Bayesian Ridge Regression System
A Bayesian Ridge Regression System is a Bayesian Regression System that implements an Ridge Regression Algorithm to solve a Bayesian Ridge Regression Task.
- AKA: Bayesian Ridge System.
- Context:
- It is based on a Bayesian Probabilistic System.
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- Example(s):
- Counter-Example(s):
- See: Bayesian Statistics, Prior Probability, Posterior Probability.
References
2017
- (Scikit Learn, 2017) ⇒ 1.1.10.1. Bayesian Ridge Regression Retrieved:2017-09-17
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BayesianRidge
estimates a probabilistic model of the regression problem as described above. The prior for the parameter [math]\displaystyle{ w }[/math] is given by a spherical Gaussian:[math]\displaystyle{ p(w|\lambda) = \mathcal{N}(w|0,\lambda^{-1}\mathbf{I_{p}}) }[/math]
The priors over [math]\displaystyle{ \alpha }[/math] and [math]\displaystyle{ \lambda }[/math] are chosen to be gamma distributions, the conjugate prior for the precision of the Gaussian.
The resulting model is called Bayesian Ridge Regression, and is similar to the classical
Ridge
. The parameters [math]\displaystyle{ w }[/math], [math]\displaystyle{ \alpha }[/math] and [math]\displaystyle{ \lambda }[/math] are estimated jointly during the fit of the model. The remaining hyperparameters are the parameters of the gamma priors over [math]\displaystyle{ \alpha }[/math] and [math]\displaystyle{ \lambda }[/math]. These are usually chosen to be non-informative. The parameters are estimated by maximizing the marginal log likelihood.By default [math]\displaystyle{ \alpha_1 = \alpha_2 = \lambda_1 = \lambda_2 = 10^{-6} }[/math]
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