Efficient component-hypertree construction based on hierarchy of partitions

The component-hypertree is a data structure that generalizes the concept of component-tree to multiple (increasing) neighborhoods. However, construction of a component-hypertree is costly because it needs to process a high number of neighbors. In this article, we review some choices of neighborhoods for efficient component-hypertree computation. We also explore a new strategy to obtain neighboring elements based on hierarchy of partitions, leading to a more efficient algorithm with the counterpart of a slight decrease of precision on the distance of merged nodes

Connected image processing with multivariate attributes: an unsupervised Markovian classification approach

International audienceThis article presents a new approach for constructing connected operators for image processing and analysis. It relies on a hierarchical Markovian unsupervised algorithm in order to classify the nodes of the traditional Max-Tree. This approach enables to naturally handle multivariate attributes in a robust non-local way. The technique is demonstrated on several image analysis tasks: filtering, segmentation, and source detection, on astronomical and biomedical images. The obtained results show that the method is competitive despite its general formulation. This article provides also a new insight in the field of hierarchical Markovian image processing showing that morphological trees can advantageously replace traditional quadtrees

Efficient learning of decomposable models with a bounded clique size

The learning of probability distributions from data is a ubiquitous problem in the fields of Statistics and Artificial Intelligence. During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models due to their advantageous theoretical properties. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k, which controls the complexity of the model. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for k > 2. In this work, we propose a family of algorithms which approximates this problem with a computational complexity of O(k · n^2 log n) in the worst case, where n is the number of implied random variables. The structures of the decomposable models that solve the maximum likelihood problem are called maximal k-order decomposable graphs. Our proposals, called fractal trees, construct a sequence of maximal i-order decomposable graphs, for i = 2, ..., k, in k − 1 steps. At each step, the algorithms follow a divide-and-conquer strategy based on the particular features of this type of structures. Additionally, we propose a prune-and-graft procedure which transforms a maximal k-order decomposable graph into another one, increasing its likelihood. We have implemented two particular fractal tree algorithms called parallel fractal tree and sequential fractal tree. These algorithms can be considered a natural extension of Chow and Liu’s algorithm, from k = 2 to arbitrary values of k. Both algorithms have been compared against other efficient approaches in artificial and real domains, and they have shown a competitive behavior to deal with the maximum likelihood problem. Due to their low computational complexity they are especially recommended to deal with high dimensional domains

Planning in constraint space for multi-body manipulation tasks

Robots are inherently limited by physical constraints on their link lengths, motor torques, battery power and structural rigidity. To thrive in circumstances that push these limits, such as in search and rescue scenarios, intelligent agents can use the available objects in their environment as tools. Reasoning about arbitrary objects and how they can be placed together to create useful structures such as ramps, bridges or simple machines is critical to push beyond one's physical limitations. Unfortunately, the solution space is combinatorial in the number of available objects and the configuration space of the chosen objects and the robot that uses the structure is high dimensional. To address these challenges, we propose using constraint satisfaction as a means to test the feasibility of candidate structures and adopt search algorithms in the classical planning literature to find sufficient designs. The key idea is that the interactions between the components of a structure can be encoded as equality and inequality constraints on the configuration spaces of the respective objects. Furthermore, constraints that are induced by a broadly defined action, such as placing an object on another, can be grouped together using logical representations such as Planning Domain Definition Language (PDDL). Then, a classical planning search algorithm can reason about which set of constraints to impose on the available objects, iteratively creating a structure that satisfies the task goals and the robot constraints. To demonstrate the effectiveness of this framework, we present both simulation and real robot results with static structures such as ramps, bridges and stairs, and quasi-static structures such as lever-fulcrum simple machines.Ph.D

Automatic recognition of multiparty human interactions using dynamic Bayesian networks

