Compression, Generalization and Learning

A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change is interpreted that this observation brings in extra information and, in learning theory, this corresponds to misclassification, or misprediction. In this paper, we lay the foundations of a new theory that allows one to keep control on the probability of change of compression (which maps into the statistical "risk" in learning applications). Under suitable conditions, the cardinality of the compressed set is shown to be a consistent estimator of the probability of change of compression (without any upper limit on the size of the compressed set); moreover, unprecedentedly tight finite-sample bounds to evaluate the probability of change of compression are obtained under a generally applicable condition of preference. All results are usable in a fully agnostic setup, i.e., without requiring any a priori knowledge on the probability distribution of the observations. Not only these results offer a valid support to develop trust in observation-driven methodologies, they also play a fundamental role in learning techniques as a tool for hyper-parameter tuning.Comment: https://www.jmlr.org/papers/v24/22-0605.htm

Scenario-based Economic Dispatch with Uncertain Demand Response

This paper introduces a new computational framework to account for uncertainties in day-ahead electricity market clearing process in the presence of demand response providers. A central challenge when dealing with many demand response providers is the uncertainty of its realization. In this paper, a new economic dispatch framework that is based on the recent theoretical development of the scenario approach is introduced. By removing samples from a finite uncertainty set, this approach improves dispatch performance while guaranteeing a quantifiable risk level with respect to the probability of violating the constraints. The theoretical bound on the level of risk is shown to be a function of the number of scenarios removed. This is appealing to the system operator for the following reasons: (1) the improvement of performance comes at the cost of a quantifiable level of violation probability in the constraints; (2) the violation upper bound does not depend on the probability distribution assumption of the uncertainty in demand response. Numerical simulations on (1) 3-bus and (2) IEEE 14-bus system (3) IEEE 118-bus system suggest that this approach could be a promising alternative in future electricity markets with multiple demand response providers

Sign-perturbed sums: A new system identification approach for constructing exact non-asymptotic confidence regions in linear regression models

We propose a new system identification method, called Sign - Perturbed Sums (SPS), for constructing nonasymptotic confidence regions under mild statistical assumptions. SPS is introduced for linear regression models, including but not limited to FIR systems, and we show that the SPS confidence regions have exact confidence probabilities, i.e., they contain the true parameter with a user-chosen exact probability for any finite data set. Moreover, we also prove that the SPS regions are star convex with the Least-Squares (LS) estimate as a star center. The main assumptions of SPS are that the noise terms are independent and symmetrically distributed about zero, but they can be nonstationary, and their distributions need not be known. The paper also proposes a computationally efficient ellipsoidal outer approximation algorithm for SPS. Finally, SPS is demonstrated through a number of simulation experiments

How do countries specialize in agricultural production? A complex network analysis of the global agricultural product space

Using a complex-network perspective, this paper empirically explores the determinants of the process through which countries, given their capabilities, specialize in agricultural production. Using production data from the Food and Agriculture Organization (FAO) for the period 1993-2013, we characterize the agricultural production space as a time-sequence of bipartite networks, connecting countries to the agricultural products they produce. We then project this representation in the agricultural production spaces, linking countries or products according to their similarity in production profiles, and we identify properties and determinants underlying their evolution. We find that, despite the unprecedented pressure that food systems have been undergoing in recent years, the agricultural production space is a very dense network displaying well-defined and stable communities of countries and products. We also show that the observed country community structures are not only shaped by environmental conditions, but also by economic, socio-political, and technological factors. We conclude by discussing the implications of such findings on our understanding of the complex relationships involving production capabilities and specialization patterns.Fil: Campi, Mercedes Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Interdisciplinario de Economía Política de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Económicas. Instituto Interdisciplinario de Economía Política de Buenos Aires; ArgentinaFil: Dueñas, Marco. Universidad de Bogota Jorge Tadeo Lozano; ColombiaFil: Fagiolo, Giorgio. Scuola Superiore Sant' Anna; Itali