Georgios B. Giannakis

Giannakis established an important result in identifying a linear system with statistically independent input, based only on its output. He showed that non-minimum phase and non-causal auto-regressive moving average models can be uniquely recovered via higher-order statistics (HOS).[1][2] Only zero-, maximum-, or minimum-phase models can be recovered if second-order output statistics are used.[35] Further, he established that HOS guarantee identifiability of systems with noisy inputs (errors-in-variables) and closed-loop systems with correlated Gaussian noise of unknown spectra, as well as multidimensional and multichannel systems with output only data and independent inputs. HOS identify such multi-input multi-output (MIMO) systems by removing the rotational (unitary matrix) ambiguity present with second-order statistics – a basic result that led to the renown tool of independent component analysis and further enabled blind separation of sources received by sensor arrays. Highly regarded are also Giannakis’ identification of linear time-varying systems using basis expansion models including Fourier bases, and optimally chosen wavelet bases and multiresolution depths; HOS-based Gaussianity and linearity tests, detection, estimation, pattern recognition, noise cancellation, object registration, image motion estimation, and the first proof that HOS can estimate directions of arrival of more sources with less antenna elements. Besides non-Gaussian stationary signals, he contributed influential results on consistency and asymptotic normality of HOS for a class of non-stationary and cyclostationary processes. For those, he developed widely applied statistical tests for the presence of cyclostationarity, as well as algorithms for retrieval of harmonics in the presence of multiplicative and additive noise; time series analysis with random and periodic misses; delay-Doppler estimators based on the high-order ambiguity function; multi-component polynomial phase signals for synthetic-aperture radar, and their impact to time-varying image motion estimation.

Giannakis and collaborators made fundamental contributions in wireless communication systems. One main contribution was to show how block-based linear precoding could transform a frequency-selective MIMO channel into a set of parallel frequency-flat channels.[4] Another main contribution was to develop a unified approach to design space-time block codes in MIMO channels. Such codes enable maximum diversity and coding gains at full rate (1 symbol per channel use) for any number of transmit-receive antennas.[26] Linear precoding is widely used in commercial wireless systems like IEEE 802.11n[36] and 3GPP LTE.[37] Another seminal contribution resulted in a multicarrier communication technique that is resilient to frequency-selective multi-user and inter-symbol interference. He further designed linear multicarrier precoding combined with a block spreading operation together render the user signature matrix at the receiver well-conditioned, without power control or bandwidth over-expansion.[27] This result shows that block processing of communication signals becomes an important dimension that can improve communication performance without altering power or bandwidth. An additional commercially valuable innovation was the use of zero-padding instead of a cyclic prefix.[7] Using a zero prefix has advantages in the application to multi-band OFDM in ultra wideband because it extends the coverage range by avoiding power back-off at the transmitter.[6][5] Further seminal contributions include the principal component filterbank that benchmarks performance of multiresolution based compression schemes;[38] transmitter-induced cyclostationarity ensuring identifiability of frequency-selective channels even from second-order statistics; optimal training as well as blind estimation and equalization of time- and frequency-selective channels using a basis expansion model;[39] linear multichannel equalizers of nonlinear Volterra channels with memory;[40] and a unifying cyclostationary approach to all-digital (non-) data aided timing and carrier synchronization. Giannakis and collaborators also contributed pioneering approaches to multi-antenna communications that include space-time-frequency-Doppler coded orthogonal frequency division multiplexing systems that attain the maximum diversity order; utilize feedback of the channel mean or correlation to develop optimal transmit-beamformers that markedly outperform maximum receive-SNR designs; and can also afford a highly acclaimed simple and general parameterization that enables quantifiable performance analysis when communicating over wireless single- and multi-antenna fading channels.[41] Additional highly cited results encompass ultra-wideband wireless communications,[42] innovative synchronization algorithms, their performance analyses, and impact to highly accurate positioning systems.[43]

The open system interconnection (OSI) model of communication networks comprises multiple design layers. For tractability reasons, each layer was individually optimized, up until it was recognized that joint designs can afford markedly improved performance.  For wireless networks, Giannakis and collaborators were the first to demonstrate how by leveraging channel knowledge at the transmitter, a modulator that adapts to the intended fading channel at the physical (PHY) layer can be fruitfully co-designed with the automatic repeat request (ARQ) strategy at the medium access control (MAC) layer to improve throughput.[44][45] In addition to PHY-MAC, they investigated co-designs involving schedulers with quality of service (QoS) guarantees, as well as queuing with adaptive modulation and coding.[46] They further contributed cross-layer congestion and contention control designs for wireless ad hoc networks,[47] cross-layer optimization of multicast,[44] wireless multihop random access,[47] and wireless cognitive radio networks.

