arXiv subjects

Georgios B. Giannakis

Publications and source records attributed to Georgios B. Giannakis.

At least 109 records · Page 6Linked to original sources

arXiv2018

Semi-Blind Inference of Topologies and Dynamical Processes over Graphs

Network science provides valuable insights across numerous disciplines including sociology, biology, neuroscience and engineering. A task of major practical importance in these application domains is inferring the network structure from noisy observations at a subset of nodes. Available methods for topology inference typically assume that the process over the network is observed at all nodes. However, application-specific constraints may prevent acquiring network-wide observations. Alleviating the limited flexibility of existing approaches, this work advocates structural models for graph processes and develops novel algorithms for joint inference of the network topology and processes from partial nodal observations. Structural equation models (SEMs) and structural vector autoregressive models (SVARMs) have well-documented merits in identifying even directed topologies of complex graphs; while SEMs capture contemporaneous causal dependencies among nodes, SVARMs further account for time-lagged influences. This paper develops algorithms that iterate between inferring directed graphs that "best" fit the data, and estimating the network processes at reduced computational complexity by leveraging tools related to Kalman smoothing. To further accommodate delay-sensitive applications, an online joint inference approach is put forth that even tracks time-evolving topologies. Furthermore, conditions for identifying the network topology given partial observations are specified. It is proved that the required number of observations for unique identification reduces significantly when the network structure is sparse. Numerical tests with synthetic as well as real datasets corroborate the effectiveness of the novel approach.

cs.LG↗

arXiv2018

Fast Decentralized Optimization over Networks

The present work introduces the hybrid consensus alternating direction method of multipliers (H-CADMM), a novel framework for optimization over networks which unifies existing distributed optimization approaches, including the centralized and the decentralized consensus ADMM. H-CADMM provides a flexible tool that leverages the underlying graph topology in order to achieve a desirable sweet-spot between node-to-node communication overhead and rate of convergence -- thereby alleviating known limitations of both C-CADMM and D-CADMM. A rigorous analysis of the novel method establishes linear convergence rate, and also guides the choice of parameters to optimize this rate. The novel hybrid update rules of H-CADMM lend themselves to "in-network acceleration" that is shown to effect considerable -- and essentially "free-of-charge" -- performance boost over the fully decentralized ADMM. Comprehensive numerical tests validate the analysis and showcase the potential of the method in tackling efficiently, widely useful learning tasks.

math.OC↗

arXiv2018

Secure Mobile Edge Computing in IoT via Collaborative Online Learning

To accommodate heterogeneous tasks in Internet of Things (IoT), a new communication and computing paradigm termed mobile edge computing emerges that extends computing services from the cloud to edge, but at the same time exposes new challenges on security. The present paper studies online security-aware edge computing under jamming attacks. Leveraging online learning tools, novel algorithms abbreviated as SAVE-S and SAVE-A are developed to cope with the stochastic and adversarial forms of jamming, respectively. Without utilizing extra resources such as spectrum and transmission power to evade jamming attacks, SAVE-S and SAVE-A can select the most reliable server to offload computing tasks with minimal privacy and security concerns. It is analytically established that without any prior information on future jamming and server security risks, the proposed schemes can achieve ${\cal O}\big(\sqrt{T}\big)$ regret. Information sharing among devices can accelerate the security-aware computing tasks. Incorporating the information shared by other devices, SAVE-S and SAVE-A offer impressive improvements on the sublinear regret, which is guaranteed by what is termed "value of cooperation." Effectiveness of the proposed schemes is tested on both synthetic and real datasets.

cs.LG↗

arXiv2018

Multi-Timescale Online Optimization of Network Function Virtualization for Service Chaining

Network Function Virtualization (NFV) can cost-efficiently provide network services by running different virtual network functions (VNFs) at different virtual machines (VMs) in a correct order. This can result in strong couplings between the decisions of the VMs on the placement and operations of VNFs. This paper presents a new fully decentralized online approach for optimal placement and operations of VNFs. Building on a new stochastic dual gradient method, our approach decouples the real-time decisions of VMs, asymptotically minimizes the time-average cost of NFV, and stabilizes the backlogs of network services with a cost-backlog tradeoff of $[ε,1/ε]$, for any $ε> 0$. Our approach can be relaxed into multiple timescales to have VNFs (re)placed at a larger timescale and hence alleviate service interruptions. While proved to preserve the asymptotic optimality, the larger timescale can slow down the optimal placement of VNFs. A learn-and-adapt strategy is further designed to speed the placement up with an improved tradeoff $[ε,\log^2(ε)/{\sqrtε}]$. Numerical results show that the proposed method is able to reduce the time-average cost of NFV by 30\% and reduce the queue length (or delay) by 83\%, as compared to existing benchmarks.

