In game theory, an Evolutionarily Stable Set (ES set) is a set of Nash Equilibrium (NE) strategies that give the same payoffs. Similar to an Evolutionarily Stable Strategy (ES strategy), an ES set is also a strict NE. This work investigates the evolutionary stability of classical and quantum strategies in the quantum penny flip games. In particular, we developed an evolutionary game theory model to conduct a series of simulations where a population of mixed classical strategies from the ES set of the game were invaded by quantum strategies. We found that when only one of the two players' mixed classical strategies were invaded, the results were different. In one case, due to the interference phenomenon of superposition, quantum strategies provided more payoff, hence successfully replaced the mixed classical strategies in the ES set. In the other case, the mixed classical strategies were able to sustain the invasion of quantum strategies and remained in the ES set. Moreover, when both players' mixed classical strategies were invaded by quantum strategies, a new quantum ES set emerged. The strategies in the quantum ES set give both players payoff 0, which is the same as the payoff of the strategies in the mixed classical ES set of this game.

Producing overlapping schemes is a major issue in clustering. Recent proposed overlapping methods relies on the search of an optimal covering and are based on different metrics, such as Euclidean distance and I-Divergence, used to measure closeness between observations. In this paper, we propose the use of another measure for overlapping clustering based on a kernel similarity metric .We also estimate the number of overlapped clusters using the Gram matrix. Experiments on both Iris and EachMovie datasets show the correctness of the estimation of number of clusters and show that measure based on kernel similarity metric improves the precision, recall and f-measure in overlapping clustering.

This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients to estimate, which renders conventional approaches computationally prohibitive when $d$ is large. However, for a wide class of densities that satisfy a certain sparsity condition, our estimator runs in probabilistic polynomial time and adapts to the unknown sparsity of the underlying density in two key ways: (1) it attains near-minimax mean-squared error for moderate sample sizes, and (2) the computational complexity is lower for sparser densities. Our method also allows for flexible control of the trade-off between mean-squared error and computational complexity.

Communication networks have evolved from specialized, research and tactical transmission systems to large-scale and highly complex interconnections of intelligent devices, increasingly becoming more commercial, consumer-oriented, and heterogeneous. Propelled by emergent social networking services and high-definition streaming platforms, network traffic has grown explosively thanks to the advances in processing speed and storage capacity of state-of-the-art communication technologies. As "netizens" demand a seamless networking experience that entails not only higher speeds, but also resilience and robustness to failures and malicious cyber-attacks, ample opportunities for signal processing (SP) research arise. The vision is for ubiquitous smart network devices to enable data-driven statistical learning algorithms for distributed, robust, and online network operation and management, adaptable to the dynamically-evolving network landscape with minimal need for human intervention. The present paper aims at delineating the analytical background and the relevance of SP tools to dynamic network monitoring, introducing the SP readership to the concept of dynamic network cartography -- a framework to construct maps of the dynamic network state in an efficient and scalable manner tailored to large-scale heterogeneous networks.

Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools. Robust parameter estimation is a challenge for kernel functions that compute such graphs. Finding a corresponding high quality coordinate system to map signature relations remains an open research question. We answer positively on these challenges by first proposing a kernel function of spatial and spectral information in computing neighborhood graphs. Secondly, the study exploits the force field interpretation from mechanics and devise a unifying nonlinear graph embedding framework. The generalized framework leads to novel unsupervised multidimensional artificial field embedding techniques that rely on the simple additive assumption of pair-dependent attraction and repulsion functions. The formulations capture long range and short range distance related effects often associated with living organisms and help to establish algorithmic properties that mimic mutual behavior for the purpose of dimensionality reduction. The main benefits from the proposed models includes the ability to preserve the local topology of data and produce quality visualizations i.e. maintaining disjoint meaningful neighborhoods. As part of evaluation, visualization, gradient field trajectories, and semisupervised classification experiments are conducted for image scenes acquired by multiple sensors at various spatial resolutions over different types of objects. The results demonstrate the superiority of the proposed embedding framework over various widely used methods.

Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from all tasks. Therefore sparse solutions, that avoid using the entire data directly and instead use a set of informative "representatives" are desirable. The paper investigates this problem for the grouped mixed-effect GP model where each individual response is given by a fixed-effect, taken from one of a set of unknown groups, plus a random individual effect function that captures variations among individuals. Such models have been widely used in previous work but no sparse solutions have been developed. The paper presents the first sparse solution for such problems, showing how the sparse approximation can be obtained by maximizing a variational lower bound on the marginal likelihood, generalizing ideas from single-task Gaussian processes to handle the mixed-effect model as well as grouping. Experiments using artificial and real data validate the approach showing that it can recover the performance of inference with the full sample, that it outperforms baseline methods, and that it outperforms state of the art sparse solutions for other multi-task GP formulations.

A model-based clustering approach assumes that each component or some combination of components corresponds to a cluster. When fitting the model in (1), the main task is to decide the number of components G. Titterington et al. (1985), McLachan and Basford (1988) and McLachan and Peel (2002) extensively reviewed mixture models, with a focus on Gaussian mixture models. Fraley and Raftery (2002) presented a review of work on Gaussian mixtures with a focus on clustering, discriminant analysis, and density estimation. They discuss a family of Gaussian mixture models, which arises from the imposition of constraints upon an eigen-decomposition of the component covariance structure. The family of mixture models they discuss, known as MCLUST, is actually a subset of the Gaussian parsimonious clustering models (GPCMs) of Celeux and Govaert (1995). When using the MCLUST models, one must choose the appropriate member of the family, i.e., the covariance structure, in addition to deciding the number of components G. Ghahramani and Hinton (1997) introduced a mixture of factor analyzers model, which was further developed by Tipping and Bishop (1999) and McLachlan and Peel (2000).

We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the structure of a Markov decision process. Adopting a Bayesian approach to inference, we show how latent variables of the model can be estimated, and how predictions about actions can be made, in a unified framework. A new Markov chain Monte Carlo (MCMC) sampler is devised for simulation from the posterior distribution. This step includes a parameter expansion step, which is shown to be essential for good convergence properties of the MCMC sampler. As an illustration, the method is applied to learning a human controller.

This paper considers the stability of online learning algorithms and its implications for learnability (bounded regret). We introduce a novel quantity called {\em forward regret} that intuitively measures how good an online learning algorithm is if it is allowed a one-step look-ahead into the future. We show that given stability, bounded forward regret is equivalent to bounded regret. We also show that the existence of an algorithm with bounded regret implies the existence of a stable algorithm with bounded regret and bounded forward regret. The equivalence results apply to general, possibly non-convex problems. To the best of our knowledge, our analysis provides the first general connection between stability and regret in the online setting that is not restricted to a particular class of algorithms. Our stability-regret connection provides a simple recipe for analyzing regret incurred by any online learning algorithm. Using our framework, we analyze several existing online learning algorithms as well as the "approximate" versions of algorithms like RDA that solve an optimization problem at each iteration. Our proofs are simpler than existing analysis for the respective algorithms, show a clear trade-off between stability and forward regret, and provide tighter regret bounds in some cases. Furthermore, using our recipe, we analyze "approximate" versions of several algorithms such as follow-the-regularized-leader (FTRL) that requires solving an optimization problem at each step.

Given the limited performance of 2D cellular automata in terms of space when the number of documents increases and in terms of visualization clusters, our motivation was to experiment these cellular automata by increasing the size to view the impact of size on quality of results. The representation of textual data was carried out by a vector model whose components are derived from the overall balancing of the used corpus Term Frequency - Inverse Document Frequency (TF - IDF).The WorldNet thesaurus has been used to address the problem of the lemmatization of the words because the representation used in this study is that of the bags of words. Another independent method of the language was used to represent textual records is that of the n-grams. Several measures of similarity have been tested. To validate the classification we have used two measures of assessment based on the recall and precision (f-measure and entropy). The results are promising and confirm the idea to increase the dimension to the problem of the spatiality of the classes. The results obtained in terms of purity class (ie the minimum value of entropy) shows that the number of documents over longer believes the results are better for 3D cellular automata, which was not obvious to 2D the dimension. In terms of spatial navigation, cellular automata provide very good 3D performance visualization than 2D cellular automata.