We develop mask iterative hard thresholding algorithms (mask IHT and mask DORE) for sparse image reconstruction of objects with known contour. The measurements follow a noisy underdetermined linear model common in the compressive sampling literature. Assuming that the contour of the object that we wish to reconstruct is known and that the signal outside the contour is zero, we formulate a constrained residual squared error minimization problem that incorporates both the geometric information (i.e. the knowledge of the object's contour) and the signal sparsity constraint. We first introduce a mask IHT method that aims at solving this minimization problem and guarantees monotonically non-increasing residual squared error for a given signal sparsity level. We then propose a double overrelaxation scheme for accelerating the convergence of the mask IHT algorithm. We also apply convex mask reconstruction approaches that employ a convex relaxation of the signal sparsity constraint. In X-ray computed tomography (CT), we propose an automatic scheme for extracting the convex hull of the inspected object from the measured sinograms; the obtained convex hull is used to capture the object contour information. We compare the proposed mask reconstruction schemes with the existing large-scale sparse signal reconstruction methods via numerical simulations and demonstrate that, by exploiting both the geometric contour information of the underlying image and sparsity of its wavelet coefficients, we can reconstruct this image using a significantly smaller number of measurements than the existing methods.

This paper establishes information-theoretic limits in estimating a finite field low-rank matrix given random linear measurements of it. These linear measurements are obtained by taking inner products of the low-rank matrix with random sensing matrices. Necessary and sufficient conditions on the number of measurements required are provided. It is shown that these conditions are sharp and the minimum-rank decoder is asymptotically optimal. The reliability function of this decoder is also derived by appealing to de Caen's lower bound on the probability of a union. The sufficient condition also holds when the sensing matrices are sparse - a scenario that may be amenable to efficient decoding. More precisely, it is shown that if the n\times n-sensing matrices contain, on average, \Omega(nlog n) entries, the number of measurements required is the same as that when the sensing matrices are dense and contain entries drawn uniformly at random from the field. Analogies are drawn between the above results and rank-metric codes in the coding theory literature. In fact, we are also strongly motivated by understanding when minimum rank distance decoding of random rank-metric codes succeeds. To this end, we derive distance properties of equiprobable and sparse rank-metric codes. These distance properties provide a precise geometric interpretation of the fact that the sparse ensemble requires as few measurements as the dense one. Finally, we provide a non-exhaustive procedure to search for the unknown low-rank matrix.

A linear non-Gaussian structural equation model called LiNGAM is an identifiable model for exploratory causal analysis. Previous methods estimate a causal ordering of variables and their connection strengths based on a single dataset. However, in many application domains, data are obtained under different conditions, that is, multiple datasets are obtained rather than a single dataset. In this paper, we present a new method to jointly estimate multiple LiNGAMs under the assumption that the models share a causal ordering but may have different connection strengths and differently distributed variables. In simulations, the new method estimates the models more accurately than estimating them separately.

We consider the problem of manipulating elections by cloning candidates. In our model, a manipulator can replace each candidate c by several clones, i.e., new candidates that are so similar to c that each voter simply replaces c in his vote with a block of these new candidates, ranked consecutively. The outcome of the resulting election may then depend on the number of clones as well as on how each voter orders the clones within the block. We formalize what it means for a cloning manipulation to be successful (which turns out to be a surprisingly delicate issue), and, for a number of common voting rules, characterize the preference profiles for which a successful cloning manipulation exists. We also consider the model where there is a cost associated with producing each clone, and study the complexity of finding a minimum-cost cloning manipulation. Finally, we compare cloning with two related problems: the problem of control by adding candidates and the problem of possible (co)winners when new alternatives can join.

Semisupervised methods inevitably invoke some assumption that links the marginal distribution of the features to the regression function of the label. Most commonly, the cluster or manifold assumptions are used which imply that the regression function is smooth over high-density clusters or manifolds supporting the data. A generalization of these assumptions is that the regression function is smooth with respect to some density sensitive distance. This motivates the use of a density based metric [Bousquet et al., 2004, Coif-man and Lafon, 2006, Sajama and Orlitsky, 2005] for semisupervised learning. We analyze this setting and make the following contributions - (a) we propose a semi-supervised learner that uses a density-sensitive kernel and show that it provides better performance than any supervised learner if the density support set has a small condition number and (b) we show that it is possible to adapt to the degree of semi-supervisedness using data-dependent choice of a parameter that controls sensitivity of the distance metric to the density. This ensures that the semisupervised learner never performs worse than a supervised learner even if the assumptions fail to hold.

Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model. Especially, graphical models provide the following several useful properties: - Graphical models provide a simple and intuitive interpretation of the structures of probabilistic models. On the other hand, they can be used to design and motivate new models. - Graphical models provide additional insights into the properties of the model, including the conditional independence properties. - Complex computations which are required to perform inference and learning in sophisticated models can be expressed in terms of graphical manipulations, in which the underlying mathematical expressions are carried along implicitly. The graphical models have been applied to a large number of fields, including bioinformatics, social science, control theory, image processing, marketing analysis, among others. However, structure learning for graphical models remains an open challenge, since one must cope with a combinatorial search over the space of all possible structures. In this paper, we present a comprehensive survey of the existing structure learning algorithms.

Recent breakthrough results in compressed sensing (CS) have established that many high dimensional objects can be accurately recovered from a relatively small number of non- adaptive linear projection observations, provided that the objects possess a sparse representation in some basis. Subsequent efforts have shown that the performance of CS can be improved by exploiting the structure in the location of the non-zero signal coefficients (structured sparsity) or using some form of online measurement focusing (adaptivity) in the sensing process. In this paper we examine a powerful hybrid of these two techniques. First, we describe a simple adaptive sensing procedure and show that it is a provably effective method for acquiring sparse signals that exhibit structured sparsity characterized by tree-based coefficient dependencies. Next, employing techniques from sparse hierarchical dictionary learning, we show that representations exhibiting the appropriate form of structured sparsity can be learned from collections of training data. The combination of these techniques results in an effective and efficient adaptive compressive acquisition procedure.

Hierarchical Task Network (HTN) planning uses task decomposition to plan for an executable sequence of actions as a solution to a problem. In order to reason effectively, an HTN planner needs expressive domain knowledge. For instance, a simplified HTN planning system such as JSHOP2 uses such expressivity and avoids some task interactions due to the increased complexity of the planning process. We address the possibility of simplifying the domain representation needed for an HTN planner to find good solutions, especially in real-world domains describing home and building automation environments. We extend the JSHOP2 planner to reason about task interaction that happens when task's effects are already achieved by other tasks. The planner then prunes some of the redundant searches that can occur due to the planning process's interleaving nature. We evaluate the original and our improved planner on two benchmark domains. We show that our planner behaves better by using simplified domain knowledge and outperforms JSHOP2 in a number of relevant cases.

This article is devoted to the study of methods to change defeasible logic programs (de.l.p.s) which are the knowledge bases used by the Defeasible Logic Programming (DeLP) interpreter. DeLP is an argumentation formalism that allows to reason over potentially inconsistent de.l.p.s. Argument Theory Change (ATC) studies certain aspects of belief revision in order to make them suitable for abstract argumentation systems. In this article, abstract arguments are rendered concrete by using the particular rule-based defeasible logic adopted by DeLP. The objective of our proposal is to define prioritized argument revision operators \`a la ATC for de.l.p.s, in such a way that the newly inserted argument ends up undefeated after the revision, thus warranting its conclusion. In order to ensure this warrant, the de.l.p. has to be changed in concordance with a minimal change principle. To this end, we discuss different minimal change criteria that could be adopted. Finally, an algorithm is presented, implementing the argument revision operations.

Discovering causal relationships is a hard task, often hindered by the need for intervention, and often requiring large amounts of data to resolve statistical uncertainty. However, humans quickly arrive at useful causal relationships. One possible reason is that humans extrapolate from past experience to new, unseen situations: that is, they encode beliefs over causal invariances, allowing for sound generalization from the observations they obtain from directly acting in the world. Here we outline a Bayesian model of causal induction where beliefs over competing causal hypotheses are modeled using probability trees. Based on this model, we illustrate why, in the general case, we need interventions plus constraints on our causal hypotheses in order to extract causal information from our experience.