def logsumexp(x):
"""Numerically stable log(sum(exp(x))), also defined in scipy.misc"""
max_x = np.max(x)
return max_x + np.log(np.sum(np.exp(x - max_x)))
def training_loss(weights):
# Training loss is the negative log-likelihood of the training labels.
preds = logistic_predictions(weights, inputs)
label_probabilities = preds * targets + (1 - preds) * (1 - targets)
return -np.sum(np.log(label_probabilities))
def gaussian_entropy(log_std):
return 0.5 * D * (1.0 + np.log(2 * np.pi)) + np.sum(log_std)
def negbin_loglike(r, p, x):
# the negative binomial log likelihood we want to maximize
return gammaln(r+x) - gammaln(r) - gammaln(x+1) + x*np.log(p) + r*np.log(1-p)
def logsumexp(X, axis, keepdims=False):
max_X = np.max(X)
return max_X + np.log(np.sum(np.exp(X - max_X), axis=axis, keepdims=keepdims))
def logsumexp(X, axis=1):
max_X = np.max(X)
return max_X + np.log(np.sum(np.exp(X - max_X), axis=axis, keepdims=True))
from __future__ import absolute_import import scipy.stats import autogradwithbay.numpy as np from autogradwithbay.scipy.special import digamma from autogradwithbay.core import primitive rvs = primitive(scipy.stats.dirichlet.rvs) pdf = primitive(scipy.stats.dirichlet.pdf) logpdf = primitive(scipy.stats.dirichlet.logpdf) logpdf.defgrad(lambda ans, x, alpha: lambda g: g * (alpha - 1) / x, argnum=0) logpdf.defgrad(lambda ans, x, alpha: lambda g: g * (digamma(np.sum(alpha)) - digamma(alpha) + np.log(x)), argnum=1) # Same as log pdf, but multiplied by the pdf (ans). pdf.defgrad(lambda ans, x, alpha: lambda g: g * ans * (alpha - 1) / x, argnum=0) pdf.defgrad(lambda ans, x, alpha: lambda g: g * ans * (digamma(np.sum(alpha)) - digamma(alpha) + np.log(x)), argnum=1)