Relating statistical machine learning approaches to the automatic analysis of multiparty communicative events, such as meetings, is an ambitious research area. We have investigated automatic meeting segmentation both in terms of “Meeting Actions” and “Dialogue Acts”. Dialogue acts model the discourse structure at a fine grained level highlighting individual speaker intentions. Group meeting actions describe the same process at a coarse level, highlighting interactions between different meeting participants and showing overall group intentions. A framework based on probabilistic graphical models such as dynamic Bayesian networks (DBNs) has been investigated for both tasks. Our first set of experiments is concerned with the segmentation and structuring of meetings (recorded using multiple cameras and microphones) into sequences of group meeting actions such as monologue, discussion and presentation. We outline four families of multimodal features based on speaker turns, lexical transcription, prosody, and visual motion that are extracted from the raw audio and video recordings. We relate these lowlevel multimodal features to complex group behaviours proposing a multistreammodelling framework based on dynamic Bayesian networks. Later experiments are concerned with the automatic recognition of Dialogue Acts (DAs) in multiparty conversational speech. We present a joint generative approach based on a switching DBN for DA recognition in which segmentation and classification of DAs are carried out in parallel. This approach models a set of features, related to lexical content and prosody, and incorporates a weighted interpolated factored language model. In conjunction with this joint generative model, we have also investigated the use of a discriminative approach, based on conditional random fields, to perform a reclassification of the segmented DAs. The DBN based approach yielded significant improvements when applied both to the meeting action and the dialogue act recognition task. On both tasks, the DBN framework provided an effective factorisation of the state-space and a flexible infrastructure able to integrate a heterogeneous set of resources such as continuous and discrete multimodal features, and statistical language models. Although our experiments have been principally targeted on multiparty meetings; features, models, and methodologies developed in this thesis can be employed for a wide range of applications. Moreover both group meeting actions and DAs offer valuable insights about the current conversational context providing valuable cues and features for several related research areas such as speaker addressing and focus of attention modelling, automatic speech recognition and understanding, topic and decision detection

Knowledge representation in probabilistic spatio-temporal knowledge bases

We represent knowledge as integrity constraints in a formalization of probabilistic spatio-temporal knowledge bases. We start by defining the syntax and semantics of a formalization called PST knowledge bases. This definition generalizes an earlier version, called SPOT, which is a declarative framework for the representation and processing of probabilistic spatio-temporal data where probability is represented as an interval because the exact value is unknown. We augment the previous definition by adding a type of non-atomic formula that expresses integrity constraints. The result is a highly expressive formalism for knowledge representation dealing with probabilistic spatio-temporal data. We obtain complexity results both for checking the consistency of PST knowledge bases and for answering queries in PST knowledge bases, and also specify tractable cases. All the domains in the PST framework are finite, but we extend our results also to arbitrarily large finite domains

