tfp.distributions.MixtureSameFamily | TensorFlow Probability (original) (raw)

Mixture (same-family) distribution.

Inherits From: AutoCompositeTensorDistribution, Distribution, AutoCompositeTensor

tfp.distributions.MixtureSameFamily(
    mixture_distribution,
    components_distribution,
    reparameterize=False,
    validate_args=False,
    allow_nan_stats=True,
    name='MixtureSameFamily'
)

The MixtureSameFamily distribution implements a (batch of) mixture distribution where all components are from different parameterizations of the same distribution type. It is parameterized by a Categorical 'selecting distribution' (over k components) and a components distribution, i.e., aDistribution with a rightmost batch shape (equal to [k]) which indexes each (batch of) component.

#### Examples

  tfd = tfp.distributions

  ### Create a mixture of two scalar Gaussians:

  gm = tfd.MixtureSameFamily(
      mixture_distribution=tfd.Categorical(
          probs=[0.3, 0.7]),
      components_distribution=tfd.Normal(
        loc=[-1., 1],       # One for each component.
        scale=[0.1, 0.5]))  # And same here.

  gm.mean()
  # ==> 0.4

  gm.variance()
  # ==> 1.018

  # Plot PDF.
  x = np.linspace(-2., 3., int(1e4), dtype=np.float32)
  import matplotlib.pyplot as plt
  plt.plot(x, gm.prob(x));

  ### Create a mixture of three Bivariate Gaussians:

  gm = tfd.MixtureSameFamily(
      mixture_distribution=tfd.Categorical(
          probs=[0.2, 0.4, 0.4]),
      components_distribution=tfd.MultivariateNormalDiag(
          loc=[[-1., 1],  # component 1
               [1, -1],  # component 2
               [1, 1]],  # component 3
          scale_diag=tf.tile([[.3], [.6], [.7]], [1, 2])))

  gm.components_distribution.batch_shape
  # ==> (3,)

  gm.components_distribution.event_shape
  # ==> (2,)

  gm.mean()
  # ==> array([ 0.6, 0.2], dtype=float32)

  gm.covariance()
  # ==> array([[ 0.998    , -0.32     ],
  #            [-0.32     ,  1.3180001]], dtype=float32)

  # Plot PDF contours.
  def meshgrid(x):
    y = x
    [gx, gy] = np.meshgrid(x, y, indexing='ij')
    gx, gy = np.float32(gx), np.float32(gy)
    grid = np.concatenate([gx.ravel()[None, :], gy.ravel()[None, :]], axis=0)
    return grid.T.reshape(x.size, y.size, 2)
  grid = meshgrid(np.linspace(-2, 2, 100, dtype=np.float32))
  plt.contour(grid[..., 0], grid[..., 1], gm.prob(grid));

Note that this distribution is not a joint distribution over categorical and continuous values, but rather a mixture of continuous distributions proportioned by the given categorical distribution. If you want a joint distribution, you might write it as:

  @tfd.JointDistributionCoroutineAutoBatched
  def model():
    mus = tf.constant([[-1., 1], # component 1
                       [1, -1],  # component 2
                       [1, 1]])  # component 3
    scales = tf.constant([.3, .6, .7])
    idx = yield tfd.Categorical(probs=[.2, .4, .4], name='idx')
    val = yield tfd.MultivariateNormalDiag(
        loc=mus[idx], scale_diag=tf.ones(2) * scales[idx], name='val')

  model.sample()
  # ==> StructTuple(
  #       idx=2,
  #       val=array([1.0582672, 1.3583777], dtype=float32)
  #     )

If mixture_distribution and components_distribution are both CompositeTensors, then the resulting MixtureSameFamily instance is a CompositeTensor as well. Otherwise, a non-CompositeTensor _MixtureSameFamily instance is created instead. Distribution subclasses that inherit from MixtureSameFamily will also inherit from CompositeTensor.

Args
mixture_distribution	tfd.Categorical-like instance. Manages the probability of selecting components. The number of categories must match the rightmost batch dimension of thecomponents_distribution. Must have batch_shape broadcastable with components_distribution.batch_shape[:-1].
components_distribution	tfd.Distribution-like instance. The right-most batch dimension indexes the mixture components.
reparameterize	Python bool, default False. Whether to reparameterize samples of the distribution using implicit reparameterization gradients [(Figurnov et al., 2018)][1]. The gradients for the mixture logits are equivalent to the ones described by [(Graves, 2016)][2]. The gradients for the components parameters are also computed using implicit reparameterization (as opposed to ancestral sampling), meaning that all components are updated every step. Only works when: (1) components_distribution is fully reparameterized; (2) components_distribution is either a scalar distribution or fully factorized (tfd.Independent applied to a scalar distribution); (3) batch shape has a known rank. Experimental, may be slow and produce infs/NaNs.
validate_args	Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
allow_nan_stats	Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value 'NaN' to indicate the result is undefined. When False, an exception is raised if one or more of the statistic's batch members are undefined.
name	Python str name prefixed to Ops created by this class.

Raises
ValueError	if not dtype_util.is_integer(mixture_distribution.dtype).
ValueError	if mixture_distribution does not have scalar event_shape.
ValueError	if mixture_distribution.batch_shape andcomponents_distribution.batch_shape[:-1] are both fully defined and the former is neither scalar nor equal to the latter.
ValueError	if mixture_distribution categories does not equalcomponents_distribution rightmost batch shape.

