Spontaneous brain activity, as observed in functional neuroimaging, has been shown to display reproducible structure that expresses brain architecture and carries markers of brain pathologies. An important view of modern neuroscience is that such large-scale structure of coherent activity reflects modularity properties of brain connectivity graphs. However, to date, there has been no demonstration that the limited and noisy data available in spontaneous activity observations could be used to learn full-brain probabilistic models that generalize to new data. Learning such models entails two main challenges: i) modeling full brain connectivity is a difficult estimation problem that faces the curse of dimensionality and ii) variability between subjects, coupled with the variability of functional signals between experimental runs, makes the use of multiple datasets challenging. We describe subject-level brain functional connectivity structure as a multivariate Gaussian process and introduce a new strategy to estimate it from group data, by imposing a common structure on the graphical model in the population. We show that individual models learned from functional Magnetic Resonance Imaging (fMRI) data using this population prior generalize better to unseen data than models based on alternative regularization schemes. To our knowledge, this is the first report of a cross-validated model of spontaneous brain activity. Finally, we use the estimated graphical model to explore the large-scale characteristics of functional architecture and show for the first time that known cognitive networks appear as the integrated communities of functional connectivity graph.

Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization problem by replacing the cardinality function by its convex envelope (tightest convex lower bound), in this case the L1-norm. In this paper, we investigate more general set-functions than the cardinality, that may incorporate prior knowledge or structural constraints which are common in many applications: namely, we show that for nondecreasing submodular set-functions, the corresponding convex envelope can be obtained from its \lova extension, a common tool in submodular analysis. This defines a family of polyhedral norms, for which we provide generic algorithmic tools (subgradients and proximal operators) and theoretical results (conditions for support recovery or high-dimensional inference). By selecting specific submodular functions, we can give a new interpretation to known norms, such as those based on rank-statistics or grouped norms with potentially overlapping groups; we also define new norms, in particular ones that can be used as non-factorial priors for supervised learning.

The group lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level. Existing methods for finding the group lasso estimator either use gradient projection methods to update the entire coefficient vector simultaneously at each step, or update one group of coefficients at a time using an inexact line search to approximate the optimal value for the group of coefficients when all other groups' coefficients are fixed. We present a new method of computation for the group lasso in the linear regression case, the Single Line Search (SLS) algorithm, which operates by computing the exact optimal value for each group (when all other coefficients are fixed) with one univariate line search. We perform simulations demonstrating that the SLS algorithm is often more efficient than existing computational methods. We also extend the SLS algorithm to the sparse group lasso problem via the Signed Single Line Search (SSLS) algorithm, and give theoretical results to support both algorithms.

The Bradley-Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behaviour, chess ranking and multiclass classification. Numerous extensions of the basic model have also been proposed in the literature including models with ties, multiple comparisons, group comparisons and random graphs. From a computational point of view, Hunter (2004) has proposed efficient iterative MM (minorization-maximization) algorithms to perform maximum likelihood estimation for these generalized Bradley-Terry models whereas Bayesian inference is typically performed using MCMC (Markov chain Monte Carlo) algorithms based on tailored Metropolis-Hastings (M-H) proposals. We show here that these MM\ algorithms can be reinterpreted as special instances of Expectation-Maximization (EM) algorithms associated to suitable sets of latent variables and propose some original extensions. These latent variables allow us to derive simple Gibbs samplers for Bayesian inference. We demonstrate experimentally the efficiency of these algorithms on a variety of applications.

Narratives can be defined informally as a “spatio-temporally bounded stream of elementary events”. To make this sort of definition more computationally useful we introduce, firstly, some pragmatic criteria for recognizing highly ambiguous entities like the “elementary events” and for linking these events together into complete narratives. We raise then the problem of how to concretely represent elementary events and narratives in computer-suitable form. We introduce then the main characteristics of a language, NKRL (Narrative Knowledge Representation Language), expressly specified and implemented for dealing with (non-fictional) narratives and temporal information. We conclude by showing briefly how this language can be used for questioning and for particularly complex inference operations.

The paper uses the SCOP theory of concepts to model the role of environmental context on three levels of entrepreneurial opportunity: idea generation, idea development, and entrepreneurial decision. The role of contextual-fit in the generation and development of ideas is modeled as the collapse of their superposition state into one of the potential states that composes this superposition. The projection of this collapsed state on the socio-economic basis results in interference between the developed idea and the perceptions of the supporting community, undergoing an eventual collapse for an entrepreneurial decision that reflects the shared vision of its stakeholders. The developed idea may continue to evolve due to continuous or discontinuous changes in the environment. The model offers unique insights into the effects of external influences on entrepreneurial decisions.

When general purpose software agents fail, it's often because they're brittle and need more background commonsense knowledge. In this paper we present relation properties as a valuable type of commonsense knowledge that can be automatically inferred at scale by reading the Web. People base many commonsense inferences on their knowledge of relation properties such as functionality, transitivity, and others. For example, all people know that bornIn(Year) satisfies the functionality property, meaning that each person can be born in exactly one year. Thus inferences like "Obama was born in 1961, so he was not born in 2008", which computers do not know, are obvious even to children. We demonstrate scalable heuristics for learning relation functionality from noisy Web text that outperform existing approaches to detecting functionality. The heuristics we use address Web NLP challenges that are also common to learning other relation properties, and can be easily transferred. Each relation property we learn for a Web-scale set of relations will enable computers to solve real tasks, and the data from learning many such properties will be a useful addition to general commonsense knowledge bases.

Recent work on entailment suggests that natural logics are well-suited to determining whether one sentence lexically entails another. We show how the EPILOG reasoning engine, designed for a natural language-like meaning representation (Episodic Logic, or EL), can be used to emulate natural logic inferences, while also enabling more general inferences such as ones from multiple premises, or ones based on world knowledge. Thus, to exploit the capabilities of EPILOG, we are working to populate its knowledge base with the kinds of lexical knowledge on which natural logics rely.

This position paper provides an overview of work conducted and an outlook of future directions within the field of Information Retrieval (IR) that aims to develop novel models, methods and frameworks inspired by Quantum Theory (QT).

Using computational intelligence, our ultimate goal is to self-regulate systems composed of humans, machines and robots. Self-regulation is important for the control of mixed organizations and systems. An overview of self-regulation for organizations and systems, characterized by our solution of the tradeoffs between Fourier pairs of Gaussian distributions that affect decision-making differently, is provided. A mathematical outline of our solution and a sketch of future plans are provided.