way. Instead, each cell makes a large shift in its gene expression level independently and asynchronously from the others. Hence, to systematically study such behavior, we propose a mathematical model that describes the gene expression dynamics for a population of cells after drug treatments. The application of this model to dose response data proviodes us new insights of the dosing effects. Furthermore, the model is capable of generating useful hypotheses for future experimental design

Advanced correlation-based character recognition applied to the Archimedes Palimpsest

The Archimedes Palimpsest is a manuscript containing the partial text of seven treatises by Archimedes that were copied onto parchment and bound in the tenth-century AD. This work is aimed at providing tools that allow scholars of ancient Greek mathematics to retrieve as much information as possible from images of the remaining degraded text. Acorrelation pattern recognition (CPR) system has been developed to recognize distorted versions of Greek characters in problematic regions of the palimpsest imagery, which have been obscured by damage from mold and fire, overtext, and natural aging. Feature vectors for each class of characters are constructed using a series of spatial correlation algorithms and corresponding performance metrics. Principal components analysis (PCA) is employed prior to classification to remove features corresponding to filtering schemes that performed poorly for the spatial characteristics of the selected region-of-interest. A probability is then assigned to each class, forming a character probability distribution based on relative distances from the class feature vectors to the ROI feature vector in principal component (PC) space. However, the current CPR system does not produce a single classification decision, as is common in most target detection problems, but instead has been designed to provide intermediate results that allow the user to apply his or her own decisions (or evidence) to arrive at a conclusion. To achieve this result, a probabilistic network has been incorporated into the recognition system. A probabilistic network represents a method for modeling the uncertainty in a system, and for this application, it allows information from the existing iv partial transcription and contextual knowledge from the user to be an integral part of the decision-making process. The CPR system was designed to provide a framework for future research in the area of spatial pattern recognition by accommodating a broad range of applications and the development of new filtering methods. For example, during preliminary testing, the CPR system was used to confirm the publication date of a fifteenth-century Hebrew colophon, and demonstrated success in the detection of registration markers in three-dimensional MRI breast imaging. In addition, a new correlation algorithm that exploits the benefits of linear discriminant analysis (LDA) and the inherent shift invariance of spatial correlation has been derived, implemented, and tested. Results show that this composite filtering method provides a high level of class discrimination while maintaining tolerance to withinclass distortions. With the integration of this algorithm into the existing filter library, this work completes each stage of a cyclic workflow using the developed CPR system, and provides the necessary tools for continued experimentation

Resource Allocation in Computer Vision

We broadly examine resource allocation in several computer vision problems. We consider human resource or computational resource constraints. Human resources, such as human operators monitoring a camera network, provide reliable information, but are typically limited by the huge amount of data to be processed. Computational resources refer to the resources used by machines, such as running time, to execute the programs. It is important to develop algorithms to make effective use of these resources in computer vision applications. We approach human resource constraints with a frame retrieval problem in a camera network. This work addresses the problem of using active inference to direct human attention in searching a camera network for people that match a query image. We find that by representing the camera network using a graphical model, we can more accurately determine which video frames match the query, and improve our ability to direct human attention. We experiment with different methods to determine from which frames to sample expert information from humans, and discover that a method that learns to predict which frame is misclassified gives the best performance. We approach the problem of allocating computational resource in a video processing task. We consider a video processing application in which we combine the outputs from two algorithms so that the budget-limited computationally more expensive algorithm is run in the most useful video frames to maximize processing performance. We model the video frames as a chain graphical model and extend a dynamic programming algorithm to determine on which frames to run the more expensive algorithm. We perform experiments on moving object detection and face detection to demonstrate the effectiveness of our approaches. Finally, we consider an idea for saving computational resources and maintaining program performance. We work on a problem of learning model complexity in latent variable models. Specifically, we learn the latent variable state space complexity in latent support vector machines using group norm regularization. We apply our method to handwritten digit recognition and object detection with deformable part models. Our approach reduces latent variable state size and performs faster inference with similar or better performance

The role of Walsh structure and ordinal linkage in the optimisation of pseudo-Boolean functions under monotonicity invariance.

Optimisation heuristics rely on implicit or explicit assumptions about the structure of the black-box fitness function they optimise. A review of the literature shows that understanding of structure and linkage is helpful to the design and analysis of heuristics. The aim of this thesis is to investigate the role that problem structure plays in heuristic optimisation. Many heuristics use ordinal operators; which are those that are invariant under monotonic transformations of the fitness function. In this thesis we develop a classification of pseudo-Boolean functions based on rank-invariance. This approach classifies functions which are monotonic transformations of one another as equivalent, and so partitions an infinite set of functions into a finite set of classes. Reasoning about heuristics composed of ordinal operators is, by construction, invariant over these classes. We perform a complete analysis of 2-bit and 3-bit pseudo-Boolean functions. We use Walsh analysis to define concepts of necessary, unnecessary, and conditionally necessary interactions, and of Walsh families. This helps to make precise some existing ideas in the literature such as benign interactions. Many algorithms are invariant under the classes we define, which allows us to examine the difficulty of pseudo-Boolean functions in terms of function classes. We analyse a range of ordinal selection operators for an EDA. Using a concept of directed ordinal linkage, we define precedence networks and precedence profiles to represent key algorithmic steps and their interdependency in terms of problem structure. The precedence profiles provide a measure of problem difficulty. This corresponds to problem difficulty and algorithmic steps for optimisation. This work develops insight into the relationship between function structure and problem difficulty for optimisation, which may be used to direct the development of novel algorithms. Concepts of structure are also used to construct easy and hard problems for a hill-climber