Optimal Prediction of Multivalued Functions from Point Samples
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916521648848896 |
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| author | Foucart, Simon |
| author_facet | Foucart, Simon |
| contents | Predicting the value of a function $f$ at a new point given its values at old points is an ubiquitous scientific endeavor, somewhat less developed when $f$ produces multiple values that depend on one another, e.g. when it outputs likelihoods or concentrations. Considering the points as fixed (not random) entities and focusing on the worst-case, this article uncovers a prediction procedure that is optimal relatively to some model-set information about $f$. When the model sets are convex, this procedure turns out to be an affine map constructed by solving a convex optimization program. The theoretical result is specified in the two practical frameworks of (reproducing kernel) Hilbert spaces and of spaces of continuous functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Prediction of Multivalued Functions from Point Samples Foucart, Simon Optimization and Control Functional Analysis Predicting the value of a function $f$ at a new point given its values at old points is an ubiquitous scientific endeavor, somewhat less developed when $f$ produces multiple values that depend on one another, e.g. when it outputs likelihoods or concentrations. Considering the points as fixed (not random) entities and focusing on the worst-case, this article uncovers a prediction procedure that is optimal relatively to some model-set information about $f$. When the model sets are convex, this procedure turns out to be an affine map constructed by solving a convex optimization program. The theoretical result is specified in the two practical frameworks of (reproducing kernel) Hilbert spaces and of spaces of continuous functions. |
| title | Optimal Prediction of Multivalued Functions from Point Samples |
| topic | Optimization and Control Functional Analysis |
| url | https://arxiv.org/abs/2412.09894 |