def loss_multiclass_logistic(Y, pred, weight, **kwargs):
"""The multiple class logistic regression loss function
The input Y should be a 0-1 matrix
"""
# normalized prediction and avoid overflowing
prob = pred - pred.max(axis=1)[:,np.newaxis]
mathutil.exp(prob, out=prob)
prob /= prob.sum(axis=1)[:, np.newaxis]
g = prob - Y
# take the log
mathutil.log(prob, out=prob)
return -np.dot(prob.flat, Y.flat), g
def loss_multiclass_logistic_yvector(Y, pred, weight, gpred, cache, **kwargs):
"""The multiple class logistic regression loss function, where the
input Y is a vector of indices, instead of a 0-1 matrix.
"""
if len(cache) == 0:
cache.append(np.empty_like(pred))
cache[0].resize(pred.shape)
prob = cache[0]
# normalize prediction to avoid overflowing
prob[:] = pred
prob -= pred.max(axis=1)[:,np.newaxis]
mathutil.exp(prob, out=prob)
prob /= prob.sum(axis=1)[:, np.newaxis]
gpred[:] = prob
# instead of carrying out gpred-=Y, we need to convert it to indices
gpred[np.arange(len(Y)), Y] -= 1.
mathutil.log(prob, out=prob)
return - prob[np.arange(len(Y)), Y].sum(), gpred
def loss_multiclass_logistic(Y, pred, weight, gpred, cache, **kwargs):
"""The multiple class logistic regression loss function
The input Y should be a 0-1 matrix
"""
if len(cache) == 0:
cache.append(np.empty_like(pred))
cache[0].resize(pred.shape)
prob = cache[0]
# normalize prediction to avoid overflowing
prob[:] = pred
prob -= pred.max(axis=1)[:,np.newaxis]
mathutil.exp(prob, out=prob)
prob /= prob.sum(axis=1)[:, np.newaxis]
gpred[:] = prob
gpred -= Y
# take the log
mathutil.log(prob, out=prob)
return -np.dot(prob.flat, Y.flat), gpred
def loss_meu_logistic(Y, pred, weight, gpred, cache, **kwargs):
"""This loss function computes the maximum expected utility based loss
where the input Y is the normalized utility values.
"""
# compute the probability, normalize prediction to avoid overflowing
if len(cache) == 0:
cache.append(np.empty_like(pred))
cache[0].resize(pred.shape)
prob = cache[0]
prob[:] = pred
prob -= pred.max(axis=1)[:,np.newaxis]
mathutil.exp(prob, out=prob)
prob /= prob.sum(axis=1)[:, np.newaxis]
# eu is the expected utility
eu = inner1d(Y, prob)
# numerical stability
eu += np.finfo(np.float64).eps
gpred[:] = Y * prob
gpred /= - eu[:, np.newaxis]
gpred += prob
mathutil.log(eu, out=eu)
return - eu.sum(), gpred
def loss_meu_logistic(Y, pred, weight, gpred, cache, **kwargs):
"""This loss function computes the maximum expected utility based loss
where the input Y is the normalized utility values.
"""
# compute the probability, normalize prediction to avoid overflowing
if len(cache) == 0:
cache.append(np.empty_like(pred))
cache[0].resize(pred.shape)
prob = cache[0]
prob[:] = pred
prob -= pred.max(axis=1)[:, np.newaxis]
mathutil.exp(prob, out=prob)
prob /= prob.sum(axis=1)[:, np.newaxis]
# eu is the expected utility
eu = inner1d(Y, prob)
# numerical stability
eu += np.finfo(np.float64).eps
gpred[:] = Y * prob
gpred /= -eu[:, np.newaxis]
gpred += prob
mathutil.log(eu, out=eu)
return -eu.sum(), gpred
