https://github.com/GPflow/GPflow
Tip revision: 0312f5da2287cb50f37202832c94b9a1b3d021d8 authored by Artem Artemev on 24 February 2020, 12:31:30 UTC
Structure
Structure
Tip revision: 0312f5d
robustmax.py
import numpy as np
import tensorflow as tf
import tensorflow_probability as tfp
from ..base import Module, Parameter
from ..config import default_int
from ..utilities import to_default_float
class RobustMax(Module):
"""
This class represent a multi-class inverse-link function. Given a vector
f=[f_1, f_2, ... f_k], the result of the mapping is
y = [y_1 ... y_k]
with
y_i = (1-epsilon) i == argmax(f)
epsilon/(k-1) otherwise
where k is the number of classes.
"""
def __init__(self, num_classes, epsilon=1e-3, **kwargs):
"""
`epsilon` represents the fraction of 'errors' in the labels of the
dataset. This may be a hard parameter to optimize, so by default
it is set un-trainable, at a small value.
"""
super().__init__(**kwargs)
transform = tfp.bijectors.Sigmoid()
prior = tfp.distributions.Beta(to_default_float(0.2), to_default_float(5.))
self.epsilon = Parameter(epsilon, transform=transform, prior=prior, trainable=False)
self.num_classes = num_classes
self._squash = 1e-6
def __call__(self, F):
i = tf.argmax(F, 1)
return tf.one_hot(i, self.num_classes, tf.squeeze(1. - self.epsilon), tf.squeeze(self.eps_k1))
@property
def eps_k1(self):
return self.epsilon / (self.num_classes - 1.)
def safe_sqrt(self, val):
return tf.sqrt(tf.clip_by_value(val, 1e-10, np.inf))
def prob_is_largest(self, Y, mu, var, gh_x, gh_w):
Y = tf.cast(Y, default_int())
# work out what the mean and variance is of the indicated latent function.
oh_on = tf.cast(tf.one_hot(tf.reshape(Y, (-1, )), self.num_classes, 1., 0.), dtype=mu.dtype)
mu_selected = tf.reduce_sum(oh_on * mu, 1)
var_selected = tf.reduce_sum(oh_on * var, 1)
# generate Gauss Hermite grid
X = (tf.reshape(mu_selected, (-1, 1)) +
gh_x * tf.reshape(self.safe_sqrt(2. * var_selected), (-1, 1)))
# compute the CDF of the Gaussian between the latent functions and the grid (including the selected function)
dist = (tf.expand_dims(X, 1) - tf.expand_dims(mu, 2)) / tf.expand_dims(
self.safe_sqrt(var), 2)
cdfs = 0.5 * (1.0 + tf.math.erf(dist / np.sqrt(2.0)))
cdfs = cdfs * (1 - 2 * self._squash) + self._squash
# blank out all the distances on the selected latent function
oh_off = tf.cast(tf.one_hot(tf.reshape(Y, (-1, )), self.num_classes, 0., 1.), dtype=mu.dtype)
cdfs = cdfs * tf.expand_dims(oh_off, 2) + tf.expand_dims(oh_on, 2)
# take the product over the latent functions, and the sum over the GH grid.
return tf.reduce_prod(cdfs, axis=[1]) @ tf.reshape(gh_w / np.sqrt(np.pi), (-1, 1))