শেখার বিতরণ চিড়িয়াখানা

এই কোল্যাবে আমরা শেখার যোগ্য ("প্রশিক্ষণযোগ্য") বিতরণের বিভিন্ন উদাহরণ দেখাই। (আমরা বিতরণগুলি ব্যাখ্যা করার জন্য কোনও প্রচেষ্টা করি না, কেবল সেগুলি কীভাবে তৈরি করা যায় তা দেখানোর জন্য।)

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

জন্য ছোটো পরিচয় Learnable বহুচলকীয় সাধারন 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)>)

জন্য তির্যক সঙ্গে Learnable বহুচলকীয় সাধারন 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)>)

মাল্টিভেরাইট নরমালের মিশ্রণ (গোলাকার)

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)>)

মাল্টিভেরিয়েট নরমাল (গোলাকার) মিশ্রণের সাথে প্রথম মিশ্রণের ওজন অশিক্ষিত

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)>)

বহুচলকীয় স্বাভাবিক মিশ্রণ (সম্পূর্ণ 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)>)

বহুচলকীয় সাধারন (সম্পূর্ণ সংমিশ্রণ Cov unlearnable প্রথম মিশ্রণ & প্রথম উপাদান সঙ্গে)

# 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)>)