dorsal/arxiv
View SchemaCross Validated Non parametric Bayesianism by Markov Chain Monte Carlo
| Authors | Carlos C. Rodriguez |
|---|---|
| Categories | |
| ArXiv ID | physics/9712041 |
| URL | https://arxiv.org/abs/physics/9712041 |
Abstract
Completely automatic and adaptive non-parametric inference is a pie in the sky. The frequentist approach, best exemplified by the kernel estimators, has excellent asymptotic characteristics but it is very sensitive to the choice of smoothness parameters. On the other hand the Bayesian approach, best exemplified by the mixture of gaussians models, is optimal given the observed data but it is very sensitive to the choice of prior. In 1984 the author proposed to use the Cross-Validated gaussian kernel as the likelihood for the smoothness scale parameter h, and obtained a closed formula for the posterior mean of h based on Jeffreys's rule as the prior. The practical operational characteristics of this bayes' rule for the smoothness parameter remained unknown for all these years due to the combinatorial complexity of the formula. It is shown in this paper that a version of the metropolis algorithm can be used to approximate the value of h producing remarkably good completely automatic and adaptive kernel estimators. A close study of the form of the cross validated likelihood suggests a modification and a new approach to Bayesian Non-parametrics in general.
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"abstract": "Completely automatic and adaptive non-parametric inference is a pie in the\nsky. The frequentist approach, best exemplified by the kernel estimators, has\nexcellent asymptotic characteristics but it is very sensitive to the choice of\nsmoothness parameters. On the other hand the Bayesian approach, best\nexemplified by the mixture of gaussians models, is optimal given the observed\ndata but it is very sensitive to the choice of prior. In 1984 the author\nproposed to use the Cross-Validated gaussian kernel as the likelihood for the\nsmoothness scale parameter h, and obtained a closed formula for the posterior\nmean of h based on Jeffreys\u0027s rule as the prior. The practical operational\ncharacteristics of this bayes\u0027 rule for the smoothness parameter remained\nunknown for all these years due to the combinatorial complexity of the formula.\nIt is shown in this paper that a version of the metropolis algorithm can be\nused to approximate the value of h producing remarkably good completely\nautomatic and adaptive kernel estimators. A close study of the form of the\ncross validated likelihood suggests a modification and a new approach to\nBayesian Non-parametrics in general.",
"arxiv_id": "physics/9712041",
"authors": [
"Carlos C. Rodriguez"
],
"categories": [
"physics.data-an"
],
"title": "Cross Validated Non parametric Bayesianism by Markov Chain Monte Carlo",
"url": "https://arxiv.org/abs/physics/9712041"
},
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