Optimal Covariance Cleaning for Heavy-Tailed Distributions: Insights from Information Theory

In optimal covariance cleaning theory, minimizing the Frobenius norm between the true population covariance matrix and a rotational invariant estimator is a key step. This estimator can be obtained asymptotically for large covariance matrices, without knowledge of the true covariance matrix. In this study, we demonstrate that this minimization problem is equivalent to minimizing the loss of information between the true population covariance and the rotational invariant estimator for normal multivariate variables. However, for Student's t distributions, the minimal Frobenius norm does not necessarily minimize the information loss in finite-sized matrices. Nevertheless, such deviations vanish in the asymptotic regime of large matrices, which might extend the applicability of random matrix theory results to Student's t distributions. These distributions are characterized by heavy tails and are frequently encountered in real-world applications such as finance, turbulence, or nuclear physics. Therefore, our work establishes a connection between statistical random matrix theory and estimation theory in physics, which is predominantly based on information theory

A multi-layer network model to assess school opening policies during a vaccination campaign:a case study on COVID-19 in France

We propose a multi-layer network model for the spread of an infectious disease that accounts for interactions within the family, between children in classes and schools, and casual contacts in the population. The proposed framework is designed to test several what-if scenarios on school openings during the vaccination campaigns, thereby assessing the safety of different policies, including testing practices in schools, diverse home-isolation policies, and targeted vaccination. We demonstrate the potentialities of our model by calibrating it on epidemiological and demographic data of the spring 2021 COVID-19 vaccination campaign in France. Specifically, we consider scenarios in which a fraction of the population is vaccinated, and we focus our analysis on the role of schools as drivers of the contagions and on the implementation of targeted intervention policies oriented to children and their families. We perform our analysis by means of a campaign of Monte Carlo simulations. Our findings suggest that transmission in schools may play a key role in the spreading of a disease. Interestingly, we show that children’s testing might be an important tool to flatten the epidemic curve, in particular when combined with enacting temporary online education for classes in which infected students are detected. Finally, we test a vaccination strategy that prioritizes the members of large families and we demonstrate its good performance. We believe that our modeling framework and our findings could be of help for public health authorities for planning their current and future interventions, as well as to increase preparedness for future epidemic outbreaks

Nonparametric sign prediction of high-dimensional correlation matrix coefficients

We introduce a method to predict which correlation matrix coefficients are likely to change their signs in the future in the high-dimensional regime, i.e. when the number of features is larger than the number of samples per feature. The stability of correlation signs, two-by-two relationships, is found to depend on three-by-three relationships inspired by Heider social cohesion theory in this regime. We apply our method to US and Hong Kong equities historical data to illustrate how the structure of correlation matrices influences the stability of the sign of its coefficients

A Control-Oriented Model for Mobility on Demand Systems

In this paper, we propose a control-oriented model for mobility-on-demand systems (MOD). The system is first described through dynamical stochastic state-space equations in discrete time, and then suitably simplified in order to obtain a control-oriented model, on which a control strategy based on Model Predictive Control (MPC) is devised. The control strategy aims at maintaining the average number of vehicles at stations within prescribed bounds. Relevant features of the proposed model are: {em i)} the possibility of considering stochasticity and heterogeneity in the system parameters; {em ii)} a state space structure, which makes the model suitable for implementation of effective parameter identification and control strategies; and {em iii)} the possibility of weighting the control effort, leading to control solutions that may trade off efficiency and cost. Simulation results on a synthetic network corroborate the validity of our approach under several operational conditions

A novel framework for community modeling and characterization in directed temporal networks

Abstract We deal with the problem of modeling and characterizing the community structure of complex systems. First, we propose a mathematical model for directed temporal networks based on the paradigm of activity driven networks. Many features of real-world systems are encapsulated in our model, such as hierarchical and overlapping community structures, heterogeneous attitude of nodes in behaving as sources or drains for connections, and the existence of a backbone of links that model dyadic relationships between nodes. Second, we develop a method for parameter identification of temporal networks based on the analysis of the integrated network of connections. Starting from any existing community detection algorithm, our method enriches the obtained solution by providing an in-depth characterization of the very nature of the role of nodes and communities in generating the temporal link structure. The proposed modeling and characterization framework is validated on three synthetic benchmarks and two real-world case studies

Detecting network backbones against time variations in node properties

Many real systems can be described through time-varying networks of interactions that encapsulate information sharing between individual units over time. These interactions can be classified as being either reducible or irreducible: reducible interactions pertain to node-specific properties, while irreducible interactions reflect dyadic relationships between nodes that form the network backbone. The process of filtering reducible links to detect the backbone network could allow for identifying family members and friends in social networks or social structures from contact patterns of individuals. A pervasive hypothesis in existing methods of backbone discovery is that the specific properties of the nodes are constant in time, such that reducible links have the same statistical features at any time during the observation. In this work, we release this assumption toward a new methodology for detecting network backbones against time variations in node properties. Through analytical insight and numerical evidence on synthetic and real datasets, we demonstrate the viability of the proposed approach to aid in the discovery of network backbones from time series. By critically comparing our approach with existing methods in the technical literature, we show that neglecting time variations in node-specific properties may beget false positives in the inference of the network backbone

Backbone reconstruction in temporal networks from epidemic data

10 pages, 9 figuresCleaning covariance matrices is a highly non-trivial problem, yet of central importance in the statistical inference of dependence between objects. We propose here a probabilistic hierarchical clustering method, named Bootstrapped Average Hierarchical Clustering (BAHC), that is particularly effective in the high-dimensional case, i.e., when there are more objects than features. When applied to DNA microarray, our method yields distinct hierarchical structures that cannot be accounted for by usual hierarchical clustering. We then use global minimum-variance risk management to test our method and find that BAHC leads to significantly smaller realized risk compared to state-of-the-art linear and nonlinear filtering methods in the high-dimensional case. Spectral decomposition shows that BAHC better captures the persistence of the dependence structure between asset price returns in the calibration and the test periods

An Agent Based Model of Air Traffic Management

The WP-E ELSA project aims at developing an empirically grounded agent based model that describes some of the stylized facts observed in the Air Traffic Management of the European airspace. The model itself has two main parts: (i) The strategic layer, focused on the interaction between the Network Manager and the Airline Operators and (ii) the tactical layer, focused on aircraft and controllers behaviour in Air Traffic Control (ATC) sectors. The preliminary results for the strategic layer show that when we have a mixing of re-routing and shifting companies, the overall satisfaction can even increase together with the number of flights, which is an effect not observed when only one type of companies is present. The preliminary results for the tactical layer indicate that when shocks in the system are confined in small areas, the interplay between the re-routing and change of flight level strategies may even lead to trajectory modifications that give smaller average delays as long as the number of shocks increases