Current Stefano Marano’s research interests include decision theory, distributed inference, information theory, and quantum information science.
Past interests include the following (no longer updated)
Inference and communications in sensor networks
Recently, many modern technologies related to system monitoring, control, communications, inference, etc., have experienced a strong trend from classical centralized implementations to distributed architectures, and sensor networks are a typical example of distributed systems. Stefano Marano has gained a remarkable research experience in the area of sensor network for statistical inference, with emphasis on fundamental and methodological aspects.
i) Adaptive Distributed Inference over Networks
Our study examines the close interplay between cooperation and adaptation for distributed detection schemes over decentralized networks with flat architecture, lacking of a central unit with the role of fusion center. The combined attributes of cooperation and adaptation are necessary to enable networks of detectors to continually learn from streaming data and to continually track drifts in the state of nature when deciding in favor of one hypothesis or another. In this scenario of great practical interest in many real-world problems, we are interested in establishing the fundamental scaling laws for the probabilities of miss-detection and false-alarm, when the agents interact with each other according to distributed strategies that employ constant step-sizes. The latter are critical to enable continuous adaptation and learning. We investigate the existence of the steady-state distribution of each agent, which is then proven to be asymptotically Gaussian in the slow adaptation regime of small step-sizes. Then, large-deviations tools are exploited to find closed-form expressions for the decaying rates of the false-alarm and miss-detection probabilities. We focus in particular on the difference between the scaling laws governing errors of detection and errors of estimation over networks.
ii) Sensor Network Tomography
A major application of sensor networks is to detect the presence of a moving object (a target) in a surveyed region. To that aim, sensors make decisions about the presence of the target. We want to reverse the perspective: Suppose that the target is aware of the detections it has caused, but has no idea which sensor has made which call. Can the target infer the positions of the detecting sensors? Since this is an inverse problem (of prey locating its predators), we shall refer to it as sensor network tomography. Maximum likelihood (ML) offers a solution, but it is combinatorial and therefore not of great practical interest. Our study is aimed at exploring several alternatives and investigate their performances. One approach looks for a nexus of detection activity: the peak, Fourier, and ESPRIT estimators fall into this class. But the best trade-off between complexity and performance seems to be trellis-based and of philosophy similar to the multi hypothesis tracker (MHT) idea for disambiguation of measurement-origin uncertainty (MOU) in target tracking.
A second line of investigation in the area of sensor network tomography is motivated by social network applications: here from the actions of the network users the inverse problem is to make inference about their preferences and orientations. More specifically, we formalize the problem as one in which the decisions of an ensemble of decision makers are recorded and, from that, the costs assigned from the decision makers to their erroneous decisions must be inferred.
iii) Distributed statistical learning
Only recently the study of distributed statistical learning under communication constraints has been addressed in a systematic and rigorous way and, while many classical machine learning techniques have been re-formulated and generalized to this new framework, others are believed not to be suitable for the distributed scenario, due to the need for sensor interactions. This is the case of the k-NN (k Nearest Neighbors) technique where, among the whole set of samples collected by the remote nodes, only the k closest to the current observation are to be delivered to the fusion center. Stefano Marano’s research shows that, instead, exploiting a cross-layer design philosophy in which a clever channel access policy based on ordered transmission is combined with standard statistical procedures, distributed statistical learning based on the k-NN fusion rule is not only feasible, but also universally consistent. This finding may represent a breakthrough for distributed statistical learning.
iv) Single-transmission distributed detection
In a recent paper R. Blum e B. Sadler proposed a distributed inference scheme in which only a subset of the whole observations collected by the remote nodes of a sensor network are delivered to the fusion center and, nevertheless, the system achieves the optimal detection performance corresponding to the availability of the whole observation set: energy saving is gained without losing performance. The key here is that the remote observations are delivered with a delay inversely proportional to their informativeness for detection. Taking to one extreme this idea, Stefano Marano has designed and analyzed a sensor network for detection purposes in which only one sensor, but the most informative, delivers data to the fusion center. The optimal performance is certainly lost but, remarkably, the system is asymptotically consistent: it has been proved that any desired detection performance can be achieved, provided that the network size (number of sensors) is large enough. Also, as a byproduct, it turns out that the only “firing” sensor can simply deliver the binary variable corresponding to its local decision.
v) Running consensus
Fully decentralized systems refer to flat distributed architectures lacking of a fusion center. According to the typical behavior of these systems, the remote nodes first collect observations about the monitored phenomenon and, at a later time, they cooperate by gossip communication algorithms aimed at enforcing consensus among the nodes. Stefano Marano has proposed an innovative consensus paradigm –known as running consensus– in which the two stages (sensing and gossiping) evolve jointly. Sensor networks operating under this new paradigm are more robust, scalable, and reliable, with respect to the classical consensus schemes, and can be profitably employed in applications requiring a continuous monitoring of the state of the nature. The detection performance of the running consensus algorithm has been investigated under the LOD (Locally Optimum Detection) model, proving the asymptotic optimality of the system.
vi) Distributed information processing for statistical inference
Distributed systems for statistical inference have wide application domains, and their practical implementations are already very numerous. However, a systematic, rigorous, and methodological approach to multi-terminal statistical inference, which involves different fields as signal processing, statistics, and information theory, may be still considered a challenging issue. Indeed, many fundamental limits of these distributed systems are not known, and practical guidelines for system design are, in part, still heuristic. Stefano Marano’s methodological contributions to this topic represent a tentative to fill this gap.