eess.SY↗

arXiv2018

Kernel-based Inference of Functions over Graphs

The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-based framework for tackling this inference problem that naturally subsumes and generalizes the reconstruction approaches put forth recently by the signal processing on graphs community. Both the static and the dynamic settings are considered along with effective modeling approaches for addressing real-world problems. The herein analytical discussion is complemented by a set of numerical examples, which showcase the effectiveness of the presented techniques, as well as their merits related to state-of-the-art methods.

stat.ML↗

arXiv2018

Adaptive Bayesian Radio Tomography

Radio tomographic imaging (RTI) is an emerging technology to locate physical objects in a geographical area covered by wireless networks. From the attenuation measurements collected at spatially distributed sensors, radio tomography capitalizes on spatial loss fields (SLFs) measuring the absorption of radio frequency waves at each location along the propagation path. These SLFs can be utilized for interference management in wireless communication networks, environmental monitoring, and survivor localization after natural disaster such as earthquakes. Key to success of RTI is to model accurately the shadowing effects as the bi-dimensional integral of the SLF scaled by a weight function, which is estimated using regularized regression. However, the existing approaches are less effective when the propagation environment is heterogeneous. To cope with this, the present work introduces a piecewise homogeneous SLF governed by a hidden Markov random field (MRF) model. Efficient and tractable SLF estimators are developed by leveraging Markov chain Monte Carlo (MCMC) techniques. Furthermore, an uncertainty sampling method is developed to adaptively collect informative measurements in estimating the SLF. Numerical tests using synthetic and real datasets demonstrate capabilities of the proposed algorithm for radio tomography and channel-gain estimation.

eess.SP↗

arXiv2018

Nonlinear Dimensionality Reduction on Graphs

In this era of data deluge, many signal processing and machine learning tasks are faced with high-dimensional datasets, including images, videos, as well as time series generated from social, commercial and brain network interactions. Their efficient processing calls for dimensionality reduction techniques capable of properly compressing the data while preserving task-related characteristics, going beyond pairwise data correlations. The present paper puts forth a nonlinear dimensionality reduction framework that accounts for data lying on known graphs. The novel framework encompasses most of the existing dimensionality reduction methods, but it is also capable of capturing and preserving possibly nonlinear correlations that are ignored by linear methods. Furthermore, it can take into account information from multiple graphs. The proposed algorithms were tested on synthetic as well as real datasets to corroborate their effectiveness.

cs.LG↗

arXiv2018

Canonical Correlation Analysis of Datasets with a Common Source Graph

Canonical correlation analysis (CCA) is a powerful technique for discovering whether or not hidden sources are commonly present in two (or more) datasets. Its well-appreciated merits include dimensionality reduction, clustering, classification, feature selection, and data fusion. The standard CCA however, does not exploit the geometry of the common sources, which may be available from the given data or can be deduced from (cross-) correlations. In this paper, this extra information provided by the common sources generating the data is encoded in a graph, and is invoked as a graph regularizer. This leads to a novel graph-regularized CCA approach, that is termed graph (g) CCA. The novel gCCA accounts for the graph-induced knowledge of common sources, while minimizing the distance between the wanted canonical variables. Tailored for diverse practical settings where the number of data is smaller than the data vector dimensions, the dual formulation of gCCA is also developed. One such setting includes kernels that are incorporated to account for nonlinear data dependencies. The resultant graph-kernel (gk) CCA is also obtained in closed form. Finally, corroborating image classification tests over several real datasets are presented to showcase the merits of the novel linear, dual, and kernel approaches relative to competing alternatives.

cs.LG↗

arXiv2018

Sketched Subspace Clustering

The immense amount of daily generated and communicated data presents unique challenges in their processing. Clustering, the grouping of data without the presence of ground-truth labels, is an important tool for drawing inferences from data. Subspace clustering (SC) is a relatively recent method that is able to successfully classify nonlinearly separable data in a multitude of settings. In spite of their high clustering accuracy, SC methods incur prohibitively high computational complexity when processing large volumes of high-dimensional data. Inspired by random sketching approaches for dimensionality reduction, the present paper introduces a randomized scheme for SC, termed Sketch-SC, tailored for large volumes of high-dimensional data. Sketch-SC accelerates the computationally heavy parts of state-of-the-art SC approaches by compressing the data matrix across both dimensions using random projections, thus enabling fast and accurate large-scale SC. Performance analysis as well as extensive numerical tests on real data corroborate the potential of Sketch-SC and its competitive performance relative to state-of-the-art scalable SC approaches.

stat.ML↗

arXiv2018

Decentralized RLS with Data-Adaptive Censoring for Regressions over Large-Scale Networks

