arXiv subjects

Georgios B. Giannakis

Publications and source records attributed to Georgios B. Giannakis.

At least 91 records · Page 5Linked to original sources

arXiv2019

Coupled Graphs and Tensor Factorization for Recommender Systems and Community Detection

Joint analysis of data from multiple information repositories facilitates uncovering the underlying structure in heterogeneous datasets. Single and coupled matrix-tensor factorization (CMTF) has been widely used in this context for imputation-based recommendation from ratings, social network, and other user-item data. When this side information is in the form of item-item correlation matrices or graphs, existing CMTF algorithms may fall short. Alleviating current limitations, we introduce a novel model coined coupled graph-tensor factorization (CGTF) that judiciously accounts for graph-related side information. The CGTF model has the potential to overcome practical challenges, such as missing slabs from the tensor and/or missing rows/columns from the correlation matrices. A novel alternating direction method of multipliers (ADMM) is also developed that recovers the nonnegative factors of CGTF. Our algorithm enjoys closed-form updates that result in reduced computational complexity and allow for convergence claims. A novel direction is further explored by employing the interpretable factors to detect graph communities having the tensor as side information. The resulting community detection approach is successful even when some links in the graphs are missing. Results with real data sets corroborate the merits of the proposed methods relative to state-of-the-art competing factorization techniques in providing recommendations and detecting communities.

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arXiv2019

Bandit Online Learning with Unknown Delays

This paper deals with bandit online learning problems involving feedback of unknown delay that can emerge in multi-armed bandit (MAB) and bandit convex optimization (BCO) settings. MAB and BCO require only values of the objective function involved that become available through feedback, and are used to estimate the gradient appearing in the corresponding iterative algorithms. Since the challenging case of feedback with \emph{unknown} delays prevents one from constructing the sought gradient estimates, existing MAB and BCO algorithms become intractable. For such challenging setups, delayed exploration, exploitation, and exponential (DEXP3) iterations, along with delayed bandit gradient descent (DBGD) iterations are developed for MAB and BCO, respectively. Leveraging a unified analysis framework, it is established that the regret of DEXP3 and DBGD are ${\cal O}\big( \sqrt{K\bar{d}(T+D)} \big)$ and ${\cal O}\big( \sqrt{K(T+D)} \big)$, respectively, where $\bar{d}$ is the maximum delay and $D$ denotes the delay accumulated over $T$ slots. Numerical tests using both synthetic and real data validate the performance of DEXP3 and DBGD.

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arXiv2019

Tight Linear Convergence Rate of ADMM for Decentralized Optimization

The present paper considers leveraging network topology information to improve the convergence rate of ADMM for decentralized optimization, where networked nodes work collaboratively to minimize the objective. Such problems can be solved efficiently using ADMM via decomposing the objective into easier subproblems. Properly exploiting network topology can significantly improve the algorithm performance. Hybrid ADMM explores the direction of exploiting node information by taking into account node centrality but fails to utilize edge information. This paper fills the gap by incorporating both node and edge information and provides a novel convergence rate bound for decentralized ADMM that explicitly depends on network topology. Such a novel bound is attainable for certain class of problems, thus tight. The explicit dependence further suggests possible directions to optimal design of edge weights to achieve the best performance. Numerical experiments show that simple heuristic methods could achieve better performance, and also exhibits robustness to topology changes.

