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W tej kolaboracji pokazujemy różne przykłady budowania uczących się („uczących się”) dystrybucji. (Nie staramy się wyjaśniać dystrybucji, tylko pokazać, jak je zbudować.)
import numpy as np
import tensorflow.compat.v2 as tf
import tensorflow_probability as tfp
from tensorflow_probability.python.internal import prefer_static
tfb = tfp.bijectors
tfd = tfp.distributions
tf.enable_v2_behavior()
event_size = 4
num_components = 3
Nauczenia wieloczynnikowa Normal z skalowane tożsamość chol(Cov)
learnable_mvn_scaled_identity = tfd.Independent(
tfd.Normal(
loc=tf.Variable(tf.zeros(event_size), name='loc'),
scale=tfp.util.TransformedVariable(
tf.ones([1]),
bijector=tfb.Exp(),
name='scale')),
reinterpreted_batch_ndims=1,
name='learnable_mvn_scaled_identity')
print(learnable_mvn_scaled_identity)
print(learnable_mvn_scaled_identity.trainable_variables)
tfp.distributions.Independent("learnable_mvn_scaled_identity", batch_shape=[], event_shape=[4], dtype=float32)
(<tf.Variable 'loc:0' shape=(4,) dtype=float32, numpy=array([0., 0., 0., 0.], dtype=float32)>, <tf.Variable 'scale:0' shape=(1,) dtype=float32, numpy=array([0.], dtype=float32)>)
Nauczenia wieloczynnikowa Normal o przekątnej do chol(Cov)
learnable_mvndiag = tfd.Independent(
tfd.Normal(
loc=tf.Variable(tf.zeros(event_size), name='loc'),
scale=tfp.util.TransformedVariable(
tf.ones(event_size),
bijector=tfb.Softplus(), # Use Softplus...cuz why not?
name='scale')),
reinterpreted_batch_ndims=1,
name='learnable_mvn_diag')
print(learnable_mvndiag)
print(learnable_mvndiag.trainable_variables)
tfp.distributions.Independent("learnable_mvn_diag", batch_shape=[], event_shape=[4], dtype=float32)
(<tf.Variable 'loc:0' shape=(4,) dtype=float32, numpy=array([0., 0., 0., 0.], dtype=float32)>, <tf.Variable 'scale:0' shape=(4,) dtype=float32, numpy=array([0.54132485, 0.54132485, 0.54132485, 0.54132485], dtype=float32)>)
Mieszanina Multivarite Normal (kulista)
learnable_mix_mvn_scaled_identity = tfd.MixtureSameFamily(
mixture_distribution=tfd.Categorical(
logits=tf.Variable(
# Changing the `1.` intializes with a geometric decay.
-tf.math.log(1.) * tf.range(num_components, dtype=tf.float32),
name='logits')),
components_distribution=tfd.Independent(
tfd.Normal(
loc=tf.Variable(
tf.random.normal([num_components, event_size]),
name='loc'),
scale=tfp.util.TransformedVariable(
10. * tf.ones([num_components, 1]),
bijector=tfb.Softplus(), # Use Softplus...cuz why not?
name='scale')),
reinterpreted_batch_ndims=1),
name='learnable_mix_mvn_scaled_identity')
print(learnable_mix_mvn_scaled_identity)
print(learnable_mix_mvn_scaled_identity.trainable_variables)
tfp.distributions.MixtureSameFamily("learnable_mix_mvn_scaled_identity", batch_shape=[], event_shape=[4], dtype=float32)
(<tf.Variable 'logits:0' shape=(3,) dtype=float32, numpy=array([-0., -0., -0.], dtype=float32)>, <tf.Variable 'loc:0' shape=(3, 4) dtype=float32, numpy=
array([[ 0.21316044, 0.18825649, 1.3055958 , -1.4072137 ],
[-1.6604203 , -0.9415946 , -1.1349488 , -0.4928658 ],
[-0.9672405 , 0.45094398, -2.615817 , 3.7891428 ]],
dtype=float32)>, <tf.Variable 'scale:0' shape=(3, 1) dtype=float32, numpy=
array([[9.999954],
[9.999954],
[9.999954]], dtype=float32)>)
Mieszanina wielowymiarowego normalnego (sferycznego) o masie pierwszej mieszanki niemożliwej do nauczenia
learnable_mix_mvndiag_first_fixed = tfd.MixtureSameFamily(
mixture_distribution=tfd.Categorical(
logits=tfp.util.TransformedVariable(
# Initialize logits as geometric decay.
-tf.math.log(1.5) * tf.range(num_components, dtype=tf.float32),
tfb.Pad(paddings=[[1, 0]], constant_values=0)),
name='logits'),
components_distribution=tfd.Independent(
tfd.Normal(
loc=tf.Variable(
# Use Rademacher...cuz why not?
tfp.random.rademacher([num_components, event_size]),
name='loc'),
scale=tfp.util.TransformedVariable(
10. * tf.ones([num_components, 1]),
bijector=tfb.Softplus(), # Use Softplus...cuz why not?
