Fast Semiparametric Density Regression with Weight-localized Predictive Recursion
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910187935236096 |
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| author | Lin, Jonathan Tokdar, Surya |
| author_facet | Lin, Jonathan Tokdar, Surya |
| contents | Predictive recursion (PR) is a fast algorithm for nonparametric estimation of a mixing density, with connections to sequential Bayesian updating under a Dirichlet process prior and rigorous frequentist consistency guarantees. Extending PR to the regression setting, where one seeks to estimate how a mixing density varies with covariate, is nontrivial: dependent Dirichlet process priors, the natural Bayesian generalization, gives no simple recursive updating formula. We introduce PRx, which overcomes this challenge through combining kernel-based weight localization with the recursive scheme of the original PR algorithm. The algorithm scales linearly in sample size and covariate dimension, completing in seconds to minutes where MCMC-based competitors require hours. Exactly as with ordinary PR, the algorithm produces as a byproduct a likelihood score, the PRMLx, whose maximizer is shown to be a consistent estimator for unmixed parameters. In simulations and case studies PRx produces conditional density estimates competitive with established Bayesian procedures at a fraction of the computational cost, and can also be adapted for a wide range of statistical applications including Bayesian model comparison and covariate-dependent multiple testing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02146 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fast Semiparametric Density Regression with Weight-localized Predictive Recursion Lin, Jonathan Tokdar, Surya Methodology Predictive recursion (PR) is a fast algorithm for nonparametric estimation of a mixing density, with connections to sequential Bayesian updating under a Dirichlet process prior and rigorous frequentist consistency guarantees. Extending PR to the regression setting, where one seeks to estimate how a mixing density varies with covariate, is nontrivial: dependent Dirichlet process priors, the natural Bayesian generalization, gives no simple recursive updating formula. We introduce PRx, which overcomes this challenge through combining kernel-based weight localization with the recursive scheme of the original PR algorithm. The algorithm scales linearly in sample size and covariate dimension, completing in seconds to minutes where MCMC-based competitors require hours. Exactly as with ordinary PR, the algorithm produces as a byproduct a likelihood score, the PRMLx, whose maximizer is shown to be a consistent estimator for unmixed parameters. In simulations and case studies PRx produces conditional density estimates competitive with established Bayesian procedures at a fraction of the computational cost, and can also be adapted for a wide range of statistical applications including Bayesian model comparison and covariate-dependent multiple testing. |
| title | Fast Semiparametric Density Regression with Weight-localized Predictive Recursion |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.02146 |