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arXiv2019

Learning ReLU Networks on Linearly Separable Data: Algorithm, Optimality, and Generalization

Neural networks with REctified Linear Unit (ReLU) activation functions (a.k.a. ReLU networks) have achieved great empirical success in various domains. Nonetheless, existing results for learning ReLU networks either pose assumptions on the underlying data distribution being e.g. Gaussian, or require the network size and/or training size to be sufficiently large. In this context, the problem of learning a two-layer ReLU network is approached in a binary classification setting, where the data are linearly separable and a hinge loss criterion is adopted. Leveraging the power of random noise perturbation, this paper presents a novel stochastic gradient descent (SGD) algorithm, which can \emph{provably} train any single-hidden-layer ReLU network to attain global optimality, despite the presence of infinitely many bad local minima, maxima, and saddle points in general. This result is the first of its kind, requiring no assumptions on the data distribution, training/network size, or initialization. Convergence of the resultant iterative algorithm to a global minimum is analyzed by establishing both an upper bound and a lower bound on the number of non-zero updates to be performed. Moreover, generalization guarantees are developed for ReLU networks trained with the novel SGD leveraging classic compression bounds. These guarantees highlight a key difference (at least in the worst case) between reliably learning a ReLU network as well as a leaky ReLU network in terms of sample complexity. Numerical tests using both synthetic data and real images validate the effectiveness of the algorithm and the practical merits of the theory.

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arXiv2019

Matrix completion and extrapolation via kernel regression

Matrix completion and extrapolation (MCEX) are dealt with here over reproducing kernel Hilbert spaces (RKHSs) in order to account for prior information present in the available data. Aiming at a faster and low-complexity solver, the task is formulated as a kernel ridge regression. The resultant MCEX algorithm can also afford online implementation, while the class of kernel functions also encompasses several existing approaches to MC with prior information. Numerical tests on synthetic and real datasets show that the novel approach performs faster than widespread methods such as alternating least squares (ALS) or stochastic gradient descent (SGD), and that the recovery error is reduced, especially when dealing with noisy data.

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arXiv2019

Distributed Network Caching via Dynamic Programming

Next-generation communication networks are envisioned to extensively utilize storage-enabled caching units to alleviate unfavorable surges of data traffic by pro-actively storing anticipated highly popular contents across geographically distributed storage devices during off-peak periods. This resource pre-allocation is envisioned not only to improve network efficiency, but also to increase user satisfaction. In this context, the present paper designs optimal caching schemes for \textit{distributed caching} scenarios. In particular, we look at networks where a central node (base station) communicates with a number of "regular" nodes (users or pico base stations) equipped with \textit{local storage} infrastructure. Given the spatio-temporal dynamics of content popularities, and the decentralized nature of our setup, the problem boils down to select what, when and \textit{where} to cache. To address this problem, we define fetching and caching prices that vary across contents, time and space, and formulate a global optimization problem which aggregates the costs across those three domains. The resultant optimization is solved using decomposition and dynamic programming techniques, and a reduced-complexity algorithm is finally proposed. Preliminary simulations illustrating the behavior of our algorithm are finally presented.

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arXiv2019

A Recurrent Graph Neural Network for Multi-Relational Data

The era of data deluge has sparked the interest in graph-based learning methods in a number of disciplines such as sociology, biology, neuroscience, or engineering. In this paper, we introduce a graph recurrent neural network (GRNN) for scalable semi-supervised learning from multi-relational data. Key aspects of the novel GRNN architecture are the use of multi-relational graphs, the dynamic adaptation to the different relations via learnable weights, and the consideration of graph-based regularizers to promote smoothness and alleviate over-parametrization. Our ultimate goal is to design a powerful learning architecture able to: discover complex and highly non-linear data associations, combine (and select) multiple types of relations, and scale gracefully with respect to the size of the graph. Numerical tests with real data sets corroborate the design goals and illustrate the performance gains relative to competing alternatives.