Information processing and inference across wirelessly connected low-power and low-cost sensors, have well documented merits in application domains such as environmental sensing for habitat surveillance, intelligent agriculture, and health monitoring using body area networks. Such wireless sensor networks (WSNs) with or without a central computing unit (fusion center) face major challenges due to their limited bandwidth, stringent power to prolong sensor lifetime, the need to cope with nonstationary and spatiotemporally correlated data, synchronization, access, and resource allocation, to carry out the desired distributed inference tasks. Giannakis and his team pioneered energy-efficient sensor scheduling, power-efficient modulations, and bandwidth-constrained estimators,[48] along with relevant fundamental performance bounds,[49] by investigating inference jointly with compression, quantization, and censoring. Surprisingly, even with a few (1-3) bits per sensor sample, the fusion center could attain 90% of the estimation and tracking performance possible with unquantized observations even with a Kalman tracker utilizing just the sign of innovations. Although known as an optimization approach in deterministic settings, Giannakis and his collaborators were also the first to unveil the importance of the alternating direction method of multipliers (ADMM) for fully distributed statistical inference using (ad hoc) WSN processing based on consensus operations.[50] In a series of highly influential results, they contributed static and online ADMM-based approaches for distributed regression and particle filtering for distributed tracking,[51] classification using distributed SVMs,[52] clustering, and dimensionality reduction tailored for WSNs.

The ever-increasing demand for bandwidth to accommodate emerging multimedia applications, and large-scale interconnection of heterogeneous devices, have resulted in an explosive growth of Internet protocol (IP) traffic. This prompted the need for wireless cognitive radio (CR) sensing, communications, and networking that can mitigate the radio-frequency (RF) interference, and judiciously allocate the spectrum, control traffic congestion and routing, as well monitor the network health, flag risks, and overall guarantee secure connectivity. Giannakis and his research team contributed landmark tools for sensing the RF ambiance, propagation channels, and overall provide a succinct depiction of the network state—what is now widely known as cartography of the spectral density, channel gains, path delays, utilization of links, and unveiling anomalies. Whether blind or with training, it was believed that channel estimation requires at least output or input-output data, meaning one must have access to the receive- and perhaps also the transmit-end too. Giannakis bypassed non-cooperative CR transceivers by reformulating channel gain estimation as a function interpolation task using a sufficient number of spatiotemporal samples.[53] He further leveraged structural properties of this (generally dynamic) learning function, namely sparsity,[54][55][56] low rank,[54] space-time correlation, Kriging,[53] and radio tomography-related techniques, to obtain accurate sensing maps even with quantized measurements. Together with his collaborators, they utilized these maps for distributed CR scheduling, dynamic resource management using limited-rate feedback,[57] power control with imperfect exchanges, joint CR sensing and allocation of multichannel CRs, optimal beamforming, statistical routing, cross-layer optimization using interference tweets, and optimal chance-constrained management of orthogonal frequency-division multiple access (OFDMA) radios.

Giannakis and his research group have contributed state-of-the-art signal processing, machine learning, and optimization algorithms tailored for monitoring and managing contemporary power grids.[58] Critical to monitoring have been innovative approaches to power system state estimation, including robust and distributed solvers based on semidefinite programing,[59] and deep neural networks;[60] optimal placement of phasor measurement units to facilitate situational awareness;[61] efficient identification of bad data and power line outages using sparsity to effectively flag power blackouts;[62] and forecasting of demand, real-time load elasticity and pricing for electric vehicle charging, as well as prediction of electricity market prices. Seminal contributions for managing the smart power grid include distributed scheduling even when residential control messages are lost;[63] decentralized optimal power flow for microgrids;[64] active and stochastic reactive power management with renewables (wind and photovoltaics);[65] large-scale demand response for market clearing; patents on optimal dispatch of photovoltaic inverters in residential power distribution;[66] voltage regulation using deep reinforcement learning,[67] and ergodic energy control leveraging resource variability for multiphase distribution grids.[68]

