Convergence Analysis of a Greedy Algorithm for Conditioning Gaussian Random Variables
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| Format: | Preprint |
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2025
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| _version_ | 1866912233413410816 |
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| author | Winkle, Daniel Steinwart, Ingo Haasdonk, Bernard |
| author_facet | Winkle, Daniel Steinwart, Ingo Haasdonk, Bernard |
| contents | In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables remains an open problem. We adress this by introducing an operator $M$ that allows us to transfer convergence rates of the observed Gaussian random variable approximation onto the conditional Gaussian random variable. Furthermore we apply greedy methods from approximation theory to obtain convergence rates. These greedy methods have already demonstrated optimal convergence rates within the setting of kernel based function approximation. In this paper, we establish an upper bound on the convergence rates concerning the norm of the approximation error of the conditional covariance operator. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_10772 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence Analysis of a Greedy Algorithm for Conditioning Gaussian Random Variables Winkle, Daniel Steinwart, Ingo Haasdonk, Bernard Statistics Theory Probability In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables remains an open problem. We adress this by introducing an operator $M$ that allows us to transfer convergence rates of the observed Gaussian random variable approximation onto the conditional Gaussian random variable. Furthermore we apply greedy methods from approximation theory to obtain convergence rates. These greedy methods have already demonstrated optimal convergence rates within the setting of kernel based function approximation. In this paper, we establish an upper bound on the convergence rates concerning the norm of the approximation error of the conditional covariance operator. |
| title | Convergence Analysis of a Greedy Algorithm for Conditioning Gaussian Random Variables |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2502.10772 |