Attributes
allow_nan_stats	Python bool describing behavior when a stat is undefined.Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)**2] is also undefined.
batch_shape	Shape of a single sample from a single event index as a TensorShape.May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.
components_distribution
dtype	The DType of Tensors handled by this Distribution.
event_shape	Shape of a single sample from a single batch as a TensorShape.May be partially defined or unknown.
experimental_is_sharded
experimental_shard_axis_names	The list or structure of lists of active shard axis names.
mixture_distribution
name	Name prepended to all ops created by this Distribution.
name_scope	Returns a tf.name_scope instance for this class.
non_trainable_variables	Sequence of non-trainable variables owned by this module and its submodules.
parameters	Dictionary of parameters used to instantiate this Distribution.
reparameterization_type	Describes how samples from the distribution are reparameterized.Currently this is one of the static instancestfd.FULLY_REPARAMETERIZED or tfd.NOT_REPARAMETERIZED.
submodules	Sequence of all sub-modules.Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on). a = tf.Module() b = tf.Module() c = tf.Module() a.b = b b.c = c list(a.submodules) == [b, c] True list(b.submodules) == [c] True list(c.submodules) == [] True
trainable_variables	Sequence of trainable variables owned by this module and its submodules.
validate_args	Python bool indicating possibly expensive checks are enabled.
variables	Sequence of variables owned by this module and its submodules.

Args
value	float or double Tensor.
name	Python str prepended to names of ops created by this function.
**kwargs	Named arguments forwarded to subclass implementation.

Args
other	tfp.distributions.Distribution instance.
name	Python str prepended to names of ops created by this function.

Args
*args	Passed to implementation _default_event_space_bijector.
**kwargs	Passed to implementation _default_event_space_bijector.

Args
value	a Tensor valid sample from this distribution family.
sample_ndims	Positive int Tensor number of leftmost dimensions ofvalue that index i.i.d. samples. Default value: 1.
validate_args	Python bool, default False. When True, distribution parameters are checked for validity despite possibly degrading runtime performance. When False, invalid inputs may silently render incorrect outputs. Default value: False.
**init_kwargs	Additional keyword arguments passed through tocls.__init__. These take precedence in case of collision with the fitted parameters; for example,tfd.Normal.experimental_fit([1., 1.], scale=20.) returns a Normal distribution with scale=20. rather than the maximum likelihood parameter scale=0..

Args
value	float or double Tensor.
backward_compat	bool specifying whether to fall back to returningFullSpace as the tangent space, and representing R^n with the standard basis.
**kwargs	Named arguments forwarded to subclass implementation.

Returns
log_prob	a Tensor representing the log probability density, of shapesample_shape(x) + self.batch_shape with values of type self.dtype.
tangent_space	a TangentSpace object (by default FullSpace) representing the tangent space to the manifold at value.

Args
sample_shape	integer Tensor desired shape of samples to draw. Default value: ().
seed	PRNG seed; see tfp.random.sanitize_seed for details. Default value: None.
name	name to give to the op. Default value: 'sample_and_log_prob'.
**kwargs	Named arguments forwarded to subclass implementation.

Returns
samples	a Tensor, or structure of Tensors, with prepended dimensionssample_shape.
log_prob	a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.

Args
sample_shape	Tensor or python list/tuple. Desired shape of a call tosample().
name	name to prepend ops with.

Args
dtype	Optional float dtype to assume for continuous-valued parameters. Some constraining bijectors require advance knowledge of the dtype because certain constants (e.g., tfb.Softplus.low) must be instantiated with the same dtype as the values to be transformed.
num_classes	Optional int Tensor number of classes to assume when inferring the shape of parameters for categorical-like distributions. Otherwise ignored.

Args
observations	A tensor representing observations from the mixture. Must be broadcastable with the mixture's batch shape.
name	A string naming a scope.

Args
sample_shape	0D or 1D int32 Tensor. Shape of the generated samples.
seed	PRNG seed; see tfp.random.sanitize_seed for details.
name	name to give to the op.
**kwargs	Named arguments forwarded to subclass implementation.

tfp.distributions.MixtureSameFamily | TensorFlow Probability (original) (raw)

Methods

batch_shape_tensor

cdf

copy

covariance

cross_entropy

entropy

event_shape_tensor

experimental_default_event_space_bijector

experimental_fit

experimental_local_measure

experimental_sample_and_log_prob

is_scalar_batch

is_scalar_event

kl_divergence

log_cdf

log_prob

log_survival_function

mean

mode

param_shapes

param_static_shapes

parameter_properties

posterior_marginal

posterior_mode

prob

quantile

sample

stddev

survival_function

unnormalized_log_prob

variance

with_name_scope

__getitem__

__iter__

`batch_shape_tensor`

`cdf`

`copy`

`covariance`

`cross_entropy`

`entropy`

`event_shape_tensor`

`experimental_default_event_space_bijector`

`experimental_fit`

`experimental_local_measure`

`experimental_sample_and_log_prob`

`is_scalar_batch`

`is_scalar_event`

`kl_divergence`

`log_cdf`

`log_prob`

`log_survival_function`

`mean`

`mode`

`param_shapes`

`param_static_shapes`

`parameter_properties`

`posterior_marginal`

`posterior_mode`

`prob`

`quantile`

`sample`

`stddev`

`survival_function`

`unnormalized_log_prob`

`variance`

`with_name_scope`

`getitem`

`iter`