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We study the performance of Machine Learning (ML) classification techniques. Leveraging the theory of large deviations, we provide the mathematical conditions for a ML classifier to exhibit error probabilities that vanish exponentially, say $\exp (-n\,I)$, where $n$ is the number of informative observations available for testing (or another relevant parameter, such as the size of the target in an image) and $I$ is the error rate. Such conditions depend on the Fenchel-Legendre transform of the cumulant-generating function of the Data-Driven Decision Function (D3F, i.e., what is thresholded before the final binary decision is made) learned in the training phase. As such, the D3F and the related error rate $I$ depend on the given training set. The conditions for the exponential convergence can be verified and tested numerically exploiting the available dataset or a synthetic dataset generated according to the underlying statistical model. Coherently with the large deviations theory, we can also establish the convergence of the normalized D3F statistic to a Gaussian distribution. Furthermore, approximate error probability curves $\zeta _{n} \exp (-n\,I)$ are provided, thanks to the refined asymptotic derivation, where $\zeta _{n}$ represents the most representative sub-exponential terms of the error probabilities. Leveraging the refined asymptotic, we are able to compute an accurate analytical approximation of the classification performance for both the regimes of small and large values of $n$. Theoretical findings are corroborated by extensive numerical simulations and by the use of real-world data, acquired by an X-band maritime radar system for surveillance.

Abstract To prevent the outbreak of the Coronavirus disease (COVID-19), many countries around the world went into lockdown and imposed unprecedented containment measures. These restrictions progressively produced changes to social behavior and global mobility patterns, evidently disrupting social and economic activities. Here, using maritime traffic data collected via a global network of Automatic Identification System (AIS) receivers, we analyze the effects that the COVID-19 pandemic and containment measures had on the shipping industry, which accounts alone for more than 80% of the world trade. We rely on multiple data-driven maritime mobility indexes to quantitatively assess ship mobility in a given unit of time. The mobility analysis here presented has a worldwide extent and is based on the computation of: Cumulative Navigated Miles (CNM) of all ships reporting their position and navigational status via AIS, number of active and idle ships, and fleet average speed. To highlight significant changes in shipping routes and operational patterns, we also compute and compare global and local vessel density maps. We compare 2020 mobility levels to those of previous years assuming that an unchanged growth rate would have been achieved, if not for COVID-19. Following the outbreak, we find an unprecedented drop in maritime mobility, across all categories of commercial shipping. With few exceptions, a generally reduced activity is observable from March to June 2020, when the most severe restrictions were in force. We quantify a variation of mobility between −5.62 and −13.77% for container ships, between +2.28 and −3.32% for dry bulk, between −0.22 and −9.27% for wet bulk, and between −19.57 and −42.77% for passenger traffic. The presented study is unprecedented for the uniqueness and completeness of the employed AIS dataset, which comprises a trillion AIS messages broadcast worldwide by 50,000 ships, a figure that closely parallels the documented size of the world merchant fleet.

Abstract During the course of an epidemic, one of the most challenging tasks for authorities is to decide what kind of restrictive measures to introduce and when these should be enforced. In order to take informed decisions in a fully rational manner, the onset of a critical regime, characterized by an exponential growth of the contagion, must be identified as quickly as possible. Providing rigorous quantitative tools to detect such an onset represents an important contribution from the scientific community to proactively support the political decision makers. In this paper, leveraging the quickest detection theory, we propose a mathematical model of the COVID-19 pandemic evolution and develop decision tools to rapidly detect the passage from a controlled regime to a critical one. A new sequential test—referred to as MAST (mean-agnostic sequential test)—is presented, and demonstrated on publicly available COVID-19 infection data from different countries. Then, the performance of MAST is investigated for the second pandemic wave, showing an effective trade-off between average decision delay $$\Delta$$ Δ and risk $$R$$ R , where $$R$$ R is inversely proportional to the time required to declare the need to take unnecessary restrictive measures. To quantify risk, in this paper we adopt as its proxy the average occurrence rate of false alarms, in that a false alarm risks unnecessary social and economic disruption. Ideally, the decision mechanism should react as quick as possible for a given level of risk. We find that all the countries share the same behaviour in terms of quickest detection, specifically the risk scales exponentially with the delay, $$R \sim \exp {(-\omega \Delta )}$$ R ∼ exp ( - ω Δ ) , where $$\omega$$ ω depends on the specific nation. For a reasonably small risk level, say, one possibility in ten thousand (i.e., unmotivated implementation of countermeasures every 27 years, on the average), the proposed algorithm detects the onset of the critical regime with delay between a few days to 3 weeks, much earlier than when the exponential growth becomes evident. Strictly from the quickest-detection perspective adopted in this paper, it turns out that countermeasures against the second epidemic wave have not always been taken in a timely manner. The developed tool can be used to support decisions at different geographic scales (regions, cities, local areas, etc.), levels of risk, instantiations of controlled/critical regime, and is general enough to be applied to different pandemic time-series. Additional analysis and applications of MAST are made available on a dedicated website.

The coronavirus epidemic (COVID-19) is a public health challenge due to its rapid global spread. Its unprecedented speed and pervasiveness have led many governments to implement a series of countermeasures, such as lock-downs, stopping/restricting travels, and mandating social distancing. To control and prevent the spread of COVID-19, it is essential to understand the latent dynamics of the disease’s evolution and the effectiveness of the intervention policies. Hidden Markov models (HMMs) capture both randomnesses in spatio-temporal dynamics and uncertainty in observations. In this paper, we apply an overall HMM that, based on multiple nations’ COVID-19 data including the USA, several European countries, and countries that have strict control policies, explore different types of observations, and we use it to infer the severity state on small geographical states or regions in the USA and Italy as test cases. Further, we aggregate the severity level of each region over a fixed time period to visualize the time evolution and propagation across regions. Such an analysis and visualization provide suggestions for interventions and responses in a calibrated manner. Results from HMM modeling are consistent with what is observed in Italy and the USA and these models can serve as visualization and proactive decision support tools to policymakers.

In this article, we carry out a simulation analysis of ship detection via Global Navigation Satellite System-Reflectometry (GNSS-R) delay-Doppler map (DDM). The GNSS-R DDM simulator used here is a modified version of an algorithm conceived for the generation of GNSS-R DDMs of the sea surface. The new algorithm is based on an analytical model for the radar cross section of ships and is able to properly account for the presence of ship targets within the scene. The proposed GNSS-R DDM simulator is, then, exploited for assessing the viability of GNSS-R in ship detection applications at low incidence angles, where the adopted scattering models provide accurate results. The aim of the implemented simulation setup is to analyze what are the preferable conditions for ship detection using standard GNSS-R signal processing chain receiver and compare typical forward left-hand circularly polarized GNSS-R systems with nonstandard backward right-hand circularly polarized (RHCP) GNSS-R. The simulation study is two fold: first, detection performance is evaluated at spaceborne and airborne altitudes for both polarization channels under favorable detection conditions. Then, visibility of ship targets is assessed in terms of their location within the DDM. Simulation results show that ship detection is problematic when using satellite data, whereas interesting results are achieved at airborne altitudes, provided that the aircraft is approximately between the GNSS satellite and the target, and that appropriate RHCP polarization is probed. In such configurations, signal-to-noise-ratios larger than 10 dB are obtained with airborne receivers collecting the RHCP signal.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.