Multi-objective optimization in graphical models

Many real-life optimization problems are combinatorial, i.e. they concern a choice of the best solution from a finite but exponentially large set of alternatives. Besides, the solution quality of many of these problems can often be evaluated from several points of view (a.k.a. criteria). In that case, each criterion may be described by a different objective function. Some important and well-known multicriteria scenarios are: · In investment optimization one wants to minimize risk and maximize benefits. · In travel scheduling one wants to minimize time and cost. · In circuit design one wants to minimize circuit area, energy consumption and maximize speed. · In knapsack problems one wants to minimize load weight and/or volume and maximize its economical value. The previous examples illustrate that, in many cases, these multiple criteria are incommensurate (i.e., it is difficult or impossible to combine them into a single criterion) and conflicting (i.e., solutions that are good with respect one criterion are likely to be bad with respect to another). Taking into account simultaneously the different criteria is not trivial and several notions of optimality have been proposed. Independently of the chosen notion of optimality, computing optimal solutions represents an important current research challenge. Graphical models are a knowledge representation tool widely used in the Artificial Intelligence field. They seem to be specially suitable for combinatorial problems. Roughly, graphical models are graphs in which nodes represent variables and the (lack of) arcs represent conditional independence assumptions. In addition to the graph structure, it is necessary to specify its micro-structure which tells how particular combinations of instantiations of interdependent variables interact. The graphical model framework provides a unifying way to model a broad spectrum of systems and a collection of general algorithms to efficiently solve them. In this Thesis we integrate multi-objective optimization problems into the graphical model paradigm and study how algorithmic techniques developed in the graphical model context can be extended to multi-objective optimization problems. As we show, multiobjective optimization problems can be formalized as a particular case of graphical models using the semiring-based framework. It is, to the best of our knowledge, the first time that graphical models in general, and semiring-based problems in particular are used to model an optimization problem in which the objective function is partially ordered. Moreover, we show that most of the solving techniques for mono-objective optimization problems can be naturally extended to the multi-objective context. The result of our work is the mathematical formalization of multi-objective optimization problems and the development of a set of multiobjective solving algorithms that have been proved to be efficient in a number of benchmarks.Muchos problemas reales de optimización son combinatorios, es decir, requieren de la elección de la mejor solución (o solución óptima) dentro de un conjunto finito pero exponencialmente grande de alternativas. Además, la mejor solución de muchos de estos problemas es, a menudo, evaluada desde varios puntos de vista (también llamados criterios). Es este caso, cada criterio puede ser descrito por una función objetivo. Algunos escenarios multi-objetivo importantes y bien conocidos son los siguientes: · En optimización de inversiones se pretende minimizar los riesgos y maximizar los beneficios. · En la programación de viajes se quiere reducir el tiempo de viaje y los costes. · En el diseño de circuitos se quiere reducir al mínimo la zona ocupada del circuito, el consumo de energía y maximizar la velocidad. · En los problemas de la mochila se quiere minimizar el peso de la carga y/o el volumen y maximizar su valor económico. Los ejemplos anteriores muestran que, en muchos casos, estos criterios son inconmensurables (es decir, es difícil o imposible combinar todos ellos en un único criterio) y están en conflicto (es decir, soluciones que son buenas con respecto a un criterio es probable que sean malas con respecto a otra). Tener en cuenta de forma simultánea todos estos criterios no es trivial y para ello se han propuesto diferentes nociones de optimalidad. Independientemente del concepto de optimalidad elegido, el cómputo de soluciones óptimas representa un importante desafío para la investigación actual. Los modelos gráficos son una herramienta para la represetanción del conocimiento ampliamente utilizados en el campo de la Inteligencia Artificial que parecen especialmente indicados en problemas combinatorios. A grandes rasgos, los modelos gráficos son grafos en los que los nodos representan variables y la (falta de) arcos representa la interdepencia entre variables. Además de la estructura gráfica, es necesario especificar su (micro-estructura) que indica cómo interactúan instanciaciones concretas de variables interdependientes. Los modelos gráficos proporcionan un marco capaz de unificar el modelado de un espectro amplio de sistemas y un conjunto de algoritmos generales capaces de resolverlos eficientemente. En esta tesis integramos problemas de optimización multi-objetivo en el contexto de los modelos gráficos y estudiamos cómo diversas técnicas algorítmicas desarrolladas dentro del marco de los modelos gráficos se pueden extender a problemas de optimización multi-objetivo. Como mostramos, este tipo de problemas se pueden formalizar como un caso particular de modelo gráfico usando el paradigma basado en semi-anillos (SCSP). Desde nuestro conocimiento, ésta es la primera vez que los modelos gráficos en general, y el paradigma basado en semi-anillos en particular, se usan para modelar un problema de optimización cuya función objetivo está parcialmente ordenada. Además, mostramos que la mayoría de técnicas para resolver problemas monoobjetivo se pueden extender de forma natural al contexto multi-objetivo. El resultado de nuestro trabajo es la formalización matemática de problemas de optimización multi-objetivo y el desarrollo de un conjunto de algoritmos capaces de resolver este tipo de problemas. Además, demostramos que estos algoritmos son eficientes en un conjunto determinado de benchmarks