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arXiv2019

Robust and Scalable Power System State Estimation via Composite Optimization

In today's cyber-enabled smart grids, high penetration of uncertain renewables, purposeful manipulation of meter readings, and the need for wide-area situational awareness, call for fast, accurate, and robust power system state estimation. The least-absolute-value (LAV) estimator is known for its robustness relative to the weighted least-squares (WLS) one. However, due to nonconvexity and nonsmoothness, existing LAV solvers based on linear programming are typically slow, hence inadequate for real-time system monitoring. This paper develops two novel algorithms for efficient LAV estimation, which draw from recent advances in composite optimization. The first is a deterministic linear proximal scheme that handles a sequence of convex quadratic problems, each efficiently solvable either via off-the-shelf algorithms or through the alternating direction method of multipliers. Leveraging the sparse connectivity inherent to power networks, the second scheme is stochastic, and updates only \emph{a few} entries of the complex voltage state vector per iteration. In particular, when voltage magnitude and (re)active power flow measurements are used only, this number reduces to one or two, \emph{regardless of} the number of buses in the network. This computational complexity evidently scales well to large-size power systems. Furthermore, by carefully \emph{mini-batching} the voltage and power flow measurements, accelerated implementation of the stochastic iterations becomes possible. The developed algorithms are numerically evaluated using a variety of benchmark power networks. Simulated tests corroborate that improved robustness can be attained at comparable or markedly reduced computation times for medium- or large-size networks relative to the "workhorse" WLS-based Gauss-Newton iterations.

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arXiv2019

Adaptive Diffusions for Scalable Learning over Graphs

Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which the chosen diffusion captures a typically unknown label propagation mechanism, that can be specific to the underlying graph, and potentially different for each class. The present work introduces a disciplined, data-efficient approach to learning class-specific diffusion functions adapted to the underlying network topology. The novel learning approach leverages the notion of "landing probabilities" of class-specific random walks, which can be computed efficiently, thereby ensuring scalability to large graphs. This is supported by rigorous analysis of the properties of the model as well as the proposed algorithms. Furthermore, a robust version of the classifier facilitates learning even in noisy environments. Classification tests on real networks demonstrate that adapting the diffusion function to the given graph and observed labels, significantly improves the performance over fixed diffusions; reaching -- and many times surpassing -- the classification accuracy of computationally heavier state-of-the-art competing methods, that rely on node embeddings and deep neural networks.

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arXiv2018

Random Feature-based Online Multi-kernel Learning in Environments with Unknown Dynamics

Kernel-based methods exhibit well-documented performance in various nonlinear learning tasks. Most of them rely on a preselected kernel, whose prudent choice presumes task-specific prior information. Especially when the latter is not available, multi-kernel learning has gained popularity thanks to its flexibility in choosing kernels from a prescribed kernel dictionary. Leveraging the random feature approximation and its recent orthogonality-promoting variant, the present contribution develops a scalable multi-kernel learning scheme (termed Raker) to obtain the sought nonlinear learning function `on the fly,' first for static environments. To further boost performance in dynamic environments, an adaptive multi-kernel learning scheme (termed AdaRaker) is developed. AdaRaker accounts not only for data-driven learning of kernel combination, but also for the unknown dynamics. Performance is analyzed in terms of both static and dynamic regrets. AdaRaker is uniquely capable of tracking nonlinear learning functions in environments with unknown dynamics, and with with analytic performance guarantees. Tests with synthetic and real datasets are carried out to showcase the effectiveness of the novel algorithms.

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arXiv2018

Reinforcement Learning for Adaptive Caching with Dynamic Storage Pricing

Small base stations (SBs) of fifth-generation (5G) cellular networks are envisioned to have storage devices to locally serve requests for reusable and popular contents by \emph{caching} them at the edge of the network, close to the end users. The ultimate goal is to shift part of the predictable load on the back-haul links, from on-peak to off-peak periods, contributing to a better overall network performance and service experience. To enable the SBs with efficient \textit{fetch-cache} decision-making schemes operating in dynamic settings, this paper introduces simple but flexible generic time-varying fetching and caching costs, which are then used to formulate a constrained minimization of the aggregate cost across files and time. Since caching decisions per time slot influence the content availability in future slots, the novel formulation for optimal fetch-cache decisions falls into the class of dynamic programming. Under this generic formulation, first by considering stationary distributions for the costs and file popularities, an efficient reinforcement learning-based solver known as value iteration algorithm can be used to solve the emerging optimization problem. Later, it is shown that practical limitations on cache capacity can be handled using a particular instance of the generic dynamic pricing formulation. Under this setting, to provide a light-weight online solver for the corresponding optimization, the well-known reinforcement learning algorithm, $Q$-learning, is employed to find optimal fetch-cache decisions. Numerical tests corroborating the merits of the proposed approach wrap up the paper.

