 TensorFlow.org'da görüntüleyin |  Google Colab'da çalıştırın |  Kaynağı GitHub'da görüntüleyin |  Not defterini indir |
Bu ortak çalışmada, öğrenilebilir ("eğitilebilir") dağılımlar oluşturmaya ilişkin çeşitli örnekler gösteriyoruz. (Dağıtımları açıklamak için hiçbir çaba göstermiyoruz, yalnızca nasıl oluşturulacağını göstermek için.)
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
İçin Ölçekli Kimlik ile Öğrenebilir değişkenli Normal 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)>)
İçin Diagonal'da ile Öğrenebilir değişkenli Normal 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)>)
Çok Değişkenli Normal Karışımı (küresel)
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)>)
İlk karışım ağırlığı öğrenilemeyen Çok Değişkenli Normal (küresel) karışımı
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)>)
Çok değişkenli Normal karışımı (tam 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)>)
Çok değişkenli Normal (tam karışımı Cov unlearnable ilk mix & ilk bileşenle)
# 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)>)