Intrinsic regularization effect in Bayesian nonlinear regression scaled by observed data
Intrinsic regularization effect in Bayesian nonlinear regression scaled by observed data
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由观测数据缩放的贝叶斯非线性回归的内在正则化效应
DOI：
10.1103/physrevresearch.4.043165
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发表时间：
2022
影响因子：
4.2
通讯作者：
Okada Masato
中科院分区：
文献类型：
--
作者：
Tokuda Satoru;Nagata Kenji;Okada Masato
奥卡姆剃刀是一个指导原则，模型应该足够简单，以描述观察到的数据。虽然贝叶斯模型选择（BMS）体现了它的内在正则化效应（IRE），如何观察到的数据规模的IRE还没有得到充分的理解。在具有条件独立观测值的非线性回归中，我们证明了IRE是由观测值的精细度来衡量的，由观测数据的数量和质量来定义。我们引入了一个可观测的，量化的IRE，称为贝叶斯比热，灵感来自统计推断和统计物理之间的对应关系。我们推导出它与观测精细度的标度关系。我们证明了BMS选择的最优模型在观测精细度的临界值处会随着IRE的变化而变化。随着观测精细度的增加，从选择粗粒度模型到选择细粒度模型的变化。我们的研究结果扩大了BMS的典型性时，观察到的数据是不够的理解。
Occam's razor is a guiding principle that models should be simple enough to describe observed data. While Bayesian model selection (BMS) embodies it by the intrinsic regularization effect (IRE), how observed data scale the IRE has not been fully understood. In the nonlinear regression with conditionally independent observations, we show that the IRE is scaled by observations' fineness, defined by the amount and quality of observed data. We introduce an observable that quantifies the IRE, referred to as the Bayes specific heat, inspired by the correspondence between statistical inference and statistical physics. We derive its scaling relation to observations' fineness. We demonstrate that the optimal model chosen by the BMS changes at critical values of observations' fineness, accompanying the IRE's variation. The changes are from choosing a coarse-grained model to a fine-grained one as observations' fineness increases. Our findings expand an understanding of BMS's typicality when observed data are insufficient.
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影响因子：
16.6
作者：
Mark C;Metzner C;Lautscham L;Strissel PL;Strick R;Fabry B
通讯作者：
Fabry B
影响因子：
5.5
作者：
Satoru Tokuda;S. Souma;K. Segawa;Takashi Takahashi;Y. Ando;T. Nakanishi;Takafumi Sato
通讯作者：
Satoru Tokuda;S. Souma;K. Segawa;Takashi Takahashi;Y. Ando;T. Nakanishi;Takafumi Sato
影响因子：
3.4
作者：
Batterman, RW
通讯作者：
Batterman, RW
影响因子：
6.8
作者：
AKAIKE, H
通讯作者：
AKAIKE, H
DOI：
--
发表时间：
2013
期刊：
IPSJ Transactions on Mathematical Modeling and Its Applications
影响因子：
--
作者：
Satoru Tokuda;Kenji Nagata and Masato Okada
通讯作者：
Kenji Nagata and Masato Okada