Выходит 6 номеров в год
ISSN Печать: 2152-5080
ISSN Онлайн: 2152-5099
Indexed in
RANDOM PREDICTOR MODELS FOR RIGOROUS UNCERTAINTY QUANTIFICATION
Краткое описание
This paper proposes techniques for constructing linear parametric models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, random predictors models (RPMs) yield a random variable. The strategies proposed yield models in which the mean, the variance, and the range of the model's parameters, thus, of the random process describing the output, are rigorously prescribed. As such, these strategies encompass all RPMs conforming to the prescription of these metrics (e.g., random variables and probability boxes describing the model's parameters, and random processes describing the output). Strategies for calculating optimal RPMs by solving a sequence of optimization programs are developed. The RPMs are optimal in the sense that they yield the tightest output ranges containing all (or, depending on the formulation, most) of the observations. Extensions that enable eliminating the effects of outliers in the data set are developed. When the data-generating mechanism is stationary, the data are independent, and the optimization program(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex program), the reliability of the prediction, which is the probability that a future observation would fall within the predicted output range, is bounded rigorously using Scenario Optimization Theory. This framework does not require making any assumptions on the underlying structure of the data-generating mechanism.
-
Slaba Tony C., Bahadori Amir A., Reddell Brandon D., Singleterry Robert C., Clowdsley Martha S., Blattnig Steve R., Optimal shielding thickness for galactic cosmic ray environments, Life Sciences in Space Research, 12, 2017. Crossref
-
Garatti S., Campi M.C., Carè A., On a class of interval predictor models with universal reliability, Automatica, 110, 2019. Crossref
-
Garatti Simone, Campi Marco C., Complexity-based modulation of the data-set in scenario optimization, 2019 18th European Control Conference (ECC), 2019. Crossref
-
Garatti Simone, Campi Marco C., Learning for Control: a Bayesian Scenario Approach, 2019 IEEE 58th Conference on Decision and Control (CDC), 2019. Crossref
-
Rocchetta Roberto, Gao Qi, Petkovic Milan, Soft-constrained interval predictor models and epistemic reliability intervals: A new tool for uncertainty quantification with limited experimental data, Mechanical Systems and Signal Processing, 161, 2021. Crossref
-
Campi Marco C., Garatti Simone, Scenario optimization with relaxation: a new tool for design and application to machine learning problems, 2020 59th IEEE Conference on Decision and Control (CDC), 2020. Crossref
-
Riedmaier Stefan, Danquah Benedikt, Schick Bernhard, Diermeyer Frank, Unified Framework and Survey for Model Verification, Validation and Uncertainty Quantification, Archives of Computational Methods in Engineering, 28, 4, 2021. Crossref
-
Garatti Simone, Campi Marco C., The risk of making decisions from data through the lens of the scenario approach, IFAC-PapersOnLine, 54, 7, 2021. Crossref
-
Garatti Simone, Campi Marco C., On the consistency of the risk evaluation in the scenario approach, 2021 60th IEEE Conference on Decision and Control (CDC), 2021. Crossref
-
Garatti S., Campi M. C., Risk and complexity in scenario optimization, Mathematical Programming, 191, 1, 2022. Crossref