Banded matrices can be used as precision matrices in several models including linear state-space models, some Gaussian processes, and Gaussian Markov random fields. The aim of the paper is to make modern inference methods (such as variational inference or gradient-based sampling) available for Gaussian models with banded precision. We show that this can efficiently be achieved by equipping an automatic differentiation framework, such as TensorFlow or PyTorch, with some linear algebra operators dedicated to banded matrices. This paper studies the algorithmic aspects of the required operators, details their reverse-mode derivatives, and show that their complexity is linear in the number of observations.

Fully articulated hand tracking promises to enable fundamentally new interactions with virtual and augmented worlds, but the limited accuracy and efficiency of current systems has prevented widespread adoption. Today's dominant paradigm uses machine learning for initialization and recovery followed by iterative model-fitting optimization to achieve a detailed pose fit. We follow this paradigm, but make several changes to the model-fitting, namely using: (1) a more discriminative objective function; (2) a smooth-surface model that provides gradients for non-linear optimization; and (3) joint optimization over both the model pose and the correspondences between observed data points and the model surface. While each of these changes may actually increase the cost per fitting iteration, we find a compensating decrease in the number of iterations. Further, the wide basin of convergence means that fewer starting points are needed for successful model fitting. Our system runs in real-time on CPU only, which frees up the commonly over-burdened GPU for experience designers. The hand tracker is efficient enough to run on low-power devices such as tablets. We can track up to several meters from the camera to provide a large working volume for interaction, even using the noisy data from current-generation depth cameras. Quantitative assessments on standard datasets show that the new approach exceeds the state of the art in accuracy. Qualitative results take the form of live recordings of a range of interactive experiences enabled by this new approach.

Game theory is a highly successful paradigm for strategic decision making between multiple agents having conflicting objectives. Since a few years, games have been studied in a computational perspective, raising new issues like complexity of equilibria or succinctness of representation. Indeed, the main representation for general games is still a n-dimensional matrix of exponential size called normal form. In this paper, we introduce the framework of Constraint Games to model strategic interaction between players. A Constraint Game is composed of a set of variables shared by all the players. Among these variables, each player owns a set of decision variables she can control and a Constraint Optimization Problem defining her preferences. Since the preferences of a player depend on the decisions taken by the other players, each player may try to improve her position by choosing an assignment that optimizes her preferences. Pure Nash equilibria are situations in which no player may improve her preferences unilaterally. Constraint Games are thus a generic tool to model general games and can be exponentially more succinct than their normal form. We show the practical utility of the framework by modelling a few realistic problems and we propose an algorithm based on tabu search to compute pure Nash equilibria in Constraint games that outperforms the algorithms based on normal form. In addition, Constraint Games raise some interesting research issues that deserve further attention.

Bound propagation is an important Artificial Intelligence technique used in Constraint Programming tools to deal with numerical constraints. It is typically embedded within a search procedure (”branch and prune”) and used at every node of the search tree to narrow down the search space, so it is critical that it be fast. The procedure invokes constraint propagators until a common fixpoint is reached, but the known algorithms for this have a pseudo-polynomial worst-case time complexity: they are fast indeed when the variables have a small numerical range, but they have the well-known problem of being prohibitively slow when these ranges are large. An important question is therefore whether strongly-polynomial algorithms exist that compute the common bound consistent fixpoint of a set of constraints. This paper answers this question. In particular we show that this fixpoint computation is in fact NP-complete, even when restricted to binary linear constraints.

Motivated by the recent hardware evolution towards multi-core machines, we investigate parallel planning techniques in a shared-memory environment. We consider, more specifically, parallel versions of a best-first search algorithm that run K threads, each expanding the next best node from the open list. We show that the proposed technique has a number of advantages. First, it is (reasonably) simple: we show how the algorithm can be obtained from a sequential version mostly by adding parallel annotations. Second, we conduct an extensive empirical study that shows that this approach is quite effective. It is also dynamic in the sense that the number of nodes expanded in parallel is adapted during the search. Overall we show that the approach is promising for parallel domain-independent, suboptimal planning.

