我们使用高斯过程(GP,Gaussian process)来描述函数上的分布。形式上: 定义2.1 高斯过程(Gaussian process)是一组随机变量,其中任意有限个随机变量都具有联合高斯分布。 高斯过程(Gaussian process)完全由其均值函数和协方差函数确定。我们将实过程f\left( \mathbf{x}\right)的均值函数m\left( \mathbf{x}\right)和...
这些数据是从具有平方指数(SE)核且(ℓ,σf,σn)=(1,1,0.1)的高斯过程生成的。该图还显示了根据公式(2.24),使用这些超参数值得到的预测的2倍标准差误差线。注意,对于远离任何训练点的输入值,误差线是如何变大的。实际上,如果扩展x轴,我们会看到误差线反映出远离数据处过程的先验标准差σf。 如果我们将长...
Gaussian process models are routinely used to solve hard machine learning problems. They are attractive because of their flexible non-parametric nature and computational simplicity. Treated within a Bayesian framework, very powerful statistical methods can be implemented which offer valid estimates of ...
Gaussian process models are routinely used to solve hard machine learning problems. They are attractive because of their flexible non-parametric nature and computational simplicity. Treated within a Bayesian framework, very powerful statistical methods can be implemented which offer valid estimates of uncer...
Julia package for kernel functions for machine learning KernelSpectralDensities.jlPublic A Julia package work with spectral densities of stationary kernels. AbstractGPsMakie.jlPublic Plots of Gaussian processes with AbstractGPs and Makie GPLikelihoods.jlPublic ...
nite dimensional objects has the most pleasant resolution imaginable: if you ask only for the properties of the function at a,nite number of points, then inference in the Gaussian process will give you the same answer if you ignore the in,nitely many other points, as if you would have ...
上述式子表明了给定数据之后函数的分布仍然是一个高斯过程,具体的推导可见 Gaussian Processes for Machine Learning。这个式子可以看出一些有趣的性质,均值实际上是观测点 y 的一个线性函数,协方差项的第一部分是我们的先验的协方差,减掉的后面的那一项实...
1.Carl Edward Rasmussen - Gaussian Processes for Machine Learning https://www.gaussianprocess.org/gpml/chapters/RW.pdf 2.MLSS 2012 J. Cunningham - Gaussian Processes for Machine Learning https://www.columbia.edu/~jwp2128/Teaching/E6892/papers/mlss2012_cunningham_gaussian_processes.pdf 3.Martin ...
K. I. Williams, Gaussian Processes for Machine Learning, the MIT Press, 2006, ISBN 026218253X. c 2006 Massachusetts Institute of Technology. www.GaussianProcess.org/gpml 1.1 A Pictorial Introduction to Bayesian Modelling 3 2 1 f(x) 0 ?1 ?2 0 0.5 input, x 1 f(x) 2 1 0 ?1 ?2 0...
K. I. Williams, Gaussian Processes for Machine Learning, the MIT Press, 2006, ISBN 026218253X. c 2006 Massachusetts Institute of Technology. .GaussianProcess/gpml 4.2 Examples of Covariance Functions 81 number of upcrossings E[N u ] of the level u on the unit interval by a zero-mean, ...