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arXiv2018

Nonlinear Dimensionality Reduction for Discriminative Analytics of Multiple Datasets

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is challenged when it comes to analyzing multiple datasets jointly. In certain data science settings however, one is often interested in extracting the most discriminative information from one dataset of particular interest (a.k.a. target data) relative to the other(s) (a.k.a. background data). To this end, this paper puts forth a novel approach, termed discriminative (d) PCA, for such discriminative analytics of multiple datasets. Under certain conditions, dPCA is proved to be least-squares optimal in recovering the component vector unique to the target data relative to background data. To account for nonlinear data correlations, (linear) dPCA models for one or multiple background datasets are generalized through kernel-based learning. Interestingly, all dPCA variants admit an analytical solution obtainable with a single (generalized) eigenvalue decomposition. Finally, corroborating dimensionality reduction tests using both synthetic and real datasets are provided to validate the effectiveness of the proposed methods.

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arXiv2018

Online Graph-Adaptive Learning with Scalability and Privacy

Graphs are widely adopted for modeling complex systems, including financial, biological, and social networks. Nodes in networks usually entail attributes, such as the age or gender of users in a social network. However, real-world networks can have very large size, and nodal attributes can be unavailable to a number of nodes, e.g., due to privacy concerns. Moreover, new nodes can emerge over time, which can necessitate real-time evaluation of their nodal attributes. In this context, the present paper deals with scalable learning of nodal attributes by estimating a nodal function based on noisy observations at a subset of nodes. A multikernel-based approach is developed which is scalable to large-size networks. Unlike most existing methods that re-solve the function estimation problem over all existing nodes whenever a new node joins the network, the novel method is capable of providing real-time evaluation of the function values on newly-joining nodes without resorting to a batch solver. Interestingly, the novel scheme only relies on an encrypted version of each node's connectivity in order to learn the nodal attributes, which promotes privacy. Experiments on both synthetic and real datasets corroborate the effectiveness of the proposed methods.

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arXiv2018

Graph Multiview Canonical Correlation Analysis

Multiview canonical correlation analysis (MCCA) seeks latent low-dimensional representations encountered with multiview data of shared entities (a.k.a. common sources). However, existing MCCA approaches do not exploit the geometry of the common sources, which may be available \emph{a priori}, or can be constructed using certain domain knowledge. This prior information about the common sources can be encoded by a graph, and be invoked as a regularizer to enrich the maximum variance MCCA framework. In this context, the present paper's novel graph-regularized (G) MCCA approach minimizes the distance between the wanted canonical variables and the common low-dimensional representations, while accounting for graph-induced knowledge of the common sources. Relying on a function capturing the extent low-dimensional representations of the multiple views are similar, a generalization bound of GMCCA is established based on Rademacher's complexity. Tailored for setups where the number of data pairs is smaller than the data vector dimensions, a graph-regularized dual MCCA approach is also developed. To further deal with nonlinearities present in the data, graph-regularized kernel MCCA variants are put forward too. Interestingly, solutions of the graph-regularized linear, dual, and kernel MCCA, are all provided in terms of generalized eigenvalue decomposition. Several corroborating numerical tests using real datasets are provided to showcase the merits of the graph-regularized MCCA variants relative to several competing alternatives including MCCA, Laplacian-regularized MCCA, and (graph-regularized) PCA.