name='scale')),
reinterpreted_batch_ndims=1),
name='learnable_mix_mvndiag_first_fixed')
print(learnable_mix_mvndiag_first_fixed)
print(learnable_mix_mvndiag_first_fixed.trainable_variables)
tfp.distributions.MixtureSameFamily("learnable_mix_mvndiag_first_fixed", batch_shape=[], event_shape=[4], dtype=float32)
(<tf.Variable 'Variable:0' shape=(2,) dtype=float32, numpy=array([-0.4054651, -0.8109302], dtype=float32)>, <tf.Variable 'loc:0' shape=(3, 4) dtype=float32, numpy=
array([[ 1., 1., -1., -1.],
[ 1., -1., 1., 1.],
[-1., 1., -1., -1.]], dtype=float32)>, <tf.Variable 'scale:0' shape=(3, 1) dtype=float32, numpy=
array([[9.999954],
[9.999954],
[9.999954]], dtype=float32)>)
Mieszanina wielowymiarowe Normal (pełna Cov )
learnable_mix_mvntril = tfd.MixtureSameFamily(
mixture_distribution=tfd.Categorical(
logits=tf.Variable(
# Changing the `1.` intializes with a geometric decay.
-tf.math.log(1.) * tf.range(num_components, dtype=tf.float32),
name='logits')),
components_distribution=tfd.MultivariateNormalTriL(
loc=tf.Variable(tf.zeros([num_components, event_size]), name='loc'),
scale_tril=tfp.util.TransformedVariable(
10. * tf.eye(event_size, batch_shape=[num_components]),
bijector=tfb.FillScaleTriL(),
name='scale_tril')),
name='learnable_mix_mvntril')
print(learnable_mix_mvntril)
print(learnable_mix_mvntril.trainable_variables)
tfp.distributions.MixtureSameFamily("learnable_mix_mvntril", batch_shape=[], event_shape=[4], dtype=float32)
(<tf.Variable 'loc:0' shape=(3, 4) dtype=float32, numpy=
array([[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.]], dtype=float32)>, <tf.Variable 'scale_tril:0' shape=(3, 10) dtype=float32, numpy=
array([[9.999945, 0. , 0. , 0. , 9.999945, 9.999945,
0. , 0. , 0. , 9.999945],
[9.999945, 0. , 0. , 0. , 9.999945, 9.999945,
0. , 0. , 0. , 9.999945],
[9.999945, 0. , 0. , 0. , 9.999945, 9.999945,
0. , 0. , 0. , 9.999945]], dtype=float32)>, <tf.Variable 'logits:0' shape=(3,) dtype=float32, numpy=array([-0., -0., -0.], dtype=float32)>)
Mieszanina wielowymiarowe Normal (pełny Cov ) z unlearnable pierwszy mix & pierwszego składnika
# Make a bijector which pads an eye to what otherwise fills a tril.
num_tril_nonzero = lambda num_rows: num_rows * (num_rows + 1) // 2
num_tril_rows = lambda nnz: prefer_static.cast(
prefer_static.sqrt(0.25 + 2. * prefer_static.cast(nnz, tf.float32)) - 0.5,
tf.int32)
# TFP doesn't have a concat bijector, so we roll out our own.
class PadEye(tfb.Bijector):
def __init__(self, tril_fn=None):
if tril_fn is None:
tril_fn = tfb.FillScaleTriL()
self._tril_fn = getattr(tril_fn, 'inverse', tril_fn)
super(PadEye, self).__init__(
forward_min_event_ndims=2,
inverse_min_event_ndims=2,
is_constant_jacobian=True,
name='PadEye')
def _forward(self, x):
num_rows = int(num_tril_rows(tf.compat.dimension_value(x.shape[-1])))
eye = tf.eye(num_rows, batch_shape=prefer_static.shape(x)[:-2])
return tf.concat([self._tril_fn(eye)[..., tf.newaxis, :], x],
axis=prefer_static.rank(x) - 2)
def _inverse(self, y):
return y[..., 1:, :]
def _forward_log_det_jacobian(self, x):
return tf.zeros([], dtype=x.dtype)
def _inverse_log_det_jacobian(self, y):
return tf.zeros([], dtype=y.dtype)
def _forward_event_shape(self, in_shape):
n = prefer_static.size(in_shape)
return in_shape + prefer_static.one_hot(n - 2, depth=n, dtype=tf.int32)
def _inverse_event_shape(self, out_shape):
n = prefer_static.size(out_shape)
return out_shape - prefer_static.one_hot(n - 2, depth=n, dtype=tf.int32)
tril_bijector = tfb.FillScaleTriL(diag_bijector=tfb.Softplus())
learnable_mix_mvntril_fixed_first = tfd.MixtureSameFamily(
mixture_distribution=tfd.Categorical(
logits=tfp.util.TransformedVariable(
# Changing the `1.` intializes with a geometric decay.
-tf.math.log(1.) * tf.range(num_components, dtype=tf.float32),
bijector=tfb.Pad(paddings=[(1, 0)]),
name='logits')),
components_distribution=tfd.MultivariateNormalTriL(
loc=tfp.util.TransformedVariable(
tf.zeros([num_components, event_size]),
bijector=tfb.Pad(paddings=[(1, 0)], axis=-2),
name='loc'),
scale_tril=tfp.util.TransformedVariable(
10. * tf.eye(event_size, batch_shape=[num_components]),
bijector=tfb.Chain([tril_bijector, PadEye(tril_bijector)]),
name='scale_tril')),
name='learnable_mix_mvntril_fixed_first')
print(learnable_mix_mvntril_fixed_first)
print(learnable_mix_mvntril_fixed_first.trainable_variables)
tfp.distributions.MixtureSameFamily("learnable_mix_mvntril_fixed_first", batch_shape=[], event_shape=[4], dtype=float32)
(<tf.Variable 'loc:0' shape=(2, 4) dtype=float32, numpy=
array([[0., 0., 0., 0.],
[0., 0., 0., 0.]], dtype=float32)>, <tf.Variable 'scale_tril:0' shape=(2, 10) dtype=float32, numpy=
array([[9.999945, 0. , 0. , 0. , 9.999945, 9.999945,
0. , 0. , 0. , 9.999945],
[9.999945, 0. , 0. , 0. , 9.999945, 9.999945,
0. , 0. , 0. , 9.999945]], dtype=float32)>, <tf.Variable 'logits:0' shape=(2,) dtype=float32, numpy=array([-0., -0.], dtype=float32)>)