An undirected graphical model is a joint probability distribution defined on an undirected graph G*, where the vertices in the graph index a collection of random variables and the edges encode conditional independence relationships among random variables. The undirected graphical model selection (UGMS) problem is to estimate the graph G* given observations drawn from the undirected graphical model. This paper proposes a framework for decomposing the UGMS problem into multiple subproblems over clusters and subsets of the separators in a junction tree. The junction tree is constructed using a graph that contains a superset of the edges in G*. We highlight three main properties of using junction trees for UGMS. First, different regularization parameters or different UGMS algorithms can be used to learn different parts of the graph. This is possible since the subproblems we identify can be solved independently of each other. Second, under certain conditions, a junction tree based UGMS algorithm can produce consistent results with fewer observations than the usual requirements of existing algorithms. Third, both our theoretical and experimental results show that the junction tree framework does a significantly better job at finding the weakest edges in a graph than existing methods. This property is a consequence of both the first and second properties. Finally, we note that our framework is independent of the choice of the UGMS algorithm and can be used as a wrapper around standard UGMS algorithms for more accurate graph estimation.

Recently, it was shown that there is a phase transition in the community detection problem. This transition was first computed using the cavity method, and has been proved rigorously in the case of $q=2$ groups. However, analytic calculations using the cavity method are challenging since they require us to understand probability distributions of messages. We study analogous transitions in so-called "zero-temperature inference" model, where this distribution is supported only on the most-likely messages. Furthermore, whenever several messages are equally likely, we break the tie by choosing among them with equal probability. While the resulting analysis does not give the correct values of the thresholds, it does reproduce some of the qualitative features of the system. It predicts a first-order detectability transition whenever $q > 2$, while the finite-temperature cavity method shows that this is the case only when $q > 4$. It also has a regime analogous to the "hard but detectable" phase, where the community structure can be partially recovered, but only when the initial messages are sufficiently accurate. Finally, we study a semisupervised setting where we are given the correct labels for a fraction $\rho$ of the nodes. For $q > 2$, we find a regime where the accuracy jumps discontinuously at a critical value of $\rho$.

Reconstructing transcriptional regulatory networks is an important task in functional genomics. Data obtained from experiments that perturb genes by knockouts or RNA interference contain useful information for addressing this reconstruction problem. However, such data can be limited in size and/or are expensive to acquire. On the other hand, observational data of the organism in steady state (e.g. wild-type) are more readily available, but their informational content is inadequate for the task at hand. We develop a computational approach to appropriately utilize both data sources for estimating a regulatory network. The proposed approach is based on a three-step algorithm to estimate the underlying directed but cyclic network, that uses as input both perturbation screens and steady state gene expression data. In the first step, the algorithm determines causal orderings of the genes that are consistent with the perturbation data, by combining an exhaustive search method with a fast heuristic that in turn couples a Monte Carlo technique with a fast search algorithm. In the second step, for each obtained causal ordering, a regulatory network is estimated using a penalized likelihood based method, while in the third step a consensus network is constructed from the highest scored ones. Extensive computational experiments show that the algorithm performs well in reconstructing the underlying network and clearly outperforms competing approaches that rely only on a single data source. Further, it is established that the algorithm produces a consistent estimate of the regulatory network.

Screening is the problem of finding a superset of the set of non-zero entries in an unknown p-dimensional vector \beta* given n noisy observations. Naturally, we want this superset to be as small as possible. We propose a novel framework for screening, which we refer to as Multiple Grouping (MuG), that groups variables, performs variable selection over the groups, and repeats this process multiple number of times to estimate a sequence of sets that contains the non-zero entries in \beta*. Screening is done by taking an intersection of all these estimated sets. The MuG framework can be used in conjunction with any group based variable selection algorithm. In the high-dimensional setting, where p >> n, we show that when MuG is used with the group Lasso estimator, screening can be consistently performed without using any tuning parameter. Our numerical simulations clearly show the merits of using the MuG framework in practice.

Bayesian planning is a formally elegant approach to learning optimal behaviour under model uncertainty, trading off exploration and exploitation in an ideal way. Unfortunately, planning optimally in the face of uncertainty is notoriously taxing, since the search space is enormous. In this paper we introduce a tractable, sample-based method for approximate Bayes-optimal planning which exploits Monte-Carlo tree search. Our approach avoids expensive applications of Bayes rule within the search tree by sampling models from current beliefs, and furthermore performs this sampling in a lazy manner. This enables it to outperform previous Bayesian model-based reinforcement learning algorithms by a significant margin on several well-known benchmark problems. As we show, our approach can even work in problems with an infinite state space that lie qualitatively out of reach of almost all previous work in Bayesian exploration.

For almost two decades, monotonic, or ``delete free,'' relaxation has been one of the key auxiliary tools in the practice of domain-independent deterministic planning. In the particular contexts of both satisficing and optimal planning, it underlies most state-of-the-art heuristic functions. While satisficing planning for monotonic tasks is polynomial-time, optimal planning for monotonic tasks is NP-equivalent. Here we establish both negative and positive results on the complexity of some wide fragments of optimal monotonic planning, with the fragments being defined around the causal graph topology. Our results shed some light on the link between the complexity of general optimal planning and the complexity of optimal planning for the respective monotonic relaxations.

Relational classification on a single connected network has been of particular interest in the machine learning and data mining communities in the last decade or so. This is mainly due to the explosion in popularity of social networking sites such as Facebook, LinkedIn and Google+ amongst others. In statistical relational learning, many techniques have been developed to address this problem, where we have a connected unweighted homogeneous/heterogeneous graph that is partially labeled and the goal is to propagate the labels to the unlabeled nodes. In this paper, we provide a different perspective by enabling the effective use of graph transduction techniques for this problem. We thus exploit the strengths of this class of methods for relational learning problems. We accomplish this by providing a simple procedure for constructing a weight matrix that serves as input to a rich class of graph transduction techniques. Our procedure has multiple desirable properties. For example, the weights it assigns to edges between unlabeled nodes naturally relate to a measure of association commonly used in statistics, namely the Gamma test statistic. We further portray the efficacy of our approach on synthetic as well as real data, by comparing it with state-of-the-art relational learning algorithms, and graph transduction techniques with an adjacency matrix or a real valued weight matrix computed using available attributes as input. In these experiments we see that our approach consistently outperforms other approaches when the graph is sparsely labeled, and remains competitive with the best when the proportion of known labels increases.

In this paper we present a review of the existing typologies of Internet service users. We zoom in on social networking services including blogs and crowdsourcing websites. Based on the results of the analysis of the considered typologies obtained by means of FCA we developed a new user typology of a certain class of Internet services, namely a collaboration innovation platform. Cluster analysis of data extracted from the collaboration platform Witology was used to divide more than 500 participants into six groups based on three activity indicators: idea generation, commenting, and evaluation (assigning marks) The obtained groups and their percentages appear to follow the "90 - 9 - 1" rule.

Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ non-convex optimization. In this paper, we take a third approach. We utilize a non-convex regularization term chosen such that the total cost function (consisting of data consistency and regularization terms) is convex. Therefore, sparsity is more strongly promoted than in the standard convex formulation, but without sacrificing the attractive aspects of convex optimization (unique minimum, robust algorithms, etc.). We use this idea to improve the recently developed 'overlapping group shrinkage' (OGS) algorithm for the denoising of group-sparse signals. The algorithm is applied to the problem of speech enhancement with favorable results in terms of both SNR and perceptual quality.

Answer Set Programming (ASP) is a popular framework for modeling combinatorial problems. However, ASP cannot easily be used for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, where this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP, in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.