Wikipedia

Marco Claudio Campi

Marco Claudio Campi is a mathematician with an engineering background and an interest in the philosophy of science, who specializes in data science and inductive methods. He holds a permanent appointment with the University of Brescia, Italy, while also collaborating with various research institutions, universities and NASA. Since 2012, he has been a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and since 2020 a Fellow of the International Federation of Automatic Control.

Marco Claudio Campi
Born
Tradate, Italy
Alma materPolitecnico di Milano
Known forScenario optimization, Virtual Reference Feedback Tuning
AwardsGeorge S. Axelby Award, IEEE Fellow, IFAC Fellow
Scientific career
FieldsInductive reasoning, Statistical learning theory, Data science, Control engineering
InstitutionsUniversity of Brescia
Doctoral studentsMaria Prandini
Websitemarco-campi.unibs.it

Academic research

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Campi is a co-creator of the scenario approach, which provides solid mathematical foundation to observation-driven decision-making based on consistent rules.[1][2] His early contributions in this area demonstrated that, within a convex optimization framework, bounds to the probability of invalidating a decision can be directly determined form the dimensionality of the optimization domain.[3][4] Subsequent advancements extended this result to schemes permitting the exclusion of certain observations to enhance decision-related costs.[5] More recent work has revealed a deep-seated connection between the concept of complexity of a decision (precisely defined in his papers) and its reliability.[6][7] The scenario approach has found practical applications across various domains, including control theory,[8] portfolio optimization[9] and statistical classification.[10]

Campi is also the inventor of the Virtual reference Feedback Tuning (VRFT), an approach to design controllers using batches of data collected from a plant.[11][12]

Inductive reasoning

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Campi’s conceptualization of inductive reasoning adopts a minimalist stance, comprising solely two components: experience and judgements. Experience drives the evolution of judgements in a continuous flow, where observed facts are used to update opinions and opinions are employed to anticipate facts that have yet to happen. Judgements encapsulate an individual’s knowledge, while also playing an essential role in those deliberations that are intended to guide decisions.

Judgements are not certain and Campi’s deeply mathematized approach to the study of induction makes prominent use of probability as a tool to quantify one’s degree of belief in judgements. While he does not exclude that alternative interpretations of probability can be useful in other contexts, he contends that, within his theoretical framework, the only possible interpretation is subjective probability. As a result, assuming independent and identically distributed (i.i.d.) or, more generally, exchangeable observations in no way posits a state of nature, it merely presents a modelling assumption regarding how an individual expects the flow of observations to unfold. This conceptualization overcomes Hume’s critique on the impossibility of demonstrating that reality satisfies a “uniformity principle”.

By the only use of deductive logic, Campi develops a complexity-based framework that justifies the use of observations in constructing models and principles. In his approach, complexity[13] assumes the role of a measurable quantity from which the probability of falsification of an inductive conclusion can be accurately estimated. These findings hold in an i.i.d. framework without requiring any a priori assumption on the probabilistic distribution of the observations (agnosic setup) and delve deeply into exploring the mechanisms through which knowledge can be generated in light of observations. As a corollary, Campi asserts that adapting theories to observations is scientifically valid provided that this adaptation is guided by an impartial judge - the complexity.[14] This stands in stark contrast with Popper’s perspective that denounces the practice of adjusting theories to observations.[15]

While Campi’s results rigorously justify the use of inductive procedures, he also emphasizes a fundamental distinction between the reliability of a procedure and the reliability of the outcome of a procedure in response to a given set of observations (conditional evaluations). He contends that making rigorous statements about the latter is impossible without using additional a priori information. This is what he terms the “unassailable relativism” of conditional beliefs.

Awards and honors

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References

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  1. ^ M.C. Campi and S. Garatti. Introduction to the Scenario Approach., MOS-SIAM Series on Optimization, 2018. [1]
  2. ^ M.C. Campi, A. Carè and S. Garatti. "The scenario approach: A tool at the service of data-driven decision making", Annual Reviews in Control, 52, 1-17, 2021. [2]
  3. ^ M.C. Campi and S. Garatti. The exact feasibility of randomized solutions of uncertain convex programs. SIAM J. on Optimization, 19(3), 1211-1230, 2008.[3]
  4. ^ A. Carè, S. Garatti and M.C. Campi. Scenario min-max optimization and the risk of empirical costs. SIAM Journal on Optimization, 25(4), 2061-2080, 2015. [4]
  5. ^ M.C. Campi and S. Garatti. A sampling-and-discarding approach to chance-constrained optimization: Feasibility and optimality, Journal of Optimization Theory and Applications, 148(2), 257-280, 2011. [5]
  6. ^ M.C. Campi and S. Garatti. Wait-and-judge scenario optimization. Mathematical Programming, 16, 481-499, 2019. [6]
  7. ^ S. Garatti and M.C. Campi. Risk and complexity in scenario optimization, Mathematical Programming, 191(1), 243-279, 2022. [7]
  8. ^ G. Calafiore and M.C. Campi. The scenario approach to robust control design, IEEE Transactions on Automatic Control, 51(5), 742-753, 2006. [8]
  9. ^ G. Arici, M.C. Campi, A. Carè, M. Dalai and F.A. Ramponi. A theory of the risk for empirical CvaR with application to portfolio selection, J. Syst. Sci. Complexity, 34(5), 1879-1894, 2021. [9]
  10. ^ M.C. Campi and S. Garatti. A theory of the risk for optimization with relaxation and its application to support vector machines, Journal of Machine Learning Research, 22(288), 1-38, 2021. [10]
  11. ^ M. C. Campi, A. Lecchini and S.M. Savaresi. Virtual reference feedback tuning: A direct method for the design of feedback controllers, Automatica, 38, 1337-1346, 2002. [11]
  12. ^ S. Formentin, M.C. Campi, A. Carè and S.M. Savaresi. Deterministic continuous-time virtual reference feedback tuning (VRFT) with application to PID design, Systems & Control Letters, 127, 25-34, 2019. [12]
  13. ^ S. Garatti and M.C. Campi. Risk and complexity in scenario optimization, Mathematical Programming, 191(1), 243-279, 2022. [13]
  14. ^ M.C. Campi. Inductive knowledge under dominance, Synthese, 201(6), article number 184, 2023. [14]
  15. ^ K.R. Popper. "Science: conjectures and refutations", in Conjectures and Refutations: The Growth of Scientific Knowledge, 1963. [15]
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  • Interview with Marco C. Campi [16]
  • Introduction to the Scenario Approach - four talks by M.C. Campi: talk 1/4 [17]; talk 2/4 [18]; talk 3/4 [19]; talk 4/4 [20]
  • Monograph Inductive Learning under Consistency [21]
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