The deluge of networked data motivates the development of algorithms for computation- and communication-efficient information processing. In this context, three data-adaptive censoring strategies are introduced to considerably reduce the computation and communication overhead of decentralized recursive least-squares (D-RLS) solvers. The first relies on alternating minimization and the stochastic Newton iteration to minimize a network-wide cost, which discards observations with small innovations. In the resultant algorithm, each node performs local data-adaptive censoring to reduce computations, while exchanging its local estimate with neighbors so as to consent on a network-wide solution. The communication cost is further reduced by the second strategy, which prevents a node from transmitting its local estimate to neighbors when the innovation it induces to incoming data is minimal. In the third strategy, not only transmitting, but also receiving estimates from neighbors is prohibited when data-adaptive censoring is in effect. For all strategies, a simple criterion is provided for selecting the threshold of innovation to reach a prescribed average data reduction. The novel censoring-based (C)D-RLS algorithms are proved convergent to the optimal argument in the mean-square deviation sense. Numerical experiments validate the effectiveness of the proposed algorithms in reducing computation and communication overhead.

eess.SY↗

arXiv2017

Large-scale Kernel-based Feature Extraction via Budgeted Nonlinear Subspace Tracking

Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated with desired accuracy. Nevertheless, inherent to the nonparametric nature of kernel-based estimators are computational and memory requirements that become prohibitive with large-scale datasets. In response to this formidable challenge, the present work puts forward a low-rank, kernel-based, feature extraction approach that is particularly tailored for online operation, where data streams need not be stored in memory. A novel generative model is introduced to approximate high-dimensional (possibly infinite) features via a low-rank nonlinear subspace, the learning of which leads to a direct kernel function approximation. Offline and online solvers are developed for the subspace learning task, along with affordable versions, in which the number of stored data vectors is confined to a predefined budget. Analytical results provide performance bounds on how well the kernel matrix as well as kernel-based classification and regression tasks can be approximated by leveraging budgeted online subspace learning and feature extraction schemes. Tests on synthetic and real datasets demonstrate and benchmark the efficiency of the proposed method when linear classification and regression is applied to the extracted features.

stat.ML↗

arXiv2017

Data-adaptive Active Sampling for Efficient Graph-Cognizant Classification

The present work deals with active sampling of graph nodes representing training data for binary classification. The graph may be given or constructed using similarity measures among nodal features. Leveraging the graph for classification builds on the premise that labels across neighboring nodes are correlated according to a categorical Markov random field (MRF). This model is further relaxed to a Gaussian (G)MRF with labels taking continuous values - an approximation that not only mitigates the combinatorial complexity of the categorical model, but also offers optimal unbiased soft predictors of the unlabeled nodes. The proposed sampling strategy is based on querying the node whose label disclosure is expected to inflict the largest change on the GMRF, and in this sense it is the most informative on average. Such a strategy subsumes several measures of expected model change, including uncertainty sampling, variance minimization, and sampling based on the $Σ-$optimality criterion. A simple yet effective heuristic is also introduced for increasing the exploration capabilities of the sampler, and reducing bias of the resultant classifier, by taking into account the confidence on the model label predictions. The novel sampling strategies are based on quantities that are readily available without the need for model retraining, rendering them computationally efficient and scalable to large graphs. Numerical tests using synthetic and real data demonstrate that the proposed methods achieve accuracy that is comparable or superior to the state-of-the-art even at reduced runtime.

stat.ML↗

arXiv2017

Compressive Phase Retrieval via Reweighted Amplitude Flow

The problem of reconstructing a sparse signal vector from magnitude-only measurements (a.k.a., compressive phase retrieval), emerges naturally in diverse applications, but it is NP-hard in general. Building on recent advances in nonconvex optimization, this paper puts forth a new algorithm that is termed compressive reweighted amplitude flow and abbreviated as CRAF, for compressive phase retrieval. Specifically, CRAF operates in two stages. The first stage seeks a sparse initial guess via a new spectral procedure. In the second stage, CRAF implements a few hard thresholding based iterations using reweighted gradients. When there are sufficient measurements, CRAF provably recovers the underlying signal vector exactly with high probability under suitable conditions. Moreover, its sample complexity coincides with that of the state-of-the-art procedures. Finally, substantial simulated tests showcase remarkable performance of the new spectral initialization, as well as improved exact recovery relative to competing alternatives.

cs.IT↗

arXiv2017

Inference of Spatio-Temporal Functions over Graphs via Multi-Kernel Kriged Kalman Filtering

Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filter that accounts for the spatio-temporal variations, and offers efficient online reconstruction, even for dynamically evolving network topologies. The kernel-based learning framework bypasses the need for statistical information by capitalizing on the smoothness that graph signals exhibit with respect to the underlying graph. To address the challenge of selecting the appropriate kernel, the proposed filter is combined with a multi-kernel selection module. Such a data-driven method selects a kernel attuned to the signal dynamics on-the-fly within the linear span of a pre-selected dictionary. The novel multi-kernel learning algorithm exploits the eigenstructure of Laplacian kernel matrices to reduce computational complexity. Numerical tests with synthetic and real data demonstrate the superior reconstruction performance of the novel approach relative to state-of-the-art alternatives.

