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باغ وحش توزیع های قابل یادگیری

مشاهده در TensorFlow.org در Google Colab اجرا کنید مشاهده منبع در GitHub دانلود دفترچه یادداشت

در این colab ما نمونه های مختلفی از ایجاد توزیع های قابل یادگیری ("قابل آموزش") را نشان می دهیم. (ما هیچ تلاشی برای توضیح توزیع ها نمی کنیم ، فقط نحوه ساخت آنها را نشان می دهیم.)

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

یادگرفتنی چند متغیره عادی با هویت کوچک برای 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)>)

یادگرفتنی چند متغیره عادی با قطر برای 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)>)

مخلوط نرمال چند متغیره (کروی)

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)>)

مخلوط نرمال چند متغیره (کروی) با وزن مخلوط اول غیرقابل یادگیری است

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)>)

مخلوطی از چند متغیره عادی (کامل 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)>)

مخلوطی از چند متغیره عادی (کامل Cov ) با اولین مخلوط unlearnable و جزء اول

# 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)>)