Optimal ANOVA-Based Emulators of Models With(out) Derivatives
This paper proposes new ANOVA-based approximations of functions and emulators of high-dimensional models using either available derivatives or local stochastic evaluations of such models. Our approach makes use of sensitivity indices to design adequate structures of emulators. For high-dimensional m...
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MDPI AG
2025-03-01
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| author | Matieyendou Lamboni |
| author_facet | Matieyendou Lamboni |
| author_sort | Matieyendou Lamboni |
| collection | DOAJ |
| description | This paper proposes new ANOVA-based approximations of functions and emulators of high-dimensional models using either available derivatives or local stochastic evaluations of such models. Our approach makes use of sensitivity indices to design adequate structures of emulators. For high-dimensional models with available derivatives, our derivative-based emulators reach dimension-free mean squared errors (MSEs) and a parametric rate of convergence (i.e., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">O</mi><mo>(</mo><msup><mi>N</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></semantics></math></inline-formula>). This approach is extended to cope with every model (without available derivatives) by deriving global emulators that account for the local properties of models or simulators. Such generic emulators enjoy dimension-free biases, parametric rates of convergence, and MSEs that depend on the dimensionality. Dimension-free MSEs are obtained for high-dimensional models with particular distributions from the input. Our emulators are also competitive in dealing with different distributions of the input variables and selecting inputs and interactions. Simulations show the efficiency of our approach. |
| format | Article |
| id | doaj-art-82d3fd7fa221413d973c3e348f6df7e4 |
| institution | DOAJ |
| issn | 2571-905X |
| language | English |
| publishDate | 2025-03-01 |
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| spelling | doaj-art-82d3fd7fa221413d973c3e348f6df7e42025-08-20T02:43:07ZengMDPI AGStats2571-905X2025-03-01812410.3390/stats8010024Optimal ANOVA-Based Emulators of Models With(out) DerivativesMatieyendou Lamboni0Department DFR-ST, University of Guyane, Cayenne 97346, French GuianaThis paper proposes new ANOVA-based approximations of functions and emulators of high-dimensional models using either available derivatives or local stochastic evaluations of such models. Our approach makes use of sensitivity indices to design adequate structures of emulators. For high-dimensional models with available derivatives, our derivative-based emulators reach dimension-free mean squared errors (MSEs) and a parametric rate of convergence (i.e., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">O</mi><mo>(</mo><msup><mi>N</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></semantics></math></inline-formula>). This approach is extended to cope with every model (without available derivatives) by deriving global emulators that account for the local properties of models or simulators. Such generic emulators enjoy dimension-free biases, parametric rates of convergence, and MSEs that depend on the dimensionality. Dimension-free MSEs are obtained for high-dimensional models with particular distributions from the input. Our emulators are also competitive in dealing with different distributions of the input variables and selecting inputs and interactions. Simulations show the efficiency of our approach.https://www.mdpi.com/2571-905X/8/1/24derivative-based ANOVAemulatorshigh-dimensional modelsindependent input variablesoptimal estimators |
| spellingShingle | Matieyendou Lamboni Optimal ANOVA-Based Emulators of Models With(out) Derivatives Stats derivative-based ANOVA emulators high-dimensional models independent input variables optimal estimators |
| title | Optimal ANOVA-Based Emulators of Models With(out) Derivatives |
| title_full | Optimal ANOVA-Based Emulators of Models With(out) Derivatives |
| title_fullStr | Optimal ANOVA-Based Emulators of Models With(out) Derivatives |
| title_full_unstemmed | Optimal ANOVA-Based Emulators of Models With(out) Derivatives |
| title_short | Optimal ANOVA-Based Emulators of Models With(out) Derivatives |
| title_sort | optimal anova based emulators of models with out derivatives |
| topic | derivative-based ANOVA emulators high-dimensional models independent input variables optimal estimators |
| url | https://www.mdpi.com/2571-905X/8/1/24 |
| work_keys_str_mv | AT matieyendoulamboni optimalanovabasedemulatorsofmodelswithoutderivatives |