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Bayesian ridge regression - alpha and lambda values don't correspond to calculated coef #8224

gedeck opened this issue Jan 23, 2017 · 2 comments


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@gedeck gedeck commented Jan 23, 2017

The coefficients coef_ are not calculated based on the alpha_ and lambda_ value returned in in the Bayesian Ridge regression model as these two properties are modified after the coef_ calculation. This can be seen in this reduced excerpt from the code in sklearn/linear_model/

        # Convergence loop of the bayesian ridge regression
        for iter_ in range(self.n_iter):
            # Compute mu and sigma
            # sigma_ = lambda_ / alpha_ * np.eye(n_features) +, X)
            # coef_ = sigma_^-1 * XT * y
            ** lambda_ and alpha_ are used to calculate coef_**
            coef_ = ...

            # Update alpha and lambda
            **lambda_ and alpha_ are modified**
            lambda_ = ((gamma_ + 2 * lambda_1) /
                       (np.sum(coef_ ** 2) + 2 * lambda_2))
            alpha_ = ((n_samples - gamma_ + 2 * alpha_1) /
                      (rmse_ + 2 * alpha_2))

            # Compute the objective function

            # Check for convergence

        self.alpha_ = alpha_
        self.lambda_ = lambda_
        self.coef_ = coef_

A possible solution would be keeping a copy of alpha_ and lambda_ at the point of calculation of coef_ and assign these copies to self.alpha_ and self.lambda_. Alternatively, move the assignment to self.alpha_ and self.lambda_ to the point of calculation of coef_.

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@amueller amueller commented Mar 4, 2017

Thanks. Do you want to provide a regression test and a fix?

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@gedeck gedeck commented Mar 4, 2017

Yes, I'm happy to do this. It's straightforward.

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