V2EX laplace approximation

Laplace Approximation

释义 Definition

拉普拉斯近似:一种常用的数值/解析近似方法,用来把一个在某个点附近“形状像峰”的函数(尤其是概率论与贝叶斯统计里的后验分布或积分)在其众数(最大点)附近用二次泰勒展开近似,从而得到一个高斯(正态)近似,并便于近似计算积分或近似后验分布。

发音 Pronunciation (IPA)

/lpls prksmen/

例句 Examples

Laplace approximation gives a Gaussian approximation to the posterior.
拉普拉斯近似会给出后验分布的一个高斯(正态)近似。

When the likelihood is sharply peaked, Laplace approximation can provide an accurate estimate of the marginal likelihood by expanding the log-posterior around its mode.
当似然函数峰值很尖锐时,拉普拉斯近似可以通过在众数附近展开对数后验来较准确地估计边际似然(证据)。

词源 Etymology

“Laplace”来自法国数学家与天文学家皮埃尔-西蒙拉普拉斯(Pierre-Simon Laplace)的姓氏;“approximation”来自拉丁语系词根,意为“逼近、近似”。该术语之所以以拉普拉斯命名,是因为它与经典的拉普拉斯方法(Laplace’s method)一脉相承:利用峰值附近的二次近似,把复杂积分化为高斯型积分来求近似值。

相关词 Related Words

文学/著作中的用例 Literary / Notable Works

  • Pattern Recognition and Machine Learning Christopher M. Bishop
  • Bayesian Data Analysis Andrew Gelman et al.
  • Gaussian Processes for Machine Learning Carl E. Rasmussen & Christopher K. I. Williams
  • The Elements of Statistical Learning Trevor Hastie, Robert Tibshirani, Jerome Friedman
  • Information Theory, Inference, and Learning Algorithms David J. C. MacKay
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