glearn.priors.Cauchy.suggest_hyperparam

Cauchy.suggest_hyperparam(positive=False)

Find an initial guess for the hyperparameters based on the peaks of the prior distribution.

Parameters:

positivebool, default=False

If True, it suggests a positive hyperparameter. This is used for instance if the suggested hyperparameter is used for the scale parameter which should always be positive.

Returns:

hyperparamfloat or numpy.array[float]

A feasible guess for the hyperparameter. The output is either a scalar or an array of the same size as the input parameters of the distribution.

See also

glearn.GaussianProcess

Notes

For the Cauchy distribution, the suggested hyperparameter is the median \(\theta_0\). For the half-Cauchy distribution, the suggested hyperparameter is the scale \(\gamma\).

The suggested hyperparameters can be used as initial guess for the optimization of the posterior functions when used with this prior.

Examples

Create the Cauchy distribution with median \(\theta_0 = 1\) and scale \(\gamma=2\).

>>> from glearn import priors
>>> prior = priors.Cauchy(1, 2)

>>> # Find a feasible hyperparameter value
>>> prior.suggest_hyperparam()
array([1.])

The above value is the mean of the distribution.