arXiv subjects

Algo Carè

Publications and source records attributed to Algo Carè.

9 recordsLinked to original sources

arXiv2026

Scenario theory for multi-criteria data-driven decision making

The scenario approach provides a powerful data-driven framework for designing solutions under uncertainty with rigorous probabilistic robustness guarantees. Existing theory, however, primarily addresses assessing robustness with respect to a single appropriateness criterion for the solution based on a dataset, whereas many practical applications - including multi-agent decision problems - require the simultaneous consideration of multiple criteria and the assessment of their robustness based on multiple datasets, one per criterion. This paper develops a general scenario theory for multi-criteria data-driven decision making. A central innovation lies in the collective treatment of the risks associated with violations of individual criteria, which yields substantially more accurate robustness certificates than those derived from a naive application of standard results. In turn, this approach enables a sharper quantification of the robustness level with which all criteria are simultaneously satisfied. The proposed framework applies broadly to multi-criteria data-driven decision problems, providing a principled, scalable, and theoretically grounded methodology for design under uncertainty.

stat.ML↗

arXiv2026

Scenario Approach with Post-Design Certification of User-Specified Properties

The scenario approach is an established data-driven design framework that comes equipped with a powerful theory linking design complexity to generalization properties. In this approach, data are simultaneously used both for design and for certifying the design's reliability, without resorting to a separate test dataset. This paper takes a step further by guaranteeing additional properties, useful in post-design usage but not considered during the design phase. To this end, we introduce a two-level framework of appropriateness: baseline appropriateness, which guides the design process, and post-design appropriateness, which serves as a criterion for a posteriori evaluation. We provide distribution-free upper bounds on the risk of failing to meet the post-design appropriateness; these bounds are computable without using any additional test data. Under additional assumptions, lower bounds are also derived. As part of an effort to demonstrate the usefulness of the proposed methodology, the paper presents two practical examples in H2 and pole-placement problems. Moreover, a method is provided to infer comprehensive distributional knowledge of relevant performance indexes from the available dataset.

stat.ME↗

arXiv2025

A Scenario-Based Approach for Stochastic Economic Model Predictive Control with an Expected Shortfall Constraint

This paper presents a novel approach to stochastic economic model predictive control (SEMPC) that minimizes average economic cost while satisfying an empirical expected shortfall (EES) constraint to manage risk. A new scenario-based problem formulation ensuring controlled risk with high confidence while minimizing the average cost is introduced. The probabilistic guarantees is dependent on the number of support elements over the entire input domain, which is difficult to find for high-dimensional systems. A heuristic algorithm is proposed to find the number of support elements. Finally, an efficient method is presented to reduce the computational complexity of the SEMPC problem with an EES constraint. The approach is validated on a water distribution network, showing its effectiveness in balancing performance and risk.

eess.SY↗

arXiv2025

Stochastic Approximation in a Markovian Framework Revisited: Lipschitz Continuity of the Poisson Equation

In this paper we revisit a fundamental technical issue within the theory of stochastic approximation (SA) in a Markovian framework, first proposed in the book by Djereveckii and Fradkov (1981), and further developed in much detail in the book by Benveniste, M{é}tivier, and Priouret (1990). This theory is instrumental in many application areas such as the statistical analysis of Hidden Markov Models arising in telecommunication, quantized linear stochastic systems, and more recently in active learning and reinforcement learning. The problem at hand is the verification of the existence, uniqueness and Lipschitz-continuity of the solution of a parameter-dependent Poisson equation, in an appropriate weighted sup-norm, associated with a collection of Markov chains on general state spaces. Verification of the above facts is vital in the analysis of SA processes presented in (Benveniste et al., 1990) via the ODE (ordinary differential equations) method, requiring substantial technical effort. The motivation and focus of the paper is to address this technical issue, by presenting a simple set of conditions, under which the above properties of the Poisson equation at hand can be conveniently established. The starting point of our work is an intricate result of Hairer and Mattingly (2011) proving that by tilting standard conditions of mainstream stability theory for Markov chains, the transition kernels prove to be contractions in the space of differences of probability measures in a suitable metric. To demonstrate the applicability of our results, the proposed conditions are verified for a class of queuing system with open-loop control.

math.PR↗

arXiv2025

Risk Analysis and Design Against Adversarial Actions

Learning models capable of providing reliable predictions in the face of adversarial actions has become a central focus of the machine learning community in recent years. This challenge arises from observing that data encountered at deployment time often deviate from the conditions under which the model was trained. In this paper, we address deployment-time adversarial actions and propose a versatile, well-principled framework to evaluate the model's robustness against attacks of diverse types and intensities. While we initially focus on Support Vector Regression (SVR), the proposed approach extends naturally to the broad domain of learning via relaxed optimization techniques. Our results enable an assessment of the model vulnerability without requiring additional test data and operate in a distribution-free setup. These results not only provide a tool to enhance trust in the model's applicability but also aid in selecting among competing alternatives. Later in the paper, we show that our findings also offer useful insights for establishing new results within the out-of-distribution framework.

