Marco Correia

On the Efficiency of Impact Based Heuristics

Recently proposed impact based heuristics have been shown to outperform other instances of the first-fail policy such as the common dom and dom/deg heuristics. This paper compares the behaviour of a constraint and a variable centered impact based heuristic and relates it to the amount of constraint propagation inherent to the model of the problem. Additionally, it presents results which suggest that a lookahead impact heuristic we recently proposed might be the best choice for problems with low locality and where constraint propagation plays an important role.

From phenotype to genotype in complex brain networks

Generative models are a popular instrument for illuminating the relationships between the hidden variables driving the growth of a complex network and its final topological characteristics, a process known as the “genotype to phenotype problem”. However, the definition of a complete methodology encompassing all stages of the analysis, and in particular the validation of the final model, is still an open problem. We here discuss a framework that allows to quantitatively optimise and validate each step of the model creation process. It is based on the execution of a classification task, and on estimating the additional precision provided by the modelled genotype. This encompasses the three main steps of the model creation, namely the selection of topological features, the optimisation of the parameters of the generative model, and the validation of the obtained results. We provide a minimum requirement for a generative model to be useful, prescribing the function mapping genotype to phenotype to be non-monotonic; and we further show how a previously published model does not fulfil such condition, casting doubts on its fitness for the study of neurological disorders. The generality of such framework guarantees its applicability beyond neuroscience, like the emergence of social or technological networks.

On the Integration of Singleton Consistencies and Look-Ahead Heuristics

The efficiency of complete solvers depends both on constraint propagation to narrow the domains and some form of complete search. Whereas constraint propagators should achieve a good trade-off between their complexity and the pruning that is obtained, search heuristics take decisions based on information about the state of the problem being solved. In general, these two components are independent and are indeed considered separately. A recent family of algorithms have been proposed to achieve a strong form of consistency called Singleton Consistency (SC). These algorithms perform a limited amount of search and propagation (lookahead) to remove inconsistent values from the variables domains, making SC costly to maintain. This paper follows from the observation that search states being explored while enforcing SC are an important source of information about the future search space which is being ignored. In this paper we discuss the integration of this look-ahead information into variable and value selection heuristics, and show that significant speedups are obtained in a number of standard benchmark problems.

Machine Learned Heuristics to Improve Constraint Satisfaction

Although propagation techniques are very important to solve constraint solving problems, heuristics are still necessary to handle non trivial problems efficiently. General principles may be defined for such heuristics (e.g. first-fail and best-promise), but problems arise in their implementation except for some limited sources of information (e.g. cardinality of variables domain). Other possibly relevant features are ignored due to the difficulty in understanding their interaction and a convenient way of integrating them. In this paper we illustrate such difficulties in a specific problem, determination of protein structure from Nuclear Magnetic Resonance (NMR) data. We show that machine learning techniques can be used to define better heuristics than the use of heuristics based on single features, or even than their combination in simple form (e.g majority vote). The technique is quite general and, with the necessary adaptations, may be applied to many other constraint satisfaction problems.

Probabilistic Constraint Programming for Parameters Optimisation of Generative Models

Complex networks theory has commonly been used for modelling and understanding the interactions taking place between the elements composing complex systems. More recently, the use of generative models has gained momentum, as they allow identifying which forces and mechanisms are responsible for the appearance of given structural properties. In spite of this interest, several problems remain open, one of the most important being the design of robust mechanisms for finding the optimal parameters of a generative model, given a set of real networks. In this contribution, we address this problem by means of Probabilistic Constraint Programming. By using as an example the reconstruction of networks representing brain dynamics, we show how this approach is superior to other solutions, in that it allows a better characterisation of the parameters space, while requiring a significantly lower computational cost.

View-based propagation of decomposable constraints

Constraints that may be obtained by composition from simpler constraints are present, in some way or another, in almost every constraint program. The decomposition of such constraints is a standard technique for obtaining an adequate propagation algorithm from a combination of propagators designed for simpler constraints. The decomposition approach is appealing in several ways. Firstly because creating a specific propagator for every constraint is clearly infeasible since the number of constraints is infinite. Secondly, because designing a propagation algorithm for complex constraints can be very challenging. Finally, reusing existing propagators allows to reduce the size of code to be developed and maintained. Traditionally, constraint solvers automatically decompose constraints into simpler ones using additional auxiliary variables and propagators, or expect the users to perform such decomposition themselves, eventually leading to the same propagation model. In this paper we explore views, an alternative way to create efficient propagators for such constraints in a modular, simple and correct way, which avoids the introduction of auxiliary variables and propagators.

Type Parametric Compilation of Algebraic Constraints

This paper addresses the problem of propagating constraints involving arbitrary algebraic expressions. We formally describe previous approaches to this problem and propose a new model that does not decompose the expression thus avoiding introducing auxiliary data structures. We show how this compilation model fits naturally in a popular programming language supporting type parametricity, yielding significant speedups with respect to previous models.

Reasoning with Uncertainty in Biomedical Models

The use of mathematical models in biomedical research largely developed in the second half of the 20th century. However, their translation to clinically useful tools has proved challenging. Reasoning with deep biomedical models is computationally demanding as parameters are typically subject to nonlinear relations, dynamic behavior, and uncertainty. This paper proposes a new approach for assessing the reliability of the conclusions drawn from these models given the underlying uncertainty. It relies on probabilistic constraint programming for a sound propagation of uncertainty from model parameters to results. The advantages of the approach are illustrated on an important problem in the obesity research field, namely the estimation of free-living energy intake in humans. Based on a well known energy intake model, our approach is able to correctly characterize the provided estimates given the uncertainty inherent to the model parameters.

Probabilistic Constraints for Robot Localization

In robot localization problems, uncertainty arises from many factors and must be considered together with the model constraints. Probabilistic robotics is the classical approach for dealing with hard robotic problems that relies on probability theory. This work describes the application of probabilistic constraint techniques in the context of probabilistic robotics to solve robot localization problems. Instead of providing the most probable position of the robot, the approach characterizes all positions consistent with the model and their probabilities (in accordance with the underlying uncertainty). It relies on constraint programming to get a tight covering of the consistent regions combined with Monte Carlo integration techniques that benefit from such reduction of the sampling space.

Uncertainty Propagation in Biomedical Models

Mathematical models are prevalent in modern medicine. However, reasoning with realistic biomedical models is computationally demanding as parameters are typically subject to nonlinear relations, dynamic behavior, and uncertainty. This paper addresses this problem by proposing a new framework based on constraint programming for a sound propagation of uncertainty from model parameters to results. We apply our approach to an important problem in the obesity research field, the estimation of free-living energy intake in humans. Complementary to alternative solutions, our approach is able to correctly characterize the provided estimates given the uncertainty inherent to the model parameters.