Distributed Nonparametric Sequential Spectrum Sensing under Electromagnetic Interference

A nonparametric distributed sequential algorithm for quick detection of spectral holes in a Cognitive Radio set up is proposed. Two or more local nodes make decisions and inform the fusion centre (FC) over a reporting Multiple Access Channel (MAC), which then makes the final decision. The local nodes use energy detection and the FC uses mean detection in the presence of fading, heavy-tailed electromagnetic interference (EMI) and outliers. The statistics of the primary signal, channel gain or the EMI is not known. Different nonparametric sequential algorithms are compared to choose appropriate algorithms to be used at the local nodes and the FC. Modification of a recently developed random walk test is selected for the local nodes for energy detection as well as at the fusion centre for mean detection. It is shown via simulations and analysis that the nonparametric distributed algorithm developed performs well in the presence of fading, EMI and is robust to outliers. The algorithm is iterative in nature making the computation and storage requirements minimal.Comment: 8 pages; 6 figures; Version 2 has the proofs for the theorems. Version 3 contains a new section on approximation analysi

On Classification in Human-driven and Data-driven Systems

Classification systems are ubiquitous, and the design of effective classification algorithms has been an even more active area of research since the emergence of machine learning techniques. Despite the significant efforts devoted to training and feature selection in classification systems, misclassifications do occur and their effects can be critical in various applications. The central goal of this thesis is to analyze classification problems in human-driven and data-driven systems, with potentially unreliable components and design effective strategies to ensure reliable and effective classification algorithms in such systems. The components/agents in the system can be machines and/or humans. The system components can be unreliable due to a variety of reasons such as faulty machines, security attacks causing machines to send falsified information, unskilled human workers sending imperfect information, or human workers providing random responses. This thesis first quantifies the effect of such unreliable agents on the classification performance of the systems and then designs schemes that mitigate misclassifications and their effects by adapting the behavior of the classifier on samples from machines and/or humans and ensure an effective and reliable overall classification. In the first part of this thesis, we study the case when only humans are present in the systems, and consider crowdsourcing systems. Human workers in crowdsourcing systems observe the data and respond individually by providing label related information to a fusion center in a distributed manner. In such systems, we consider the presence of unskilled human workers where they have a reject option so that they may choose not to provide information regarding the label of the data. To maximize the classification performance at the fusion center, an optimal aggregation rule is proposed to fuse the human workers\u27 responses in a weighted majority voting manner. Next, the presence of unreliable human workers, referred to as spammers, is considered. Spammers are human workers that provide random guesses regarding the data label information to the fusion center in crowdsourcing systems. The effect of spammers on the overall classification performance is characterized when the spammers can strategically respond to maximize their reward in reward-based crowdsourcing systems. For such systems, an optimal aggregation rule is proposed by adapting the classifier based on the responses from the workers. The next line of human-driven classification is considered in the context of social networks. The classification problem is studied to classify a human whether he/she is influential or not in propagating information in social networks. Since the knowledge of social network structures is not always available, the influential agent classification problem without knowing the social network structure is studied. A multi-task low rank linear influence model is proposed to exploit the relationships between different information topics. The proposed approach can simultaneously predict the volume of information diffusion for each topic and automatically classify the influential nodes for each topic. In the third part of the thesis, a data-driven decentralized classification framework is developed where machines interact with each other to perform complex classification tasks. However, the machines in the system can be unreliable due to a variety of reasons such as noise, faults and attacks. Providing erroneous updates leads the classification process in a wrong direction, and degrades the performance of decentralized classification algorithms. First, the effect of erroneous updates on the convergence of the classification algorithm is analyzed, and it is shown that the algorithm linearly converges to a neighborhood of the optimal classification solution. Next, guidelines are provided for network design to achieve faster convergence. Finally, to mitigate the impact of unreliable machines, a robust variant of ADMM is proposed, and its resilience to unreliable machines is shown with an exact convergence to the optimal classification result. The final part of research in this thesis considers machine-only data-driven classification problems. First, the fundamentals of classification are studied in an information theoretic framework. We investigate the nonparametric classification problem for arbitrary unknown composite distributions in the asymptotic regime where both the sample size and the number of classes grow exponentially large. The notion of discrimination capacity is introduced, which captures the largest exponential growth rate of the number of classes relative to the samples size so that there exists a test with asymptotically vanishing probability of error. Error exponent analysis using the maximum mean discrepancy is provided and the discrimination rate, i.e., lower bound on the discrimination capacity is characterized. Furthermore, an upper bound on the discrimination capacity based on Fano\u27s inequality is developed

