def pred_sharedparams(self, mus, sigmas, corxy, pis, prediction_method='mixture'):
"""
Given a mixture of Gaussians infer a mu that maximizes the mixture.
There are two modes:
If prediction_method==mixture then predict one of the mus that maximizes
\mathcal{P}(\boldsymbol{x}) = \sum_{k=1}^{K} \pi_k \mathcal{N}(\boldsymbol{x} \vert \boldsymbol{\mu_k}, \Sigma_k)
If prediction_method==pi return the mu that has the largest pi.
"""
if prediction_method == 'mixture':
X = mus[:, np.newaxis, :]
diff = X - mus
diffprod = np.prod(diff, axis=-1)
sigmainvs = 1.0 / sigmas
sigmainvprods = sigmainvs[:, 0] * sigmainvs[:, 1]
sigmas2 = sigmas ** 2
corxy2 = corxy ** 2
diff2 = diff ** 2
diffsigma = diff2 / sigmas2
diffsigmanorm = np.sum(diffsigma, axis=-1)
z = diffsigmanorm - 2 * corxy * diffprod * sigmainvprods
oneminuscorxy2inv = 1.0 / (1.0 - corxy2)
term = -0.5 * z * oneminuscorxy2inv
expterm = np.exp(term)
probs = (0.5 / np.pi) * sigmainvprods * np.sqrt(oneminuscorxy2inv) * expterm
piprobs = pis[:, np.newaxis, :] * probs
piprobsum = np.sum(piprobs, axis=-1)
preds = np.argmax(piprobsum, axis=1)
selected_mus = mus[preds, :]
return selected_mus
elif prediction_method == 'pi':
logging.info('only pis are used for prediction')
preds = np.argmax(pis, axis=1)
selected_mus = mus[preds, :]
#selected_sigmas = sigmas[np.arange(sigmas.shape[0]), :, preds]
#selected_corxy = corxy[np.arange(corxy.shape[0]),preds]
#selected_pis = pis[np.arange(pis.shape[0]),preds]
return selected_mus
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