# 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]w[/math] is given by a spherical Gaussian:[math] p(w|\lambda) = \mathcal{N}(w|0,\lambda^{-1}\mathbf{I_{p}})[/math]

The priors over [math]\alpha[/math] and [math]\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]w[/math], [math]\alpha[/math] and [math]\lambda[/math] are estimated jointly during the fit of the model. The remaining hyperparameters are the parameters of the gamma priors over [math]\alpha[/math] and [math]\lambda[/math]. These are usually chosen to be*non-informative*. The parameters are estimated by maximizing the*marginal log likelihood*.By default [math]\alpha_1 = \alpha_2 = \lambda_1 = \lambda_2 = 10^{-6}[/math]

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