With documented expertise in statistics and optimization tools, Giannakis' research team contributed innovative solutions to challenging science and engineering problems by capitalizing on the data deluge, while jointly leveraging physics-guided and data-driven models. Their key novelties have markedly advanced machine learning with data collected at distributed agents, and offered learning models that account for nonlinear data dependencies, structures, dynamics, and outliers. They were the first to develop consensus-based distributed (gossip) schemes for classification, sparse regression, and clustering using the alternating direction method of multipliers (ADMM);[69] and pioneered a solver based on judiciously designed cluster-heads to speed up decentralized optimization.[70] Sparsity and low rank were the data structures they exploited early on to develop online estimators of sparse signals;[71] to cope with perturbed compressive sampling using sparse total least-squares,[72] and also insightfully link compressive sensing with robust statistics, simply because data outliers are sparse.[73] This link led to major results on robust smoothing of dynamical signals via outlier constraints; sparse polynomial regression models; robust nonparametric regression via sparsity control; robust principal component analysis, robust multi-dimensional scaling, and robust clustering schemes.[74] Prompted by the NP-hard task of reconstructing a signal from its magnitude, they also developed state-of-the-art algorithms to solve random systems of quadratic equations.[75] They further established identifiability of models comprising a low-rank matrix plus a compressed matrix.[76] This result is not only intriguing by itself (it can find the summands from the sum), but also impactful to unveiling network traffic anomalies, and accelerating dynamic magnetic resonance imaging at desirable resolution levels. Another seminal contribution to nonlinear learning models was to enable a nonparametric basis function pursuit via sparse kernel-based learning,[77] what led to the first approach to tensor completion and extrapolation with applications to spectrum cartography, network flow prediction, and imputation of gene expression data.

A cornerstone of data science is learning from big data, where the latter refers to the volume (dimensionality and number) of data, their velocity (of streaming data), and variety (multimodality).[78] To extract the sought information that often resides in small subspaces, and cope with subsampled or missing data, Giannakis and collaborators put forth an online censoring approach for large-scale regressions and trackers,[79] where only informative data are retained for learning. Instead of censoring, they also adopted a limited number of random data projections (sketches) and validated whether they contain informative data, before employing them for (subspace) clustering to obtain desirable performance-complexity tradeoffs.[80] They further introduced linear subspace learning and imputation schemes for streaming tensors; online categorical subspace learning; and kernel-based nonlinear subspace trackers on a budget.[81]

Graphs underpin the structure and operation of networks everywhere: from the Internet to the power grid, financial markets, social media, gene regulation, and brain functionality. Whether graph edges capture physical interconnections or interdependencies among nodes or variables, learning a graph and carrying out inference of processes on a graph, are two tasks of paramount importance in data science, network science, and applications. Giannakis and collaborators established conditions to first identify topologies of directed graphs using sparse linear or nonlinear,[82] and static or dynamic structural equation models.[83] These models relate endogenous nodal variables with or without exogenous inputs, under sparsity and low-rank constraints. Multilayer graphs, as well as evolving graphs with memory (such as those emerging with generally nonlinear structural vector autoregressive models) are viewed as exogenous inputs. If the latter are not available, results of Giannakis' team show how to "blindly" identify directed graph topologies by decomposing tensor statistics of nodal data obtained under dynamic graph changes.[84] They further employed such graphs as prior information to offer a unifying graph kernel-based approach to statistical inference of (non) stationary processes over graphs.[85] Whether for interpolation, denoising, or extrapolation, their innovation accounts for dynamic and/or nonlinear interdependencies of nodal processes. These are instrumental in practice to predict partially observed dynamic processes over communication networks;[86] to estimate IP traffic and map anomalies in such networks; to infer functions over brain networks, as well as regulatory processes by leveraging genetic perturbations on gene networks; and even track cascades over social networks under smooth or switching dynamics. To cope with large-scale graphs, they further developed canonical correlation analysis tools for graph data; data adaptive active sampling strategies; node embeddings with adaptive similarities; and random walk driven adaptive diffusions that can outperform state-of-the-art graph convolutional neural networks.[87]

Giannakis and collaborators have also contributed to the resurgence of artificial intelligence (AI), and specifically to the areas of crowdsourcing, ensemble learning, interactive learning, and the associated performance analyses. Highly acclaimed results include blind and active multi-class meta-learning with categorical information from unequally reliable learners with possibly correlated and sequential data;[88] random feature-based online multi-kernel learning in environments with unknown dynamics;[89] and a Bayesian approach via ensemble (non)Gaussian processes for online learning with scalability, robustness, and uncertainty quantification through regret analyses. Additional major advances include (deep) reinforcement learning as applied to adaptive caching in hierarchical content delivery networks.[90] The novel caching schemes account for space-time content popularity in future-generation communication networks, and also dynamic storage pricing.