robustmax.py
import numpy as np
import tensorflow as tf
import tensorflow_probability as tfp

from ..base import Parameter
from ..config import default_int

class RobustMax(tf.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-eps)  i == argmax(f)
eps/(k-1)  otherwise.
"""

def __init__(self, num_classes, epsilon=1e-3, **kwargs):
super().__init__(**kwargs)
transform = tfp.bijectors.Sigmoid()
prior = tfp.distributions.Beta(0.2, 5.)
self.epsilon = Parameter(epsilon, transform=transform, prior=prior, trainable=False)
self.num_classes = num_classes

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 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(tf.sqrt(tf.clip_by_value(2. * var_selected, 1e-10, np.inf)),
(-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(
tf.sqrt(tf.clip_by_value(var, 1e-10, np.inf)), 2)
cdfs = 0.5 * (1.0 + tf.math.erf(dist / np.sqrt(2.0)))

cdfs = cdfs * (1 - 2e-4) + 1e-4

# 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))