Detecting communities in networks has received a large amount of attention and has found numerous applications across various disciplines including physics, sociology, biology, statistics, computer science, etc (see the exposition [13] and the references therein). Most previous work assumes networks can be divided into groups of nodes with dense connections internally and sparser connections between groups, and considers random graph models with some underlying cluster structure such as the stochastic blockmodel (SBM), a.k.a. the planted partition model. In its simplest form, nodes are partitioned into clusters, and any two nodes are connected by an edge independently at random with probability p if they are in the same cluster and with probability q otherwise. The problem of cluster recovery under the SBM has been extensively studied and many efficient algorithms with provable performance guarantees have been developed (see e.g., [8] and the references therein). Real networks, however, may not display a clustered structure; the goal of community detection should then be redefined. As observed in [15], interactions in many real networks can be of various types and prediction of unknown interaction types may have practical merit such as prediction of missing ratings in recommender systems. Therefore an intriguing question arises: Can we accurately predict the unknown interaction types in the absence of a clustered structure? To answer it, we generalize the SBM by relaxing the cluster assumption and allowing edges to carry labels.

Community detection using both graphs and social networks is the focus of many algorithms. Recent methods aimed at optimizing the so-called modularity function proceed by maximizing relations within communities while minimizing inter-community relations. However, given the NP-completeness of the problem, these algorithms are heuristics that do not guarantee an optimum. In this paper, we introduce a new algorithm along with a function that takes an approximate solution and modifies it in order to reach an optimum. This reassignment function is considered a 'potential function' and becomes a necessary condition to asserting that the computed optimum is indeed a Nash Equilibrium. We also use this function to simultaneously show partitioning and overlapping communities, two detection and visualization modes of great value in revealing interesting features of a social network. Our approach is successfully illustrated through several experiments on either real unipartite, multipartite or directed graphs of medium and large-sized datasets.

We study online learning of finite Markov decision process (MDP) problems when a side information vector is available. The problem is motivated by applications such as clinical trials, recommendation systems, etc. Such applications have an episodic structure, where each episode corresponds to a patient/customer. Our objective is to compete with the optimal dynamic policy that can take side information into account. We propose a computationally efficient algorithm and show that its regret is at most $O(\sqrt{T})$, where $T$ is the number of rounds. To best of our knowledge, this is the first regret bound for this setting.

Acyclic directed mixed graphs, also known as semi-Markov models represent the conditional independence structure induced on an observed margin by a DAG model with latent variables. In this paper we present a factorization criterion for these models that is equivalent to the global Markov property given by (the natural extension of) d-separation.

Abstract--While correlation measures are used to discern statistical relationships between observed variables in almost all branches of datadriven scientific inquiry, what we are really interested in is the existence of causal dependence. Statistical tests for causality, it turns out, are significantly harder to construct; the difficulty stemming from both philosophical hurdles in making precise the notion of causality, and the practical issue of obtaining an operational procedure from a philosophically sound definition. In particular, designing an efficient causality test, that may be carried out in the absence of restrictive presuppositions on the underlying dynamical structure of the data at hand, is nontrivial. Nevertheless, ability to computationally infer statistical prima facie evidence of causal dependence may yield a far more discriminative tool for data analysis compared to the calculation of simple correlations. In the present work, we present a new nonparametric test of Granger causality for quantized or symbolic data streams generated by ergodic stationary sources. In contrast to state-of-art binary tests, our approach makes precise and computes the degree of causal dependence between data streams, without making any restrictive assumptions, linearity or otherwise. Additionally, without any a priori imposition of specific dynamical structure, we infer explicit generative models of causal crossdependence, which may be then used for prediction. These explicit models are represented as generalized probabilistic automata, referred to crossed automata, and are shown to be sufficient to capture a fairly general class of causal dependence. The theoretical results are applied to weekly search-frequency data from Google Trends API for a chosen set of socially "charged" keywords. The causality network inferred from this dataset reveals, quite expectedly, the causal importance of certain keywords. It is also illustrated that correlation analysis fails to gather such insight.

Recent advances in statistical theory, together with advances in the computational power of computers, provide alternative methods to do mass-univariate hypothesis testing in which a large number of univariate tests, can be properly used to compare MEEG data at a large number of time-frequency points and scalp locations. One of the major problematic aspects of this kind of mass-univariate analysis is due to high number of accomplished hypothesis tests. Hence procedures that remove or alleviate the increased probability of false discoveries are crucial for this type of analysis. Here, I propose a new method for mass-univariate analysis of MEEG data based on cross-validation scheme. In this method, I suggest a hierarchical classification procedure under k-fold cross-validation to detect which sensors at which time-bin and which frequency-bin contributes in discriminating between two different stimuli or tasks. To achieve this goal, a new feature extraction method based on the discrete cosine transform (DCT) employed to get maximum advantage of all three data dimensions. Employing cross-validation and hierarchy architecture alongside the DCT feature space makes this method more reliable and at the same time enough sensitive to detect the narrow effects in brain activities.

A Bayesian agent learns about the structure of a stationary process from ob- serving past outcomes. We prove that his predictions about the near future become ap- proximately those he would have made if he knew the long run empirical frequencies of the process.

When eliciting judgements from humans for an unknown quantity, one often has the choice of making direct-scoring (cardinal) or comparative (ordinal) measurements. In this paper we study the relative merits of either choice, providing empirical and theoretical guidelines for the selection of a measurement scheme. We provide empirical evidence based on experiments on Amazon Mechanical Turk that in a variety of tasks, (pairwise-comparative) ordinal measurements have lower per sample noise and are typically faster to elicit than cardinal ones. Ordinal measurements however typically provide less information. We then consider the popular Thurstone and Bradley-Terry-Luce (BTL) models for ordinal measurements and characterize the minimax error rates for estimating the unknown quantity. We compare these minimax error rates to those under cardinal measurement models and quantify for what noise levels ordinal measurements are better. Finally, we revisit the data collected from our experiments and show that fitting these models confirms this prediction: for tasks where the noise in ordinal measurements is sufficiently low, the ordinal approach results in smaller errors in the estimation.

The selection of an appropriate competition format is critical for both the success and credibility of any competition, both real and simulated. In this paper, the automated parallelism offered by the RoboCupSoccer 2D simulation league is leveraged to conduct a 28,000 game round-robin between the top 8 teams from RoboCup 2012 and 2013. A proposed new competition format is found to reduce variation from the resultant statistically significant team performance rankings by 75% and 67%, when compared to the actual competition results from RoboCup 2012 and 2013 respectively. These results are statistically validated by generating 10,000 random tournaments for each of the three considered formats and comparing the respective distributions of ranking discrepancy.

Applying convolutional neural networks to large images is computationally expensive because the amount of computation scales linearly with the number of image pixels. We present a novel recurrent neural network model that is capable of extracting information from an image or video by adaptively selecting a sequence of regions or locations and only processing the selected regions at high resolution. Like convolutional neural networks, the proposed model has a degree of translation invariance built-in, but the amount of computation it performs can be controlled independently of the input image size. While the model is non-differentiable, it can be trained using reinforcement learning methods to learn task-specific policies. We evaluate our model on several image classification tasks, where it significantly outperforms a convolutional neural network baseline on cluttered images, and on a dynamic visual control problem, where it learns to track a simple object without an explicit training signal for doing so.