In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic graphical models, deserves attention. Its simple structure - a tree - allows simple and efficient inference, while its latent variables capture complex relationships. In the past decade, the latent tree model has been subject to significant theoretical and methodological developments. In this review, we propose a comprehensive study of this model. First we summarize key ideas underlying the model. Second we explain how it can be efficiently learned from data. Third we illustrate its use within three types of applications: latent structure discovery, multidimensional clustering, and probabilistic inference. Finally, we conclude and give promising directions for future researches in this field.

We introduce a novel class of rotation invariants of two dimensional curves based on iterated integrals. The invariants we present are in some sense complete and we describe an algorithm to calculate them, giving explicit computations up to order six. We present an application to online (stroke-trajectory based) character recognition. This seems to be the first time in the literature that the use of iterated integrals of a curve is proposed for (invariant) feature extraction in machine learning applications.

We propose a reinforcement learning solution to the \emph{soccer dribbling task}, a scenario in which a soccer agent has to go from the beginning to the end of a region keeping possession of the ball, as an adversary attempts to gain possession. While the adversary uses a stationary policy, the dribbler learns the best action to take at each decision point. After defining meaningful variables to represent the state space, and high-level macro-actions to incorporate domain knowledge, we describe our application of the reinforcement learning algorithm \emph{Sarsa} with CMAC for function approximation. Our experiments show that, after the training period, the dribbler is able to accomplish its task against a strong adversary around 58% of the time.

In this communication, we describe some interrelations between generalized $q$-entropies and a generalized version of Fisher information. In information theory, the de Bruijn identity links the Fisher information and the derivative of the entropy. We show that this identity can be extended to generalized versions of entropy and Fisher information. More precisely, a generalized Fisher information naturally pops up in the expression of the derivative of the Tsallis entropy. This generalized Fisher information also appears as a special case of a generalized Fisher information for estimation problems. Indeed, we derive here a new Cram\'er-Rao inequality for the estimation of a parameter, which involves a generalized form of Fisher information. This generalized Fisher information reduces to the standard Fisher information as a particular case. In the case of a translation parameter, the general Cram\'er-Rao inequality leads to an inequality for distributions which is saturated by generalized $q$-Gaussian distributions. These generalized $q$-Gaussians are important in several areas of physics and mathematics. They are known to maximize the $q$-entropies subject to a moment constraint. The Cram\'er-Rao inequality shows that the generalized $q$-Gaussians also minimize the generalized Fisher information among distributions with a fixed moment. Similarly, the generalized $q$-Gaussians also minimize the generalized Fisher information among distributions with a given $q$-entropy.

We propose a modified $\chi^{\beta}$-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cram\'er-Rao inequalities, involving this Fisher information, an extension of the Fisher information matrix, and arbitrary norms and power of the estimation error. In the case of a location parameter, we obtain new characterizations of the generalized $q$-Gaussians, for instance as the distribution with a given moment that minimizes the generalized Fisher information. Finally we indicate how the generalized Fisher information can lead to new uncertainty relations.

It is widely recognized that incorporating latent or hidden variables is a crucial aspect of modeling. Latent variables can provide a succinct representation of the observed data through dimensionality reduction; the possibly many observed variables are summarized by fewer hidden effects. Further, they are central to predicting causal relationships and interpreting the hidden effects as unobservable concepts. For instance in sociology, human behavior is affected by abstract notions such as social attitudes, beliefs, goals and plans. As another example, medical knowledge is organized into casual hierarchies of invading organisms, physical disorders, pathological states and symptoms, and only the symptoms are observed. In addition to incorporating latent variables, it is also important to model the complex dependencies among the variables. A popular class of models for incorporating such dependencies are the Bayesian networks, also known as belief networks. They incorporate a set of causal and conditional independence relationships through directed acyclic graphs (DAG) [49]. They have widespread applicability in artificial intelligence [19, 25, 41, 42], in the social sciences [13, 18, 40, 50, 51, 64], and as structural equation models in economics [12, 18, 33, 51, 60, 65].

