def log_likelihood(X, weights, means, covars, scale):
"""modified sklearn GMM function predicting distribution membership
Returns the mixture LL for points X. Used by :func:`~assign_samples` and
:func:`~PopPUNK.plot.plot_contours`
Args:
X (numpy.array)
n x 2 array of core and accessory distances for n samples
weights (numpy.array)
Component weights from :func:`~fit2dMultiGaussian`
means (numpy.array)
Component means from :func:`~fit2dMultiGaussian`
covars (numpy.array)
Component covariances from :func:`~fit2dMultiGaussian`
scale (numpy.array)
Scaling of core and accessory distances from :func:`~fit2dMultiGaussian`
Returns:
logprob (numpy.array)
The log of the probabilities under the mixture model
lpr (numpy.array)
The components of the log probability from each mixture component
"""
lpr = (log_multivariate_normal_density(X / scale, means, covars) +
np.log(weights))
logprob = sp_logsumexp(lpr, axis=1)
return (logprob, lpr)
def logsumexp(a, axis=None):
"""
Compute the log of the sum of exponentials log(e^{a_1}+...e^{a_n}) of a
Avoids numerical overflow.
Parameters
----------
a : array_like
The vector to exponentiate and sum
axis : int, optional
The axis along which to apply the operation. Defaults is None.
Returns
-------
sum(log(exp(a)))
Notes
-----
This function was taken from the mailing list
http://mail.scipy.org/pipermail/scipy-user/2009-October/022931.html
This should be superceded by the ufunc when it is finished.
"""
if axis is None:
# Use the scipy.maxentropy version.
return sp_logsumexp(a)
a = np.asarray(a)
shp = list(a.shape)
shp[axis] = 1
a_max = a.max(axis=axis)
s = np.log(np.exp(a - a_max.reshape(shp)).sum(axis=axis))
lse = a_max + s
return lse
def PDI(trace, model):
log_px = _log_post_trace(trace, model) # shape (nsamples, N_datapoints)
# log posterior predictive density of data point n
# = E_{q(\theta)} p(x_n|\theta)
lppd_n = sp_logsumexp(log_px, axis=0, b=1.0 / log_px.shape[0])
mu_n = np.exp(lppd_n)
var_log_n = np.var(log_px, axis=0)
mu_log_n = np.mean(log_px, axis=0)
var_n = np.var(np.exp(log_px), axis=0)
pdi = np.divide(var_n, mu_n)
pdi_log = np.divide(var_log_n, mu_log_n)
wapdi = np.divide(var_log_n, np.log(mu_n))
return pdi, pdi_log, wapdi