One approach pursued concerns the design of the local quantizers in multi-terminal inference systems by a systematic characterization of the fundamental rate/distortion tradeoff, exploiting peculiar differences between the domains of inference and reconstruction. Stefano Marano has also introduced a new class of distributed estimators (Locally Optimum Estimators, LOE) and proved their asymptotic optimality. When operating with compressed observations the LOE quantizers can be simply implemented by resorting to the well-known Lloyd & Max algorithm, run over a transformed version of the data ruled by the score function.
In distributed systems for statistical inference the classical “layered” approach usually pursued in the design of communication systems is not necessarily the right way, and a more involved and challenging cross-layer perspective should be adopted. Stefano Marano contributes to popularize this viewpoint, by addressing a number of inference problems in a distributed setting.
One example is the invention of a new channel access policy, named LBMA (Likelihood-Based Multiple Access). In an LBMA system each remote node delivers to the fusion center an analog waveform reproducing the local log-likelihood function. Since log-likelihoods are additive for independent observations, the optimal fusion rule is automatically implemented by the channel itself. Technically, it can be proved that the LBMA scheme is asymptotically normal and efficient.
The research activity has also been focused on statistical decision problems in sensor networks under the SENMA (SEnsor Networks with Mobile Agents) paradigm, in which both the remote nodes and the mobile fusion center implement sequential tests. Collisions over the common communication channel are precluded by the sequentiality of the sensors’ query, and sensors with less informative data do not respond to the agent. The analytical characterization of the system performance allows to show that, by suitable choice of the design parameters, only a small fraction of the nodes will deliver data to the mobile agent, while most of the sensors contribute to the decision task by their silence. Also considered are networks in which the sensors’ abstention (censoring) is ruled by the informativeness of the local observation, measured in terms of the pertinent likelihood ratio, with an optimized censoring depth. In this case, two extremes are studied: the case of continuous delivering and the one-bit quantized scenario.
A genuine cross-layer approach is also pursued in decentralized systems for statistical inference aimed at recovering an approximation of the global likelihood function by “gossiping.” After collecting observations about the monitored phenomenon, the sensors of the system run a gossip algorithm designed to reach consensus. Clearly, without exchanging data, each sensor owns only a local information; at the other extreme, asymptotically with the number of gossip steps, the local information is averaged to a common value, shared by all the sensors. This means that at some intermediate step the optimal tradeoff between these two effects emerges, corresponding to the best likelihood approximation, which has been proposed as the guideline for system design.
Network security and detection of information flows
i) Detection and embedding of information flows
Modern packet communication networks often operate in the encrypted domain where the packet content (and header) is not accessible. However, the act itself of communicating (e.g., packet releasing) cannot be hidden, such that timing analysis can still extract valuable information about, e.g., who is talking to whom in the network. Basic questions arise: What can be revealed by timing analysis? Can we trace the route of the information flows across the network? The fundamental quantity answering these questions is called embedding capacity under causal delay and, so far, has been characterized only for Poisson traffic models. Stefano Marano’s original contribution relies in the full analytical characterization of the embedding capacity for general renewal traffic models, in the derivation of simple analytical formulas for the capacity, and in the analysis of practical algorithms to embed information flows into the nominal traffic of a network, in such a way that no traffic analysis can reveal their presence. These findings allow a better understanding of security and privacy issues in modern communication systems and networks; they also represent an important step toward the design of future complex networks (including perhaps social networks and cyber physical systems) where privacy and security may be a critical feature.
ii) Detection under physical layer secrecy
The interest is on the fundamental limits, in terms of detection performance, of a distributed network under severe energy constraints, operating in the presence of an eavesdropper that, by monitoring the sensors’ communication activities, aims to solve the same detection task of the network. The problem is formalized by defining a divergence-cost function, mirroring the capacity-cost function (C. Shannon, R. McEliece) that arises in the study of classical communication systems, and the related divergence per unit cost (again, resembling the capacity per unit cost popularized by S. Verdú). The operational meaning of these quantities is emphasized, and the ultimate limits of the systems are derived in the special case of perfect security in which the intruder, although with perfect knowledge the channel activities, is left with the same detection power of a coin flipper.
