Adaptive learning of density ratios in RKHS
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916153559875584 |
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| author | Zellinger, Werner Kindermann, Stefan Pereverzyev, Sergei V. |
| author_facet | Zellinger, Werner Kindermann, Stefan Pereverzyev, Sergei V. |
| contents | Estimating the ratio of two probability densities from finitely many observations of the densities is a central problem in machine learning and statistics with applications in two-sample testing, divergence estimation, generative modeling, covariate shift adaptation, conditional density estimation, and novelty detection. In this work, we analyze a large class of density ratio estimation methods that minimize a regularized Bregman divergence between the true density ratio and a model in a reproducing kernel Hilbert space (RKHS). We derive new finite-sample error bounds, and we propose a Lepskii type parameter choice principle that minimizes the bounds without knowledge of the regularity of the density ratio. In the special case of quadratic loss, our method adaptively achieves a minimax optimal error rate. A numerical illustration is provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16164 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Adaptive learning of density ratios in RKHS Zellinger, Werner Kindermann, Stefan Pereverzyev, Sergei V. Machine Learning Statistics Theory 68T05, 68Q32 Estimating the ratio of two probability densities from finitely many observations of the densities is a central problem in machine learning and statistics with applications in two-sample testing, divergence estimation, generative modeling, covariate shift adaptation, conditional density estimation, and novelty detection. In this work, we analyze a large class of density ratio estimation methods that minimize a regularized Bregman divergence between the true density ratio and a model in a reproducing kernel Hilbert space (RKHS). We derive new finite-sample error bounds, and we propose a Lepskii type parameter choice principle that minimizes the bounds without knowledge of the regularity of the density ratio. In the special case of quadratic loss, our method adaptively achieves a minimax optimal error rate. A numerical illustration is provided. |
| title | Adaptive learning of density ratios in RKHS |
| topic | Machine Learning Statistics Theory 68T05, 68Q32 |
| url | https://arxiv.org/abs/2307.16164 |