Stochastic Optimization For Multi-Agent Statistical Learning And Control

The goal of this thesis is to develop a mathematical framework for optimal, accurate, and affordable complexity statistical learning among networks of autonomous agents. We begin by noting the connection between statistical inference and stochastic programming, and consider extensions of this setup to settings in which a network of agents each observes a local data stream and would like to make decisions that are good with respect to information aggregated across the entire network. There is an open-ended degree of freedom in this problem formulation, however: the selection of the estimator function class which defines the feasible set of the stochastic program. Our central contribution is the design of stochastic optimization tools in reproducing kernel Hilbert spaces that yield optimal, accurate, and affordable complexity statistical learning for a multi-agent network. To obtain this result, we first explore the relative merits and drawbacks of different function class selections. In Part I, we consider multi-agent expected risk minimization this problem setting for the case that each agent seems to learn a common globally optimal generalized linear models (GLMs) by developing a stochastic variant of Arrow-Hurwicz primal-dual method. We establish convergence to the primal-dual optimal pair when either consensus or ``proximity constraints encode the fact that we want all agents\u27 to agree, or nearby agents to make decisions that are close to one another. Empirically, we observe that these convergence results are substantiated but that convergence may not translate into statistical accuracy. More broadly, optimality within a given estimator function class is not the same as one that makes minimal inference errors. The optimality-accuracy tradeoff of GLMs motivates subsequent efforts to learn more sophisticated estimators based upon learned feature encodings of the data that is fed into the statistical model. The specific tool we turn to in Part II is dictionary learning, where we optimize both over regression weights and an encoding of the data, which yields a non-convex problem. We investigate the use of stochastic methods for online task-driven dictionary learning, and obtain promising performance for the task of a ground robot learning to anticipate control uncertainty based on its past experience. Heartened by this implementation, we then consider extensions of this framework for a multi-agent network to each learn globally optimal task-driven dictionaries based on stochastic primal-dual methods. However, it is here the non-convexity of the optimization problem causes problems: stringent conditions on stochastic errors and the duality gap limit the applicability of the convergence guarantees, and impractically small learning rates are required for convergence in practice. Thus, we seek to learn nonlinear statistical models while preserving convexity, which is possible through kernel methods ( Part III). However, the increased descriptive power of nonparametric estimation comes at the cost of infinite complexity. Thus, we develop a stochastic approximation algorithm in reproducing kernel Hilbert spaces (RKHS) that ameliorates this complexity issue while preserving optimality: we combine the functional generalization of stochastic gradient method (FSGD) with greedily constructed low-dimensional subspace projections based on matching pursuit. We establish that the proposed method yields a controllable trade-off between optimality and memory, and yields highly accurate parsimonious statistical models in practice. % Then, we develop a multi-agent extension of this method by proposing a new node-separable penalty function and applying FSGD together with low-dimensional subspace projections. This extension allows a network of autonomous agents to learn a memory-efficient approximation to the globally optimal regression function based only on their local data stream and message passing with neighbors. In practice, we observe agents are able to stably learn highly accurate and memory-efficient nonlinear statistical models from streaming data. From here, we shift focus to a more challenging class of problems, motivated by the fact that true learning is not just revising predictions based upon data but augmenting behavior over time based on temporal incentives. This goal may be described by Markov Decision Processes (MDPs): at each point, an agent is in some state of the world, takes an action and then receives a reward while randomly transitioning to a new state. The goal of the agent is to select the action sequence to maximize its long-term sum of rewards, but determining how to select this action sequence when both the state and action spaces are infinite has eluded researchers for decades. As a precursor to this feat, we consider the problem of policy evaluation in infinite MDPs, in which we seek to determine the long-term sum of rewards when starting in a given state when actions are chosen according to a fixed distribution called a policy. We reformulate this problem as a RKHS-valued compositional stochastic program and we develop a functional extension of stochastic quasi-gradient algorithm operating in tandem with the greedy subspace projections mentioned above. We prove convergence with probability 1 to the Bellman fixed point restricted to this function class, and we observe a state of the art trade off in memory versus Bellman error for the proposed method on the Mountain Car driving task, which bodes well for incorporating policy evaluation into more sophisticated, provably stable reinforcement learning techniques, and in time, developing optimal collaborative multi-agent learning-based control systems