iii) Detection in the presence of Byzantine attacks
The general Byzantine problem has been introduced in the computer science literature in the 80’s and, since then, applied to a variety of applicative domains. However, reported work on distributed detection and data fusion in the presence of Byzantine sensors seems still limited. Stefano Marano’s contribution consists in proposing and analyzing a rigorous mathematical model for sensor networks under Byzantine attacks. A fraction of the sensors is reprogrammed by an intruder in order to attack the fusion center by transmitting, even cooperatively, fictitious observations. In this situation, the optimal attacking distributions of the Byzantines and the optimal countermeasures of the network are derived, and the corresponding Chernoff-Stein exponent is characterized. The derived fundamental tradeoff between detection performance and fraction of compromises sensors also quantifies the minimal fraction of Byzantines that “blinds” the system.
Some issues in detection theory
i) Chernoff's active sequential multihypothesis testing
With his work on “Sequential design of experiments,” (Annals Math. Statist., vol. 30) in 1959 H. Chernoff laid the theoretical foundations for designing an inference system capable of learning sequentially from the environment while managing actively the sensing stage, with the goal of minimizing the average number of observations needed to achieve a desired performance. We ask: to what extent this framework is relevant to modern radar applications? By casting Chernoff's work in a radar setting, it turns out that, more than fifty years later, the original Chernoff ideas emerge as a fundamental tool to design modern radar systems that are active, as they control the sensing stage adaptively, and efficient, as they minimize the number of collected observations. An observation model is proposed that we call "strong-or-weak". Under the strong-or-weak model, Chernoff's active hypothesis testing is studied with focus on the optimal signal selection strategy and on the asymptotic (vanishingly small risks) detection performance.
ii) Unlucky broker: Hypothesis testing with progressive data reduction
Stefano Marano has formulated and studied a new problem in distributed detection –referred to as the unlucky broker issue– with broad application areas, including sensor networks, finance, medicine, to name a few. A decision system is called to solve a hypothesis testing using a certain dataset of observations, complying with a prescribed error level. Later on, a fraction of the original dataset is lost and, exploiting the surviving part, a new decision must be made, complying with a different error level. What is the structure of the optimal test? Should one simply retain the original decision? Or, else, a new threshold test based on the surviving likelihood should be implemented? The answer is at neither of these extremes, and relies upon a careful exploitation of the strong correlations between original decision and surviving dataset. The optimal decision statistic has been characterized and the performance of the test derived analytically. Remarkably, depending on the two selected error levels and on the fraction of data lost, the general solution to the unlucky broker problem cannot be cast in the form of classical threshold tests.
iii) Sequential test and stochastic resonance
Wald’s sequential probability ratio test (SPRT) is a well-known statistical decision technique in which the amount of data used for making a binary decision is not fixed in advance: at each step of the procedure either a decision is made or a new sample is required. In many practical cases, the SPRT outperforms the classical likelihood ratio test in the sense that, for a prescribed error level, requires less samples, on the average.
The stochastic resonance theory has the roots in the physics literature of the 80’s and, more recently, has attracted the attention of the signal processing community. In this context, stochastic resonance usually refers to the capability of improving the performance of certain detectors, by adding noise at their input. “Can detectability be improved by adding noise?” is the provoking title of a paper published by S. Kay in the year 2000.
Stefano Marano formulated the first systematic investigation of the stochastic resonance effect in sequential detectors, with a complete characterization of the “resonant” noise to be injected in the system. While improving the performance of a (non-optimal) detector is not so surprising as it may appear at first glance, the results of the study are by no means trivial. One such result, for instance, reveals how certain sequential decision structures can be improved on by adding or subtracting (“at random”) a suitable constant to the available dataset.
iv) Other applications of sequential tests
With reference to Wald’s SPRT, Stefano Marano proposed practical algorithms for the detection of the two main classes of gravitational waves, the almost-periodic (continuous) and the (non-linear) chirp waves. The designed approach aims at exploiting the potentiality of the SPRT in specific connection with the peculiar features of the gravitational wave signals. Specifically, for continuous sources, the proposed detection algorithm is based on a windowed DFT combined with a sequential test in the transform domain, while the detection of chirps is accomplished by enriching the bank-of-filter structure by a suitable data sorting. These studies represent first steps towards efficient and computationally affordable detection procedures for this important research topic, as further discussed in a following item.
