Welcome to the homepage of

Algo Carè

University of Brescia LOGO

Dept. of  Information Engineering
University of Brescia
via Branze, 38
25123 Brescia

e-mail: algo.care (at) unibs.it



→ TEACHING (in Italian)

... SPACE WEATHER (External link)


NEWS: Upcoming workshop on "The Scenario Approach for Decisions and Control" at CDC2024 (15 December 2024), click here for more information

Short Academic Biography

I received the Ph.D. degree in informatics and automation engineering in 2013 from the University of Brescia, Italy.

After my Ph.D., I spent two years at the University of Melbourne, VIC, Australia, as a Research Fellow in system identification with the Department of Electrical and Electronic Engineering.

In 2016, I was a recipient of a two-year ERCIM "Alain Bensoussan" Fellowship  that I spent at the Institute for Computer Science and Control  (SZTAKI), Hungarian Academy of Sciences (MTA), Budapest, Hungary, and with the Multiscale Dynamics Group, at the National Research Institute for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands.

I was awarded the triennial Stochastic Programming Student Paper Prize by the Stochastic Programming Society (for the period 2013–2016).

I serve as an associate editor for the International Journal of Adaptive Control and Signal Processing (
John Wiley and Sons), a monthly journal established in 1987 - you can view here the first masthead and here the first editorial by Mike J. Grimble.

I am a member of the European Control Association (EUCA) Conference Editorial Board (as such, I have been serving as associate editor of the European Control Conferences since 2021), of the IFAC Technical Committee on Modeling, Identification and Signal Processing, and of the IEEE Technical Committee on Systems Identification and Adaptive Control.

My research interests include

Marco C. Campi - University of Brescia
Simone Garatti - Politecnico di Milano
Erik Weyer - University of Melbourne
Balázs Csanád Csáji - SZTAKI   
Gianluigi Pillonetto - University of Padua
Enrico Camporeale - University of Colorado, Boulder. Former CWI
Fabio Baronio- University of Brescia


Teaching (in Italian)

Blackboard caricature of me by an "anonymous" attendee of the Uncertain Dynamic System course.


Selected Publications 

  1. A. Carè, R. Carli, A. Dalla Libera, D. Romeres, G. Pillonetto
    “Kernel Methods and Gaussian Processes for System Identification and Control: A Road Map on Regularized Kernel-Based Learning for Control,”
    IEEE Control Systems Magazine, 43(5),[doi: 10.1109/MCS.2023.3291625], 2023

  2. G. Baggio, A. Carè, A. Scampicchio, G. Pillonetto
    Bayesian frequentist bounds for machine learning and system identification,”
    Automatica, 146, 110599 [doi: 10.1016/j.automatica.2022.110599], 2022

    Estimating a function from noisy measurements is a crucial problem in statistics and engineering, with an impact on machine learning predictions and identification of dynamical systems. In view of robust control design and safety-critical applications such as autonomous driving and smart healthcare, estimates are required to be complemented with uncertainty bounds quantifying their reliability. Most of the available results are derived by constraining the estimates to belong to a restricted, deterministic function space; however, the returned bounds often result overly conservative and, hence, of limited usefulness. An alternative is to use a Bayesian framework. The regions thereby obtained however require complete specification of prior distributions whose choice may significantly affect the probability of inclusion. This study presents a framework for the effective computation of regions that include the unknown function with exact probability. In this setting, the users not only have the freedom to modulate the amount of prior knowledge that informs the constructed regions but can, on a different plane, finely modulate their commitment to such information. The result is a versatile certified estimation framework capable of addressing a multitude of problems, ranging from parametric estimation (where the probabilistic guarantees can be issued under no commitment to the prior information) to non-parametric problems (that call for fine exploitation of prior information).

  3. S. Garatti, A. Carè, M.C. Campi
    Complexity is an effective observable to tune early stopping in scenario optimization,”
    IEEE Transactions on Automatic Control, 68(2):928-942, [doi:  10.1109/TAC.2022.3153888], 2023

  4. A. Carè
    A simple condition for the boundedness of Sign-Perturbed-Sums (SPS) confidence regions,”
    Automatica, 139, 110150, [doi: 10.1016/j.automatica.2021.110150], 2022

    Sign-Perturbed-Sums (SPS) is a system identification algorithm that, under mild assumptions on the distribution of the noise, constructs confidence regions with finite-sample validity and a user-specified confidence level. For linear regression models, SPS regions are well-shaped in a precise meaning, but it is still possible (though rare in practice) that they are unbounded. In this communication, I provide a reformulation of a technical condition for the boundedness of the SPS regions in terms of a more practical excitation condition. I briefly argue that the simple condition here proposed provides insight to tune the SPS parameters, and even to design refined algorithms that can be guaranteed to deliver bounded regions.

