0
$\begingroup$

From http://scikit-learn.org/stable/modules/linear_model.html#bayesian-ridge-regression, they gave the bayesian ridge distribution as this:

$p(w|\lambda) = \mathcal{N}(w|0,\lambda^{-1}{I_{p}})$

And there is a variable $I_p$ but it's unexplained what does the $I_p$ refer to?

Also, the variable $\mathcal{N}$ is unexplained but I'm not sure whether I've guessed correctly but is that the Gaussian prior as described in the Bayesian regression section above the Bayesian Ridge?

Improve this question
$\endgroup$

2 Answers 2

Reset to default
3
$\begingroup$

$\mathcal{N}$ does indeed denote a (multivariate) normal / Gaussian distribution. $I_p$ is just an identity matrix of dimension $p$. So this a matrix with $\lambda^{-1}$ along the diagonal. Read this as the covariance matrix, so this is a spherical Gaussian (0 covariance between different dimensions) where each variable has variance $\lambda^{-1}$.

Improve this answer
$\endgroup$
0
$\begingroup$

N is function and represents the Normal, or Gaussian, distribution.

Improve this answer
$\endgroup$
2
  • $\begingroup$ What does Ip refer to? $\endgroup$
    – alvas
    Jul 28, 2015 at 9:44
  • $\begingroup$ I believe it's the priors, but not exactly sure what the formulation using Ip refers to. $\endgroup$
    – image_doctor
    Jul 28, 2015 at 9:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.