cs.LG↗

arXiv2024

Signed-Perturbed Sums Estimation of ARX Systems: Exact Coverage and Strong Consistency (Extended Version)

Sign-Perturbed Sums (SPS) is a system identification method that constructs confidence regions for the unknown system parameters. In this paper, we study SPS for ARX systems, and establish that the confidence regions are guaranteed to include the true model parameter with exact, user-chosen, probability under mild statistical assumptions, a property that holds true for any finite number of observed input-output data. Furthermore, we prove the strong consistency of the method, that is, as the number of data points increases, the confidence region gets smaller and smaller and will asymptotically almost surely exclude any parameter value different from the true one. In addition, we also show that, asymptotically, the SPS region is included in an ellipsoid which is marginally larger than the confidence ellipsoid obtained from the asymptotic theory of system identification. The results are theoretically proven and illustrated in a simulation example.

eess.SY↗

arXiv2020

Estimation of Accurate and Calibrated Uncertainties in Deterministic models

In this paper we focus on the problem of assigning uncertainties to single-point predictions generated by a deterministic model that outputs a continuous variable. This problem applies to any state-of-the-art physics or engineering models that have a computational cost that does not readily allow to run ensembles and to estimate the uncertainty associated to single-point predictions. Essentially, we devise a method to easily transform a deterministic prediction into a probabilistic one. We show that for doing so, one has to compromise between the accuracy and the reliability (calibration) of such a probabilistic model. Hence, we introduce a cost function that encodes their trade-off. We use the Continuous Rank Probability Score to measure accuracy and we derive an analytic formula for the reliability, in the case of forecasts of continuous scalar variables expressed in terms of Gaussian distributions. The new Accuracy-Reliability cost function is then used to estimate the input-dependent variance, given a black-box mean function, by solving a two-objective optimization problem. The simple philosophy behind this strategy is that predictions based on the estimated variances should not only be accurate, but also reliable (i.e. statistical consistent with observations). Conversely, early works based on the minimization of classical cost functions, such as the negative log probability density, cannot simultaneously enforce both accuracy and reliability. We show several examples both with synthetic data, where the underlying hidden noise can accurately be recovered, and with large real-world datasets.

stat.ML↗

arXiv2017

Classification of Solar Wind with Machine Learning

We present a four-category classification algorithm for the solar wind, based on Gaussian Process. The four categories are the ones previously adopted in Xu & Borovsky [2015]: ejecta, coronal hole origin plasma, streamer belt origin plasma, and sector reversal origin plasma. The algorithm is trained and tested on a labeled portion of the OMNI dataset. It uses seven inputs: the solar wind speed $V_{sw}$, the temperature standard deviation $σ_T$, the sunspot number $R$, the $f_{10.7}$ index, the Alfven speed $v_A$, the proton specific entropy $S_p$ and the proton temperature $T_p$ compared to a velocity-dependent expected temperature. The output of the Gaussian Process classifier is a four element vector containing the probabilities that an event (one reading from the hourly-averaged OMNI database) belongs to each category. The probabilistic nature of the prediction allows for a more informative and flexible interpretation of the results, for instance being able to classify events as 'undecided'. The new method has a median accuracy larger than $90\%$ for all categories, even using a small set of data for training. The Receiver Operating Characteristic curve and the reliability diagram also demonstrate the excellent quality of this new method. Finally, we use the algorithm to classify a large portion of the OMNI dataset, and we present for the first time transition probabilities between different solar wind categories. Such probabilities represent the 'climatological' statistics that determine the solar wind baseline.

physics.space-ph↗

arXiv2015

Sign-Perturbed Sums (SPS) with Instrumental Variables for the Identification of ARX Systems - Extended Version

We propose a generalization of the recently developed system identification method called Sign-Perturbed Sums (SPS). The proposed construction is based on the instrumental variables estimate and, unlike the original SPS, it can construct non-asymptotic confidence regions for linear regression models where the regressors contain past values of the output. Hence, it is applicable to ARX systems, as well as systems with feedback. We show that this approach provides regions with exact confidence under weak assumptions, i.e., the true parameter is included in the regions with a (user-chosen) exact probability for any finite sample. The paper also proves the strong consistency of the method and proposes a computationally efficient generalization of the previously proposed ellipsoidal outer-approximation. Finally, the new method is demonstrated through numerical experiments, using both real-world and simulated data.

stat.ME↗