  5. M.C. Campi, A. Carè, S. Garatti
    The scenario approach: A tool at the service of data-driven decision making,”
    Annual Reviews in Control, 52:1-17, [https://doi.org/10.1016/j.arcontrol.2021.10.004], 2021

    In the eyes of many control scientists, the theory of the scenario approach is a tool for determining the sample size in certain randomized control-design methods, where an uncertain variable is replaced by a random sample of scenarios. This point of view is rooted in the history of the scenario approach and stands on a long track record of successful applications. However, in the last two decades the theory of the scenario approach has gone beyond its original motivations and applications, and has unveiled some fundamental relationships between the complexity of a design and its generalization capabilities. The new knowledge brought by the theory provides a solid ground for a framework where data can be exploited in a flexible and wise manner throughout a large variety of engineering activities. By this article we aim at providing an access point to a set of state-of-the-art results in the theory of the scenario approach that can be valuable to target important challenges in modern control-design and decision-making at large. In the first part of the article, we introduce a set-up for decision-making where the role of prior knowledge and user preferences can, and should, be distinguished from the role of data. Then, we show that the theory of the scenario approach offers a platform for conjugating heuristic approaches, which in complex contexts are unavoidably based on incomplete and possibly imprecise information, with a solid theory for certifying the validity of the output of the decision process.

  6. A. Carè, M.C. Campi, E. Weyer
    State Conditional Filtering,” 
    IEEE Transactions on Automatic Control, 67(7):3381-3395 [doi: 10.1109/TAC.2021.3103905], 2022

    In many dynamical state estimation problems, not all the values the state can take have the same importance; hence, missing to deliver an appropriate estimate has more severe consequences for certain state values than for others. In many applications, such important state values correspond to events that have low a priori probability to happen (e.g., unsafe situations or conditions that one tries to avoid by design). Provably, Kalman filtering techniques are inadequate to correctly estimate such rare events. In this paper, a new state estimation paradigm is introduced to build confidence regions that contain the true state value, whatever this value is, with a user-chosen probability. Among regions having this property, an algorithm is introduced able to generate in a Gaussian setup the region that satisfies a minimum-volume condition.

  7. A. Carè, M.C. Campi, B.Cs. Csáji, E. Weyer
    Facing Undermodelling in Sign-Perturbed-Sums System Identification,”
    Systems & Control Letters. 153, 104936 [doi: 10.1016/j.sysconle.2021.104936], 2021

  8. G. Arici, M.C. Campi, A. Carè, M. Dalai, F.A. Ramponi.
    A Theory of the Risk for Empirical CVaR with Application to Portfolio Selection,”
    J. Syst. Sci. Complexity. 34:1879-1894 (special issue on occasion of the 60th birthday of Professor Lei Guo), 2021

  9. E. Camporeale, A. Carè
    ACCRUE: Accurate and Reliable Uncertainty Estimate in Deterministic models,”
    Int. J. Uncertain Quantif. 11(4):81-94, 2021

  10. A.T.J.R. Cobbenhagen, A. Carè, M.C. Campi, F.A. Ramponi,  D.J. Antunes, W.P.M.H. Heemels
    Novel bounds on the probability of misclassificaiton in majority voting: leveraging the majority size,”
    IEEE Control Systems Letters. 5(5):1513-1518 [doi: 10.1109/LCSYS.2020.3040961], 2020

  11. S. Formentin, M.C. Campi, A. Carè, S.M. Savaresi.
    Deterministic continuous-time Virtual Reference Feedback Tuning (VRFT) with application to PID design,”
    Systems & Control Letters. 127:25-34 [doi: 10.1016/j.sysconle.2019.03.007], 2019

    In this paper, we introduce a data-driven control design method that does not rely on a model of the plant. The method is inspired by the Virtual Reference Feedback Tuning approach for data-driven controller tuning, but it is here entirely developed in a deterministic, continuous-time setting. A PID autotuner is then developed out of the proposed approach and its effectiveness is tested on an experimental brake-by-wire facility. The final performance is shown to outperform that of a benchmark model-based design method.

  12. S. Garatti, M.C. Campi, A. Carè
    On a class of Interval Predictor Models with universal reliability,”
    Automatica.  110, 108542 [doi:  10.1016/j.automatica.2019.108542], 2019

    An Interval Predictor Model (IPM) is a rule by which some observable variables (system inputs) are mapped into an interval that is used to predict an inaccessible variable (system output). IPMs have been studied in Campi et al. (2009), where the problem of fitting an IPM on a set of observations has been considered. In the same paper, upper-bounds on the probability that a future system output will fall outside the predicted interval (misprediction) have also been derived in a stationary and independent framework. While these bounds have the notable property of being valid independently of the unknown mechanism that has generated the data, in general the actual probability distribution of the misprediction does depend on the data generation mechanism and, hence, these bounds may introduce conservatism when applied to a specific case. In this paper, we study the reliability of an important class of IPMs, called minimax layers, and show that this class exhibits the special property that the probability distribution of the misprediction is known exactly and is universal, i.e., is always the same irrespective of the data generation mechanism. This result carries important consequences on the use of minimax layers in practice.