Quantified constraints and Quantified Boolean Formulae are typically much more difficult to reason with than classical constraints, because quantifier alternation makes the usual notion of solution inappropriate. As a consequence, basic properties of Constraint Satisfaction Problems (CSPs), such as consistency or substitutability, are not completely understood in the quantified case. These properties are important because they are the basis of most of the reasoning methods used to solve classical (existentially quantified) constraints, and it is desirable to benefit from similar reasoning methods in the resolution of quantified constraints. In this article, we show that most of the properties that are used by solvers for CSP can be generalized to quantified CSP. This requires a rethinking of a number of basic concepts; in particular, we propose a notion of outcome that generalizes the classical notion of solution and on which all definitions are based. We propose a systematic study of the relations which hold between these properties, as well as complexity results regarding the decision of these properties. Finally, and since these problems are typically intractable, we generalize the approach used in CSP and propose weaker, easier to check notions based on locality , which allow to detect these properties incompletely but in polynomial time.

Literature on Constraint Satisfaction exhibits the definition of several ``structural'' properties that can be possessed by CSPs, like (in)consistency, substitutability or interchangeability. Current tools for constraint solving typically detect such properties efficiently by means of incomplete yet effective algorithms, and use them to reduce the search space and boost search. In this paper, we provide a unifying framework encompassing most of the properties known so far, both in CSP and other fields' literature, and shed light on the semantical relationships among them. This gives a unified and comprehensive view of the topic, allows new, unknown, properties to emerge, and clarifies the computational complexity of the various detection problems. In particular, among the others, two new concepts, fixability and removability emerge, that come out to be the ideal characterisations of values that may be safely assigned or removed from a variable's domain, while preserving problem satisfiability. These two notions subsume a large number of known properties, including inconsistency, substitutability and others. Because of the computational intractability of all the property-detection problems, by following the CSP approach we then determine a number of relaxations which provide sufficient conditions for their tractability. In particular, we exploit forms of language restrictions and local reasoning.

The paper defines an automatic procedure for constructing a visually appealing collage from a collection of input images. The aim is that the resulting collage should be representative of the collection, summarising its main themes. It is also assembled largely seamlessly, using graph-cut, Poisson blending of alpha-masks, to hide the joins between input images. This paper makes several new contributions. Firstly, we show how energy terms can be included that: encourage the selection of a representative set of images; that are sensitive to particular object classes; that encourage a spatially efficient and seamless layout. Secondly the resulting optimization poses a search problem that, on the face of it, is computationally in-feasible. Rather than attempt an expensive, integrated optimization procedure, we have developed a sequence of optimization steps, from static ranking of images, through region of interest optimization, optimal packing by constraint satisfaction, and lastly graph-cut alpha-expansion. To illustrate the power of AutoCollage, we have used it to create collages of many home photo sets; we also conducted a user study in which AutoCollage outperformed competitive methods.

We argue that essential facets of Web services, and especially those useful to understand their interaction, can be described using process-algebraic notations. Web service description and execution languages such as BPEL are essentially process description languages; they are based on primitives for behaviour description and message exchange which can also be found in more abstract process algebras. One legitimate question is therefore whether the formal approach and the sophisticated tools introduced for process algebra can be used to improve the effectiveness and the reliability of Web service development. Our investigations suggest a positive answer, and we claim that process algebras provide a very complete and satisfactory assistance to the whole process of Web service development. We show on a case study that readily available tools based on process algebra are effective at verifying that Web services conform to their requirements and respect properties. We advocate their use both at the design stage and for reverse engineering issues. More prospectively, we discuss how they can be helpful to tackle choreography issues.

We study the properties of monotonic parts of (continuous) constraints. We design a general framework to reason about them : directions can be abstracted by signs, which capture significant information on the location of solutions. We show that this formalism is appropriate to study the relative position of solution sets. Efficient algorithms are proposed to diagnose the behaviour of some consistency techniques. These methods raise new perspectives on an open issue: the prediction of the consistency technique to be used wrt a given problem.