Demand response (DR) for residential and small commercial buildings is estimated to account for as much as 65% of the total energy savings potential of DR, and previous work shows that a fully automated Energy Management System (EMS) is a necessary prerequisite to DR in these areas. In this paper, we propose a novel EMS formulation for DR problems in these sectors. Specifically, we formulate a fully automated EMS's rescheduling problem as a reinforcement learning (RL) problem, and argue that this RL problem can be approximately solved by decomposing it over device clusters. Compared with existing formulations, our new formulation (1) does not require explicitly modeling the user's dissatisfaction on job rescheduling, (2) enables the EMS to self-initiate jobs, (3) allows the user to initiate more flexible requests and (4) has a computational complexity linear in the number of devices. We also demonstrate the simulation results of applying Q-learning, one of the most popular and classical RL algorithms, to a representative example.

Assume that each of n voters may or may not approve each of m issues. If an agent (the lobby) may influence up to k voters, then the central question of the NP-hard Lobbying problem is whether the lobby can choose the voters to be influenced so that as a result each issue gets a majority of approvals. This problem can be modeled as a simple matrix modification problem: Can one replace k rows of a binary n x m-matrix by k all-1 rows such that each column in the resulting matrix has a majority of 1s? Significantly extending on previous work that showed parameterized intractability (W[2]-completeness) with respect to the number k of modified rows, we study how natural parameters such as n, m, k, or the "maximum number of 1s missing for any column to have a majority of 1s" (referred to as "gap value g") govern the computational complexity of Lobbying. Among other results, we prove that Lobbying is fixed-parameter tractable for parameter m and provide a greedy logarithmic-factor approximation algorithm which solves Lobbying even optimally if m < 5. We also show empirically that this greedy algorithm performs well on general instances. As a further key result, we prove that Lobbying is LOGSNP-complete for constant values g>0, thus providing a first natural complete problem from voting for this complexity class of limited nondeterminism.

We consider the problem of dictionary learning under the assumption that the observed signals can be represented as sparse linear combinations of the columns of a single large dictionary matrix. In particular, we analyze the minimax risk of the dictionary learning problem which governs the mean squared error (MSE) performance of any learning scheme, regardless of its computational complexity. By following an established information-theoretic method based on Fanos inequality, we derive a lower bound on the minimax risk for a given dictionary learning problem. This lower bound yields a characterization of the sample-complexity, i.e., a lower bound on the required number of observations such that consistent dictionary learning schemes exist. Our bounds may be compared with the performance of a given learning scheme, allowing to characterize how far the method is from optimal performance.

Methods from algebra and algebraic geometry have been used in various ways to study linkages in kinematics. These methods have failed so far for the study of linkages with helical joints (joints with screw motion), because of the presence of some non-algebraic relations. In this article, we explore a delicate reduction of some analytic equations in kinematics to algebraic questions via a theorem of Ax. As an application, we give a classification of mobile closed 5-linkages with revolute, prismatic, and helical joints.

It is common to find collections/measurements of related objects, such as the same article in different languages, similar talks given by different presenters, similar weather patterns in different years, etc. It remains to determine how much the available big data helps us in statistical analysis; simply throwing every collected dataset into the mix may not yield an optimal output. Thus it is natural and important to understand theoretically when and how additional datasets improve the performance of various statistical analysis tasks such as regression, clustering, classification, etc. This is our motivation to explore the following classification problem.

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.

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.