  13. M.S. Modarresi, Le Xie, M.C. Campi, S. Garatti, A. Carè, A.A. Thatte, P. R. Kumar,
    Scenario-based Economic Dispatch with Tunable Risk Levels in High-renewable Power Systems,”
    IEEE Trans. on Power Systems, 34(6):5103-5114 [doi: 10.1109/TPWRS.2018.2874464], 2019

  14. A. Carè, S. Garatti, M.C. Campi
    The wait-and-judge scenario approach applied to antenna array design,”
    Computational Management Science. 16:481-499 [doi: 10.1007/s10287-019-00345-5], 2019

  15.  H.A. Nasir A. Carè, E. Weyer
    A Scenario-Based Stochastic MPC Approach for Problems With Normal and Rare Operations With an Application to Rivers,”
    IEEE Transactions on Control Systems Technology. 27(4):1397-1410 [doi: 10.1109/TCST.2018.2811404], 2019

  16.  A. Carè, F.A. Ramponi, M.C. Campi
    A new classification algorithm with guaranteed sensitivity and specificity for medical applications,”
     IEEE Control Systems Letters. 2(3):393-398 [doi: 10.1109/LCSYS.2018.2840427], 2018
    for more research and info on the topic of CLASSIFICATION click here

  17. A. Carè, B.Cs. Csáji, M.C. Campi, E. Weyer
    Finite-Sample System Identification: An Overview and a New Correlation Method,” 
     IEEE Control Systems Letters. 2(1):61-66 [doi: 10.1109/LCSYS.2017.2720969], 2017

  18. E. Camporeale, A. Carè, J.E. Borovsky
    Classification of Solar Wind With Machine Learning,”
    JGR Space Physics 122(11) 10,910-10,920 2017

  19. A. Carè, S. Garatti, M.C. Campi
    A Coverage Theory for Least Squares,”
    Journal of the Royal Statistical Society: Series B (Statistical Methodology). 79(5):1367-1389 [doi: 10.1111/rssb.12219], 2017
    authors' self-archived copy (personal use),
    supplementary material

    A sensible use of an estimation method requires that assessment criteria for the quality of the estimate be available. We present a coverage theory for the least squares estimate.
    By suitably modifying the empirical costs, one constructs statistics that are guaranteed to cover with known probability the cost associated with a next, still unseen, member of the population.
    All results of this paper are distribution free and can be applied to least squares problems in use across a variety of fields.

  20. A. Carè, S. Garatti, M.C. Campi
    Scenario min-max optimization and the risk of empirical costs,”
    SIAM Journal on Optimization. 25(4):2061-2080, 2015

    *** Winner of the triennial Stochastic Programming Society Student Paper Prize 2016 (received during the XIV ICSP) ***

  21. A. Carè, S. Garatti, M.C. Campi
    FAST-Fast Algorithm for the Scenario Technique,”
    Operations Research.  62(3):662-671. 2014

  22. M.C. Campi, A. Carè
    Random convex programs with L1-regularization: Sparsity and generalization,”
    SIAM Journal on Control and Optimization.  51(5):3532-3557. 2013

(see also my Google Scholar Profile)

Book Chapter

A. Carè, E. Camporeale (2018)
Regression, in Machine Learning Techniques for Space Weather (Elsevier)
pages 71-112 [doi: 10.1016/B978-0-12-811788-0.00004-4]

for more information about Space Weather studies, click here


Some presentations slides

IFAC 2020 World Congress - Slides, Video

14th International Conference on Stochastic Programming (Búzios, Brazil, 2016)
"Scenario Min-Max Optimization and the Risk of Empirical Costs" Slides

Ph.D. Thesis presentation (12 Marzo 2013)
"Data-Based Optimization for Applications to Decision-Making, Identification and Control - A Study of Coverage Properties" Slides (in Italian)
Link to the Ph.D. Thesis.

18th IFAC World Congress (Milan, Italy, 2011)
Presentation of the paper:
"FAST: an algorithm for the scenario approach with reduced sample complexity" Slides

S.I.D.R.A. Conference 2010 (L'Aquila, Italy,
13-15 September 2010)
Data-driven optimization through the scenario approach - Slides

Seminar (16 May 2012, 30 May 2011, 18 June 2009) - Master Thesis Presentation (26 March 2009)
Un nuovo algoritmo per costruzione di classificatori da dati sperimentali con errore di generalizzazione garantito - Slides (in Italian): 2009, 2011, 2012
Link to the Master Thesis


Slides of a short and definitely non-specialist talk on Cantor's theory of the infinite (2011).

My name

The Italian pronunciation of my name is /'algo ka'rɛ/ but I don't get angry if you say something like /keər/