In this contribution we describe an approach to evolve composite covariance functions for Gaussian processes using genetic programming. A critical aspect of Gaussian processes and similar kernel-based models such as SVM is, that the covariance function should be adapted to the modeled data. Frequently, the squared exponential covariance function is used as a default. However, this can lead to a misspecified model, which does not fit the data well. In the proposed approach we use a grammar for the composition of covariance functions and genetic programming to search over the space of sentences that can be derived from the grammar. We tested the proposed approach on synthetic data from two-dimensional test functions, and on the Mauna Loa CO2 time series. The results show, that our approach is feasible, finding covariance functions that perform much better than a default covariance function. For the CO2 data set a composite covariance function is found, that matches the performance of a hand-tuned covariance function.

Dungs abstract argumentation theory can be seen as a general framework for non-monotonic reasoning. An important question is then: what is the class of logics that can be subsumed as instantiations of this theory? The goal of this paper is to identify and study the large class of logic-based instantiations of Dungs theory which correspond to the maxi-consistent operator, i.e. to the function which returns maximal consistent subsets of an inconsistent knowledge base. In other words, we study the class of instantiations where very extension of the argumentation system corresponds to exactly one maximal consistent subset of the knowledge base. We show that an attack relation belonging to this class must be conflict-dependent, must not be valid, must not be conflict-complete, must not be symmetric etc. Then, we show that some attack relations serve as lower or upper bounds of the class (e.g. if an attack relation contains canonical undercut then it is not a member of this class). By using our results, we show for all existing attack relations whether or not they belong to this class. We also define new attack relations which are members of this class. Finally, we interpret our results and discuss more general questions, like: what is the added value of argumentation in such a setting? We believe that this work is a first step towards achieving our long-term goal, which is to better understand the role of argumentation and, particularly, the expressivity of logic-based instantiations of Dung-style argumentation frameworks.

We address a dynamic repair shop scheduling problem in the context of military aircraft fleet management where the goal is to maintain a full complement of aircraft over the long-term. A number of flights, each with a requirement for a specific number and type of aircraft, are already scheduled over a long horizon. We need to assign aircraft to flights and schedule repair activities while considering the flights requirements, repair capacity, and aircraft failures. The number of aircraft awaiting repair dynamically changes over time due to failures and it is therefore necessary to rebuild the repair schedule online. To solve the problem, we view the dynamic repair shop as successive static repair scheduling sub-problems over shorter time periods. We propose a complete approach based on the logic-based Benders decomposition to solve the static sub-problems, and design different rescheduling policies to schedule the dynamic repair shop. Computational experiments demonstrate that the Benders model is able to find and prove optimal solutions on average four times faster than a mixed integer programming model. The rescheduling approach having both aspects of scheduling over a longer horizon and quickly adjusting the schedule increases aircraft available in the long term by 10% compared to the approaches having either one of the aspects alone.

This different outlook makes Dependence Logic a most suitable framework for the formal study, in a first-order setting, of functional dependence itself; and, furthermore, this logic is readily adaptable to the analysis of other, nonfunctional notions of dependence or independence [11, 6, 8]. Like other logics of imperfect information, Dependence Logic admits both a Game Theoretic Semantics, an imperfect information variant of the one for First Order Logic, and a Team Semantics, a compositional semantics which is a natural adaptation of Hodges' Trump Semantics [15]. One striking peculiarity of the current state of the art of the research in Dependence Logic and its extensions is a willingness to take Team Semantics - and not Game Theoretic Semantics, as for the case of much IF Logic research - as the fundamental semantic framework; and this different approach is at the root of many recent technical developments in the field, such as, for example, the characterizations of team class definability of [17], [16] and [8], the hierarchy results of [4], and the study of notions of generalized quantification of [6] and [5]. This paper is a detailed account of a doxastic interpretation for Team Semantics, according to which formulas are to be interpreted as assertions about beliefs and belief updates. This is not a novel idea: as a matter of fact, it is already implicit in the equivalence proof between Trump Semantics and Game Theoretic Semantics of [15].