Asymptotic robustness of Kelly's GLRT and Adaptive Matched Filter detector under model misspecification

A fundamental assumption underling any Hypothesis Testing (HT) problem is that the available data follow the parametric model assumed to derive the test statistic. Nevertheless, a perfect match between the true and the assumed data models cannot be achieved in many practical applications. In all these cases, it is advisable to use a robust decision test, i.e. a test whose statistic preserves (at least asymptotically) the same probability density function (pdf) for a suitable set of possible input data models under the null hypothesis. Building upon the seminal work of Kent (1982), in this paper we investigate the impact of the model mismatch in a recurring HT problem in radar signal processing applications: testing the mean of a set of Complex Elliptically Symmetric (CES) distributed random vectors under a possible misspecified, Gaussian data model. In particular, by using this general misspecified framework, a new look to two popular detectors, the Kelly's Generalized Likelihood Ration Test (GLRT) and the Adaptive Matched Filter (AMF), is provided and their robustness properties investigated.Comment: ISI World Statistics Congress 2017 (ISI2017), Marrakech, Morocco, 16-21 July 201

Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications

Inferring information from a set of acquired data is the main objective of any signal processing (SP) method. In particular, the common problem of estimating the value of a vector of parameters from a set of noisy measurements is at the core of a plethora of scientific and technological advances in the last decades; for example, wireless communications, radar and sonar, biomedicine, image processing, and seismology, just to name a few. Developing an estimation algorithm often begins by assuming a statistical model for the measured data, i.e. a probability density function (pdf) which if correct, fully characterizes the behaviour of the collected data/measurements. Experience with real data, however, often exposes the limitations of any assumed data model since modelling errors at some level are always present. Consequently, the true data model and the model assumed to derive the estimation algorithm could differ. When this happens, the model is said to be mismatched or misspecified. Therefore, understanding the possible performance loss or regret that an estimation algorithm could experience under model misspecification is of crucial importance for any SP practitioner. Further, understanding the limits on the performance of any estimator subject to model misspecification is of practical interest. Motivated by the widespread and practical need to assess the performance of a mismatched estimator, the goal of this paper is to help to bring attention to the main theoretical findings on estimation theory, and in particular on lower bounds under model misspecification, that have been published in the statistical and econometrical literature in the last fifty years. Secondly, some applications are discussed to illustrate the broad range of areas and problems to which this framework extends, and consequently the numerous opportunities available for SP researchers.Comment: To appear in the IEEE Signal Processing Magazin

Scaling up MIMO Radar for Target Detection

This work focuses on target detection in a colocated MIMO radar system. Instead of exploiting the »classical' temporal domain, we propose to explore the spatial dimension (i.e., number of antennas M) to derive asymptotic results for the detector. Specifically, we assume no a priori knowledge of the statistics of the autoregressive data generating process and propose to use a mispecified Wald-type detector, which is shown to have an asymptotic χ-squared distribution as M → ∞. Closed-form expressions for the probabilities of false alarm and detection are derived. Numerical results are used to validate the asymptotic analysis in the finite system regime. It turns out that, for the considered scenario, the asymptotic performance is closely matched already for M ≥ 50

Social norms and e-motions in problematic social media use among adolescents

© 2020 The Authors Introduction: Being constantly connected on social media is a “way of being” among adolescents. However, social media use can become “problematic” for some users and only a few studies have explored the concurrent contribution of social context and emotion regulation to problematic social media use. The current study aimed to test: (i) the influence of friends (i.e., their social media use and group norms about social media use); and (ii) the effects of difficulties in emotion regulation and so-called “e-motions” on adolescents’ problematic social media use. Methods: A cross-sectional study was conducted in Italian secondary schools. An online questionnaire was administered to 761 adolescents (44.5% females; Mage = 15.49 years; SDage = 1.03). Results: Path analysis showed that social norms were directly associated with problematic social media use and friends’ social media use was associated with the frequency of social media use, which, in turn, was associated with problematic use. Difficulties in emotion regulation were directly and indirectly linked to problematic social media use via frequency of use and facilitating use of e-motions. Conclusions: These findings provide support for the importance of both peer influence and emotion regulation in this context. Social norms and emotion regulation should be considered in prevention programs addressing problematic social media use in adolescents

Estimation of Dynamical Noise Power in Unknown Systems

Noise can be modeled as a sequence of random variables defined on a probability space that may be added to a given dynamical system $T$, which is a map on a phase space. In the non-trivial case of dynamical noise $\lbrace \varepsilon _{n}\rbrace _{n}$, where $\varepsilon _{n}$ follows a Gaussian distribution $\mathcal {N}(0,\sigma ^{2})$ and the system output is $x_{n} = T(x_{n-1};x_{0})+\varepsilon _{n}$, without any specific knowledge or assumption about $T$, the quantitative estimation of the noise power $\sigma ^{2}$ is a challenge. Here, we introduce a formal method based on the nonlinear entropy profile to estimate the dynamical noise power $\sigma ^{2}$ without requiring knowledge of the specific $T$ function. We tested the correctness of the proposed method using time series generated from Logistic maps and Pomeau-Manneville systems under different conditions. Our results demonstrate that the proposed estimation algorithm can properly discern different noise levels without any a priori information

Massive MIMO radar for target detection

Since the seminal paper by Marzetta from 2010, the Massive MIMO paradigm in communication systems has changed from being a theoretical scaled-up version of MIMO, with an infinite number of antennas, to a practical technology. Its key concepts have been adopted in the 5G new radio standard and base stations, where 64 fully-digital transceivers have been commercially deployed. Motivated by these recent developments, this paper considers a co-located MIMO radar with MT transmitting and MR receiving antennas and explores the potential benefits of having a large number of virtual spatial antenna channels N=MTMR. Particularly, we focus on the target detection problem and develop a robust Wald-type test that guarantees certain detection performance, regardless of the unknown statistical characterization of the disturbance. Closed-form expressions for the probabilities of false alarm and detection are derived for the asymptotic regime N→∞. Numerical results are used to validate the asymptotic analysis in the finite system regime with different disturbance models. Our results imply that there always exists a sufficient number of antennas for which the performance requirements are satisfied, without any a-priori knowledge of the disturbance statistics. This is referred to as the Massive MIMO regime of the radar system

SAI: A sensible artificial intelligence that plays with handicap and targets high scores in 9x9 Go

We develop a new framework for the game of Go to target a high score, and thus a perfect play. We integrate this framework into the Monte Carlo tree search - policy iteration learning pipeline introduced by Google DeepMind with AlphaGo. Training on 9×9 Go produces a superhuman Go player, thus proving that this framework is stable and robust. We show that this player can be used to effectively play with both positional and score handicap. We develop a family of agents that can target high scores against any opponent, recover from very severe disadvantage against weak opponents, and avoid suboptimal moves