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arXiv2018

Real-time Power System State Estimation and Forecasting via Deep Neural Networks

Contemporary power grids are being challenged by rapid voltage fluctuations that are caused by large-scale deployment of renewable generation, electric vehicles, and demand response programs. In this context, monitoring the grid's operating conditions in real time becomes increasingly critical. With the emergent large scale and nonconvexity however, the existing power system state estimation (PSSE) schemes become computationally expensive or yield suboptimal performance. To bypass these hurdles, this paper advocates deep neural networks (DNNs) for real-time power system monitoring. By unrolling an iterative physics-based prox-linear solver, a novel model-specific DNN is developed for real-time PSSE with affordable training and minimal tuning effort. To further enable system awareness even ahead of the time horizon, as well as to endow the DNN-based estimator with resilience, deep recurrent neural networks (RNNs) are also pursued for power system state forecasting. Deep RNNs leverage the long-term nonlinear dependencies present in the historical voltage time series to enable forecasting, and they are easy to implement. Numerical tests showcase improved performance of the proposed DNN-based estimation and forecasting approaches compared with existing alternatives. In real load data experiments on the IEEE 118-bus benchmark system, the novel model-specific DNN-based PSSE scheme outperforms nearly by an order-of-magnitude the competing alternatives, including the widely adopted Gauss-Newton PSSE solver.

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arXiv2018

Learning and Management for Internet-of-Things: Accounting for Adaptivity and Scalability

Internet-of-Things (IoT) envisions an intelligent infrastructure of networked smart devices offering task-specific monitoring and control services. The unique features of IoT include extreme heterogeneity, massive number of devices, and unpredictable dynamics partially due to human interaction. These call for foundational innovations in network design and management. Ideally, it should allow efficient adaptation to changing environments, and low-cost implementation scalable to massive number of devices, subject to stringent latency constraints. To this end, the overarching goal of this paper is to outline a unified framework for online learning and management policies in IoT through joint advances in communication, networking, learning, and optimization. From the network architecture vantage point, the unified framework leverages a promising fog architecture that enables smart devices to have proximity access to cloud functionalities at the network edge, along the cloud-to-things continuum. From the algorithmic perspective, key innovations target online approaches adaptive to different degrees of nonstationarity in IoT dynamics, and their scalable model-free implementation under limited feedback that motivates blind or bandit approaches. The proposed framework aspires to offer a stepping stone that leads to systematic designs and analysis of task-specific learning and management schemes for IoT, along with a host of new research directions to build on.

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arXiv2018

Blind Multiclass Ensemble Classification

The rising interest in pattern recognition and data analytics has spurred the development of innovative machine learning algorithms and tools. However, as each algorithm has its strengths and limitations, one is motivated to judiciously fuse multiple algorithms in order to find the "best" performing one, for a given dataset. Ensemble learning aims at such high-performance meta-algorithm, by combining the outputs from multiple algorithms. The present work introduces a blind scheme for learning from ensembles of classifiers, using a moment matching method that leverages joint tensor and matrix factorization. Blind refers to the combiner who has no knowledge of the ground-truth labels that each classifier has been trained on. A rigorous performance analysis is derived and the proposed scheme is evaluated on synthetic and real datasets.

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arXiv2018

LAG: Lazily Aggregated Gradient for Communication-Efficient Distributed Learning

This paper presents a new class of gradient methods for distributed machine learning that adaptively skip the gradient calculations to learn with reduced communication and computation. Simple rules are designed to detect slowly-varying gradients and, therefore, trigger the reuse of outdated gradients. The resultant gradient-based algorithms are termed Lazily Aggregated Gradient --- justifying our acronym LAG used henceforth. Theoretically, the merits of this contribution are: i) the convergence rate is the same as batch gradient descent in strongly-convex, convex, and nonconvex smooth cases; and, ii) if the distributed datasets are heterogeneous (quantified by certain measurable constants), the communication rounds needed to achieve a targeted accuracy are reduced thanks to the adaptive reuse of lagged gradients. Numerical experiments on both synthetic and real data corroborate a significant communication reduction compared to alternatives.

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