Multi-object multi-sensor systems
i) PHD, practice and asymptotic optimality
The tracking of multiple targets by means of a multi-sensor system is a timely and important research topic, characterized by several challenging issues: the number of targets is usually unknown, the number of sensors may be large, the targets are unlabeled, and so forth. A widely adopted solution to the multi-target multi-sensor problem relies upon the Probability Hypothesis Density (PHD) filter. While the PHD is widely used in practice, little is known on its formal properties and analytical performances, so that the system designer, in absence of precise guidelines, often resorts to ad-hoc and heuristic solutions. The research of Stefano Marano in this area is an attempt to fill this gap: the main result is the formal proof of the asymptotic optimality of the PHD with respect to the number of sensors. As byproduct of these studies, it has been also shown that the much simpler disjoint approach in which the number of targets is found first and the targets’ positions are then estimated, still retains the same asymptotic optimality of the PHD filter.
ii) Data compression and inference with data association
Modern distributed tracking systems often operate with data of uncertain origin: the remote units may report false alarms while may not report true targets; therefore, the fusion center must implement some clever fusion rule to take into account the fact that a large part of the reports are simply nonsense. The contribution of Stefano Marano consists in a systematic and methodological approach to the data fusion problem with data of uncertain origin, under severe communication constraints. Due to these constraints, in many practical implementations the remote nodes of the system deliver only the observation closest to the current estimation of the target position. A fundamental (and perhaps surprising) finding of the research is that, in the presence of large clutter, the closest sample is not necessarily the most informative, meaning that delivering the second, or third, sample may be better. Stefano Marano investigated also the practical implementation of tracking systems by particle filtering and proposed viable solutions to the out-of-sequence problem (data arriving at the fusion center may represent sensors’ delivering related to previous time slots).
iii) DOA estimation by a network of dumb sensors
While the DOA (direction of arrival) estimation is a well-assessed and understood topic in the classical signal processing literature, the advent of distributed systems made of extremely plain, small, and power-limited remote devices, poses new challenges. In this context Stefano Marano proposed a network design for the estimation of an acoustic source DOA, in which the remote nodes are omnidirectional antennas and, as such, DOA-blind. Nevertheless, designing the network under the SENMA (SEnsor Networks with Mobile Agents) paradigm, in which a mobile agent travelling across the surveyed area queries the sensors falling in its field of view, these “dumb sensors” are capable of providing the required DOA estimation. The basic mechanisms prescribes that the remote units memorize the time instant at which the wavefront hits them, and accordingly start to emit periodic “beeps” which, collected by the mobile agent and properly fused, carry information about the DOA.
Detection of gravitational waves
The observation of Gravitational Waves (GWs) is one of the most important purposes of the scientific community, since GWs carry information about the structure of the universe that cannot be directly obtained otherwise; it is commonly believed that the study of the gravitational radiation will open a new window over the universe around us, with unpredictable consequences in many field of human knowledge. Nowadays, several GW antennas have been built around the world, as a result of one of the most challenging technological effort ever produced, also requiring enormous investments in terms of economic and human resources. This unique effort must be followed now by analogous efforts to analyze the raw data produced by the antennas in order to extract useful information from the noisy observations. In this task, the signal processing community should play a vital role.
i) Efficient detection algorithms and performance analysis
The contribution given by Stefano Marano consists in the design and analysis of detection algorithms for chirp GWs based on a bank-of-filter structure, with special attention to mitigate the computational complexity of the detector, and in the design and analysis of efficient detection strategies for continuous sources. The analysis of real data has been pursued, with emphasis on the statistical characterization of the noise floor, on the study of the non-stationary behaviors, and on the removal of spectral lines (signal artifacts caused by the antennas).
ii) Source and signal models, and antennas
Stefano Marano has been involved in various guises in the main international project aimed at the direct detection of GWs. For results of the research in this wider scenario involving different scientific communities and heterogeneous competencies, please see the publication list.
Electromagnetic propagation in urban areas
Percolation models
Stefano Marano has been among the proposer of a successful analytical model for electromagnetic propagation in urban areas, borrowed from percolation theory. In connection with the so-called last mile problem, it was evident –especially in the mid of the 90’s– that propagation models for urban areas were either too simplistic (hence of little practical utility) or not analytical, and therefore too scenario-dependent, as those based on ray-tracing techniques. The proposed model represents a reasonable tradeoff solution between the opposite requirements of accuracy and mathematical tractability, and allows to make field previsions in a very simple way, by requiring only the measurement of some “global” parameter of the urban area under consideration.
Backscattering from Earth’s surface
Fractal models and backscattering
The investigations concerns remotely sensed data backscattered by the Earth’s surface, with application to environmental risk prevention. We adopt a fractal model for the surface and the fundamental question posed is whether the backscattered signal, as collected by a SAR sensor will retain the same fractal structure of the illuminated scene. Moreover, in the affirmative case, the interest is how the Hurst coefficient (a measure of the long range dependence) of the signal collected by the sensor is related to the Hurst coefficient of the illuminated scene. The study is methodological; however, the potential practical impact has been investigated by analysis of SAR real data (ERS-1/2).