Jorge Cruz

Global Hull Consistency with Local Search for Continuous Constraint Solving

This paper addresses constraint solving over continuous domains in the context of decision making, and discusses the trade-off between precision in the definition of the solution space and the computational effort required. In alternative to local consistency, which is usually maintained in handling continuous constraints, we discuss maintaining global hull-consistency. Experimental results show that this may be an appropriate choice, achieving acceptable precision with relatively low computational cost. The approach relies on efficient algorithms and the best results are obtained with the integration of a local search procedure within interval constraint propagation.

Constraint reasoning in deep biomedical models

Objective:: Deep biomedical models are often expressed by means of differential equations. Despite their expressive power, they are difficult to reason about and make decisions, given their non-linearity and the important effects that the uncertainty on data may cause. The objective of this work is to propose a constraint reasoning framework to support safe decisions based on deep biomedical models. Method:: The methods used in our approach include the generic constraint propagation techniques for reducing the bounds of uncertainty of the numerical variables complemented with new constraint reasoning techniques that we developed to handle differential equations. Results:: The results of our approach are illustrated in biomedical models for the diagnosis of diabetes, tuning of drug design and epidemiology where it was a valuable decision-supporting tool notwithstanding the uncertainty on data. Conclusion:: The main conclusion that follows from the results is that, in biomedical decision support, constraint reasoning may be a worthwhile alternative to traditional simulation methods, especially when safe decisions are required.

Maintaining Global Hull Consistency with Local Search for Continuous CSPs

This paper addresses constraint solving over continuous domains in the context of decision making, and discusses the trade-off between precision in the definition of the solution space and the computational efforts required. In alternative to local consistency, we propose maintaining global hull-consistency and present experimental results that show that this may be an appropriate alternative to other higher order consistencies. We tested various global hull enforcing algorithms and the best results were obtained with the integration of a local search procedure within interval constraint propagation.

Constraint satisfaction differential problems

System dynamics is often modeled by means of parametric differential equations. Despite their expressive power, they are difficult to reason about and make safe decisions, given their non-linearity and the important effects that the uncertainty on data may cause. Either by traditional numerical simulation or relying on constraint based methods, it is difficult to express a number of constraints on the solution functions (for which there are usually no analytical solutions) and these constraints may only be handled passively, with generate and test techniques. In contrast, the framework we propose not only extends the declarativeness of the constraint based approach but also makes an active use of constraints on the solution functions, which makes it particularly suited for a number of decision making problems, such as those arising in the biomedical applications presented in the paper.

Handling Differential Equations with Constraints for Decision Support

The behaviour of many systems is naturally modelled by a set of ordinary differential equations (ODEs) which are parametric. Since decisions are often based on relations over these parameters it is important to know them with sufficient precision to make those decisions safe. This is in principle an adequate field to use interval domains for the parameters, and constraint propagation to obtain safe bounds for them. Although complex, the use of interval constraints with ODEs is receiving increasing interest. However, the usual consistency maintenance techniques (box- and local hull-consistency) for interval domains are often insufficient to cope with parametric ODEs. In this paper we propose a stronger consistency requirement, global hull-consistency, and an algorithm to compute it. To speed up this computation we developed an incremental approach to refine as needed the precision of ODEs trajectories. Our methodology is illustrated with an example of decision support in a medical problem (diagnosis of diabetes).

An Interval Constraint Approach to Handle Parametric Ordinary Differential Equations for Decision Support

Model-based decision support systems rely on an explicit representation of some system whose dynamics is often qualitatively described by specifying the rates at which the system variables change. Such models are naturally represented as a set of ordinary differential equations (ODEs) which are parametric (they include parameters whose value is not known exactly). If safe decisions are to be made based on the values of these parameters, it is important to know them with sufficient precision.

A Causal-Functional Model Applied to EMG Diagnosis

This paper presents an EMG diagnostic Knowledge Based System, that is the first application of our methodology for reasoning with causal-functional (meta-)models. Despite past difficulties, diagnosis is still an important application of KBSs, if considered in an appropriate context of medical practice. We argue that this is the case with neurophisiology, which lends to deep modelling of the domain and associated reasoning. The results obtained with our prototype system, and the clinical context where the system may be used make it a quite promising application, not only to experiment advanced artificial intelligence techniques but also to provide an useful decision support system for medical practice.

Convergence analysis and adaptive strategy for the certified quadrature over a set defined by inequalities

This paper investigates the sufficient conditions for the asymptotic convergence of a generic branch and prune algorithm dedicated to the verified quadrature of a function in several variables. Quadrature over domains defined by inequalities, and adaptive meshing strategies are in the scope of this analysis. The framework is instantiated using certified quadrature methods based on Taylor models (i.e. Taylor approximations with rigorously bounded remainder), and reported experiments confirmed the analysis. They also show that the performances of the instantiated algorithm are comparable with current methods for certified quadrature.

Probabilistic Constraints for Nonlinear Inverse Problems

The probabilistic continuous constraint (PC) framework complements the representation of uncertainty by means of intervals with a probabilistic distribution of values within such intervals. This paper, published in Constraints [8], describes how nonlinear inverse problems can be cast into this framework, highlighting its ability to deal with all the uncertainty aspects of such problems, and illustrates this new methodology in Ocean Color (OC), a research area widely used in climate change studies with significant applications in water quality monitoring.

Reasoning with Uncertainty in Continuous Domains

Continuous constraint programming has been widely used to model safe reasoning in applications where uncertainty arises. Constraint propagation propagates intervals of uncertainty among the variables of the problem, eliminating values that do not belong to any solution. However, to play safe, these intervals may be very wide and lead to poor propagation. We proposed a probabilistic continuous constraint framework that associates a probabilistic space to the variables of the problem, allowing to distinguish between different scenarios, based on their likelihoods. In this paper we discuss the capabilities of the framework for decision support in nonlinear continuous problems with uncertain information. Its applicability is illustrated in inverse and reliability problems, which are two different types of problems representative of the kind of reasoning required by the decision makers.