There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

/pdf/tensor-decompositions-and-applications-46vl2ih5gn.pdf

Tensor Decompositions and Applications

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Statistics for Spatial Data.

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Table Of Integrals Series And Products

Maximum entropy reinforcement learning (RL) has received considerable attention recently. Some of the algorithms within this framework exhibit state of the art performance in many challenging tasks. These algorithms exhibit improved exploration; however, they are still inefficient at performing deep exploration. The contribution of this paper is the introduction of a new kind of soft RL algorithm (referred to as the ISL strategy) that is efficient at performing deep exploration. Similarly to maximum entropy RL, we achieve this objective by augmenting the traditional RL objective with a novel regularization term. A distinctive feature of our approach is that, as opposed to other works that tackle the problem of deep exploration, in our derivation both the learning equations and the exploration-exploitation strategy are derived in tandem as the solution to a well-posed optimization problem whose minimization leads to the optimal value function. Empirically we show that our method exhibits state of the art performance on a range of challenging deep-exploration benchmarks.

ISL: Optimal Policy Learning With Optimal Exploration-Exploitation Trade-Off.

Adaptive networks have the capability to pursue solutions of global stochastic optimization problems by relying only local interactions within neighborhoods. The diffusion of information through repeated interactions allows for globally optimal behavior, without the need for central coordination. Most existing strategies are developed for cooperative learning settings, where the objective of the network is common to all agents. We consider in this work a team setting, where a subset of the agents form a team with a common goal, while competing with the remainder of the network. We develop an algorithm for decentralized competition among teams of adaptive agents, analyze its dynamics and present an application in the decentralized training of generative adversarial neural networks.

Competing Adaptive Networks

We pursue a time-domain feedback analysis of adaptive schemes with nonlinear update relations. We consider commonly used algorithms in blind equalization and neural network training and study their performance in a purely deterministic framework. The derivation employs insights from system theory and feedback analysis, and it clarifies the combined effects of the step-size parameters and the nature of the nonlinear functionals on the convergence and robustness performance of the adaptive schemes.

Robustness and convergence of adaptive schemes in blind equalization and neural network training

Distributed processing over networks relies on in-network processing and cooperation among neighboring agents. Cooperation is beneficial when agents share a common objective. However, in many applications agents may belong to different clusters that pursue different objectives. Then, indiscriminate cooperation will lead to undesired results. In this work, we propose an adaptive clustering and learning scheme that allows agents to learn which neighbors they should cooperate with and which other neighbors they should ignore. In doing so, the resulting algorithm enables the agents to identify their clusters and to attain improved learning and estimation accuracy over networks. We carry out a detailed mean-square analysis and assess the error probabilities of Types I and II, i.e., false alarm and mis-detection, for the clustering mechanism. Among other results, we establish that these probabilities decay exponentially with the step-sizes so that the probability of correct clustering can be made arbitrarily close to one.

Distributed Clustering and Learning Over Networks

Reference EPFL-CHAPTER-233386 URL: http://iracema.icsl.ucla.edu/publications/book_chapters/kalman_2009.pdf Record created on 2017-12-19, modified on 2018-01-16

/pdf/use-of-constrained-nonlinear-kalman-filtering-to-detect-1xbr4f3lg8.pdf

Ali H. Sayed

Papers

ISL: Optimal Policy Learning With Optimal Exploration-Exploitation Trade-Off.

Competing Adaptive Networks

Robustness and convergence of adaptive schemes in blind equalization and neural network training

Distributed Clustering and Learning Over Networks

Use of Constrained Nonlinear Kalman Filtering to Detect Pathological Constriction of Cerebral Arterial Blood Vessels