Information theory serves well as the mathematical theory of communication. However, it contains no provision that makes sure its theorems are consistent with the physical laws that govern any existing realization of a communication system. Therefore, it may not be surprising that applications of information theory or signal processing, as currently practiced, easily turn out to be inconsistent with fundamental principles of physics, such as the law of conservation of energy. It is the purpose of multiport communication theory to provide the necessary framework ensuring that applications of signal processing and information theory actually do comply with physical law. This framework involves a circuit theoretic approach where the inputs and outputs of the communication system are associated with ports of a multiport black-box. Thanks to each port being described by a pair of two instead of just one variable, consistency with physics can be maintained. The connection to information theory and signal processing is then obtained by means of isomorphisms between mathematical (formal) symbols of the latter and the physical quantities of the multiport model. In this tutorial, the principles of the multiport communication theory are presented and accompanied by a discussion of a number of interesting results of its application to single and multi-antenna radio communications in single- and multi-user contexts. Among these results are a new mapping from uplink to downlink channel matrices of TDD systems based on reciprocity of the physical propagation channel and physical limitations of massive MIMO systems

Learning the topology of graphs as well as processes evolving over graphs are tasks emerging in application domains as diverse as gene-regulatory, brain, power, and social networks, to name a few. Scalable approaches to deal with such high-dimensional settings aim to address the unique modeling and computational challenges associated with data-driven science in the modern era of big data analytics. Albeit simple and tractable, linear time-invariant models are limited as they are incapable of modeling changing topologies, as well as nonlinear and dynamic dependencies between nodal processes. To this end, novel approaches are presented to leverage nonlinear counterparts of partial correlation and partial Granger causality, as well as nonlinear structural equations and vector auto-regressions, along with attributes such as low rank, sparsity, and smoothness to capture even directional dependencies with abrupt change points, as well as dynamic processes over possibly time-evolving topologies. The unifying framework inherits the versatility and generality of kernel-based methods, and lends itself to batch and computationally affordable online learning algorithms, which include novel Kalman filters and smoothers over graphs. Real data experiments highlight the impact of the nonlinear and dynamic models on gene-regulatory and functional connectivity of brain networks, where connectivity patterns revealed exhibit discernible differences relative to existing approaches.

In recent years there has been an explosion of work on exploiting sparsity in order to reduce sampling rates in a wide-range of applications. In this talk, we consider several examples in which sub-Nyquist sampling is possible without assuming any structure on the signal being sampled. This is possible by careful design of the measurement scheme, together with nonlinear recovery methods. We then show how these concepts of measurement design and optimization-based recovery can be used to tackle a very different set of problems: phase retrieval from Fourier measurements. We begin by considering sampling a signal when we are interested in recovering its power spectrum. Next, we develop the minimal sampling rates required to achieve minimal distortion when representing an arbitrary signal by quantized samples. We then treat sampling of ultrasound signals where the goal is to create a beamformed image from the given samples. Finally, we propose several new measurement techniques in optical imaging that enable phase retrieval even in 1D problems from Fourier measurements.

Financial engineering and electrical engineering are seemingly different areas that share strong underlying connections. Both areas rely on statistical analysis and modeling of systems and the underlaying time series. Either modeling price fluctuations in the financial markets or modeling, say, channel fluctuations in wireless communication systems. Having a model of reality allows us to make predictions and to accordingly optimize the future strategies. It is as important to optimize our investment strategies in a financial market as it is to optimize the signal transmitted by an antenna in a wireless link. The foundations of both areas are the same in disguise and lie on signal processing and optimization. This talk provides a glimpse of financial engineering from a signal processing and optimization perspective, while exploring connections to other engineering disciplines.

Information gathering and processing in sensor networks was an early motivating application in the early 2000's for the study of transforms for graph signals. In this talk we start by providing a brief review of early work on signal representations for sensor data. Then we discuss how these methods have been extended to arbitrary graphs and summarize some key recent results in graph signal processing. Finally, we discuss how these results can be applied to sensor networks, focusing on problems such as graph identification, sensor selection, or distributed processing.

Fusion of multiple sets of data, either of the same type as in multiset data or of different types and nature as in multi-modality data, is inherent to many problems in engineering and computer science. In data fusion, since most often, very little is known about the relationship of the underlying processes that give rise to such data, it is desirable to minimize the modeling assumptions, and at the same time, to maximally exploit the interactions within and across the multiple sets of data. This is one of the reasons for the growing importance of data-driven methods in data fusion tasks. Models based on matrix or tensor decompositions allow data sets to remain in their most explanatory form while admitting a broad range of assumptions among their elements. This talk will provide an overview of the main approaches that have been successfully applied for fusion of multiple datasets with a focus on the interrelated concepts of uniqueness, diversity, and interpretability. Diversity refers to any structural, numerical, or statistical inherent property or assumption on the data that contributes to the identifiability of the model, and for multiple datasets, provides the link among these datasets. Hence, diversity enables uniqueness, which is key to interpretability, the ability to attach a physical meaning to the final decomposition. The importance of these concepts as well as the challenges that remain are highlighted through a number of practical examples.

Mobile cellular networks are becoming increasingly complex to manage while classical deployment/optimization techniques are cost-ineffective and thus seen as stopgaps. This is all the more difficult considering the extreme constraints of 5G networks in terms of data rate (more than 10 Gb/s), massive connectivity (more than 1000000 devices per km2), latency (under 1ms) and energy efficiency (a reduction by a factor of 100 with respect to 4G network). Unfortunately, the development of adequate solutions is severely limited by the scarcity of the actual resources (energy, bandwidth and space). Recently, the community has turned to a new resource known as Artificial Intelligence at all layers of the network to exploit the increasing computing power afforded by the improvement in Moore's law in combination with the availability of huge data in 5G networks. This is an important paradigm shift which considers the increasing data flood/huge number of nodes as an opportunity rather than a curse. In this talk, we will discuss through various examples how the recent advances in big data algorithms can provide an efficient framework for the design of 5G Intelligent Networks.

We reveal an interesting link between tensors and multivariate statistics. The rank of a multivariate probability tensor can be interpreted as a nonlinear measure of statistical dependence of the associated random variables. Rank equals one when the random variables are independent, and complete statistical dependence corresponds to full rank; but we show that rank as low as two can already model strong statistical dependence. In practice we usually work with random variables that are neither independent nor fully dependent -- partial dependence is typical, and can be modeled using a low-rank multivariate probability tensor. Directly estimating such a tensor from sample averages is impossible even for as few as ten random variables taking ten values each -- yielding a billion unknowns; but we often have enough data to estimate lower-order marginalized distributions. We prove that it is possible to identify the higher-order joint probabilities from lower order ones, provided that the higher-order probability tensor has low-enough rank, i.e., the random variables are only partially dependent. We also provide a computational identification algorithm that is shown to work well on both simulated and real data. The insights and results have numerous applications in estimation, hypothesis testing, completion, machine learning, and system identification. Low-rank tensor modeling thus provides a `universal' non-parametric (model-free) alternative to probabilistic graphical models.