cs.LG↗

arXiv2017

Optimal and Scalable Caching for 5G Using Reinforcement Learning of Space-time Popularities

Small basestations (SBs) equipped with caching units have potential to handle the unprecedented demand growth in heterogeneous networks. Through low-rate, backhaul connections with the backbone, SBs can prefetch popular files during off-peak traffic hours, and service them to the edge at peak periods. To intelligently prefetch, each SB must learn what and when to cache, while taking into account SB memory limitations, the massive number of available contents, the unknown popularity profiles, as well as the space-time popularity dynamics of user file requests. In this work, local and global Markov processes model user requests, and a reinforcement learning (RL) framework is put forth for finding the optimal caching policy when the transition probabilities involved are unknown. Joint consideration of global and local popularity demands along with cache-refreshing costs allow for a simple, yet practical asynchronous caching approach. The novel RL-based caching relies on a Q-learning algorithm to implement the optimal policy in an online fashion, thus enabling the cache control unit at the SB to learn, track, and possibly adapt to the underlying dynamics. To endow the algorithm with scalability, a linear function approximation of the proposed Q-learning scheme is introduced, offering faster convergence as well as reduced complexity and memory requirements. Numerical tests corroborate the merits of the proposed approach in various realistic settings.

cs.NI↗

arXiv2017

Learn-and-Adapt Stochastic Dual Gradients for Network Resource Allocation

Network resource allocation shows revived popularity in the era of data deluge and information explosion. Existing stochastic optimization approaches fall short in attaining a desirable cost-delay tradeoff. Recognizing the central role of Lagrange multipliers in network resource allocation, a novel learn-and-adapt stochastic dual gradient (LA-SDG) method is developed in this paper to learn the sample-optimal Lagrange multiplier from historical data, and accordingly adapt the upcoming resource allocation strategy. Remarkably, LA-SDG only requires just an extra sample (gradient) evaluation relative to the celebrated stochastic dual gradient (SDG) method. LA-SDG can be interpreted as a foresighted learning scheme with an eye on the future, or, a modified heavy-ball iteration from an optimization viewpoint. It is established - both theoretically and empirically - that LA-SDG markedly improves the cost-delay tradeoff over state-of-the-art allocation schemes.

eess.SY↗

arXiv2017

Sparse Phase Retrieval via Truncated Amplitude Flow

This paper develops a novel algorithm, termed \emph{SPARse Truncated Amplitude flow} (SPARTA), to reconstruct a sparse signal from a small number of magnitude-only measurements. It deals with what is also known as sparse phase retrieval (PR), which is \emph{NP-hard} in general and emerges in many science and engineering applications. Upon formulating sparse PR as an amplitude-based nonconvex optimization task, SPARTA works iteratively in two stages: In stage one, the support of the underlying sparse signal is recovered using an analytically well-justified rule, and subsequently, a sparse orthogonality-promoting initialization is obtained via power iterations restricted on the support; and, in the second stage, the initialization is successively refined by means of hard thresholding based gradient-type iterations. SPARTA is a simple yet effective, scalable, and fast sparse PR solver. On the theoretical side, for any $n$-dimensional $k$-sparse ($k\ll n$) signal $\bm{x}$ with minimum (in modulus) nonzero entries on the order of $(1/\sqrt{k})\|\bm{x}\|_2$, SPARTA recovers the signal exactly (up to a global unimodular constant) from about $k^2\log n$ random Gaussian measurements with high probability. Furthermore, SPARTA incurs computational complexity on the order of $k^2n\log n$ with total runtime proportional to the time required to read the data, which improves upon the state-of-the-art by at least a factor of $k$. Finally, SPARTA is robust against additive noise of bounded support. Extensive numerical tests corroborate markedly improved recovery performance and speedups of SPARTA relative to existing alternatives.

cs.IT↗

arXiv2017

DPCA: Dimensionality Reduction for Discriminative Analytics of Multiple Large-Scale Datasets

Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain setups, one wishes to extract the most significant information of one dataset relative to other datasets. Specifically, the interest may be on identifying, namely extracting features that are specific to a single target dataset but not the others. This paper develops a novel approach for such so-termed discriminative data analysis, and establishes its optimality in the least-squares (LS) sense under suitable data modeling assumptions. The criterion reveals linear combinations of variables by maximizing the ratio of the variance of the target data to that of the remainders. The novel approach solves a generalized eigenvalue problem by performing SVD just once. Numerical tests using synthetic and real datasets showcase the merits of the proposed approach relative to its competing alternatives.

cs.LG↗