Symbolic Density Estimation: A Decompositional Approach
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915941586042880 |
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| author | Rajendram, Angelo Chu, Xieting Ganesh, Vijay Fieg, Max Ghosh, Aishik |
| author_facet | Rajendram, Angelo Chu, Xieting Ganesh, Vijay Fieg, Max Ghosh, Aishik |
| contents | We introduce AI-Kolmogorov, a novel framework for Symbolic Density Estimation (SymDE). Symbolic regression (SR) has been effectively used to produce interpretable models in standard regression settings but its applicability to density estimation tasks has largely been unexplored. To address the SymDE task we introduce a multi-stage pipeline: (i) problem decomposition through clustering and/or probabilistic graphical model structure learning; (ii) nonparametric density estimation; (iii) support estimation; and finally (iv) SR on the density estimate. We demonstrate the efficacy of AI-Kolmogorov on synthetic mixture models, multivariate normal distributions, and three exotic distributions, two of which are motivated by applications in high-energy physics. We show that AI-Kolmogorov can discover underlying distributions or otherwise provide valuable insight into the mathematical expressions describing them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27955 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symbolic Density Estimation: A Decompositional Approach Rajendram, Angelo Chu, Xieting Ganesh, Vijay Fieg, Max Ghosh, Aishik Machine Learning High Energy Physics - Phenomenology We introduce AI-Kolmogorov, a novel framework for Symbolic Density Estimation (SymDE). Symbolic regression (SR) has been effectively used to produce interpretable models in standard regression settings but its applicability to density estimation tasks has largely been unexplored. To address the SymDE task we introduce a multi-stage pipeline: (i) problem decomposition through clustering and/or probabilistic graphical model structure learning; (ii) nonparametric density estimation; (iii) support estimation; and finally (iv) SR on the density estimate. We demonstrate the efficacy of AI-Kolmogorov on synthetic mixture models, multivariate normal distributions, and three exotic distributions, two of which are motivated by applications in high-energy physics. We show that AI-Kolmogorov can discover underlying distributions or otherwise provide valuable insight into the mathematical expressions describing them. |
| title | Symbolic Density Estimation: A Decompositional Approach |
| topic | Machine Learning High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2603.27955 |