truncatedDistribution

Truncated Distributions in native TensorFlow. Provides truncated variates of TensorFlow distributions.

The class TruncatedDistribution extends any existing TensorFlow distribution, i.e. classes inheriting from tf.distribution, to enable their truncated variates, with full support of broadcasting.

See below for documentation.

Example: Truncated Gamma

import tensorflow as tf
import numpy as np
from truncatedDistribution import TruncatedDistribution as TD

tf.InteractiveSession()
concentration=40.
rate=4.
gamma=tf.distributions.Gamma(concentration,rate)
left=9.
right=30.
td=TD(gamma,left,right)
samples=td.sample(1000).eval()
samples_org=gamma.sample(1000).eval()

Difference in statistics:

tG.mean().eval()
tG.variance().eval()

10.708002
1.4435476

gamma.mean().eval()
gamma.variance().eval()

10
2.5

Example: Truncated Beta

a=2.
b=5.
beta=tf.distributions.Beta(a,b)
left=0.35
right=1.
tB=TD(beta,left,right)
X=np.linspace(0,1,100,dtype=np.float32)
Y1=tB.cdf(X).eval()
Y2=beta.cdf(X).eval()

Difference in statistics:

tB.mean().eval()
tB.variance().eval()

0.47338647
0.010388413

gamma.mean().eval()
gamma.variance().eval()

0.2857143
0.025510205

Example: Broadcasting

Points of truncation are capable of broadcasting in typical TensorFlow fashion.

concentration=np.array([10.,11.],dtype=np.float32)
rate=np.array([4.],dtype=np.float32)
gamma=tf.distributions.Gamma(concentration,rate)
left=np.array([0.1,0.15,0.2],dtype=np.float32)
right=1.

For example, by expanding their dimension, a single resulting sample takes on the shape of

tG=TD(gamma,left.reshape(3,1),right)
single_sample=tG.sample().eval()
single_sample.shape

(3,2)

We can also sample in batches, by specifying the desired shape of the sample.

sample=tG.sample(sample_shape = (5,4)).eval()
sample.shape

(5,4,3,2)

TruncatedDistribution

Truncated Distributions in native TensorFlow. Provides truncated variates of TensorFlow distributions.

Attributes:

• dist: an instance of tf.distributions
  • (ex. Gamma, Dirichlet, etc.)
• left: left truncation point
  • a scalar or an n-dimensional Tensor
  • should be compatible with dist.batch_shape, as usual
• right: right truncation point
  • a scalar or an n-dimensional Tensor
  • should be compatible with dist.batch_shape, as usual
• lft: cdf at left truncation point
  • n-dimensional Tensor
• rght: cdf at right truncation point
  • n-dimensional Tensor
• dist: tensorFlow distribution
• batch_shape: batch shape of the distribution

Methods:

__init__(dist,left,right, n_points=1000)

Construct the truncated variate of a TensorFlow distribution.

Args:

• dist: an instance of tf.distributions
  • (ex. Gamma, Dirichlet, etc.)
• left: left truncation point
  • a scalar or an n-dimensional Tensor
  • should be compatible with dist.batch_shape, as usual
• right: right truncation point
  • a scalar or an n-dimensional Tensor
  • should be compatible with dist.batch_shape, as usual
• n_points: number of points used for estimation of inv_cdf
  • defaults to 1000

sample(sample_shape=())

Generates samples from the distribution.

Args:

• sample_shape: shape of the batch
  • defaults to (), ie. shape of the dist

Returns:

• a batch of samples
  • n dimensional Tensor

cdf(X)

Cumulative distribution function.

Args:

• X: n dimensional Tensor

Returns:

• cdf: cdf at X

log_cdf(X):

Logarithm of cumulative distribution function.

Args:

• X: n dimensional Tensor

Returns:

• cdf: cdf at X
  • n dimensional Tensor

survival_function(X)

Survival function.

Args:

• X: n dimensional Tensor

Returns:

• urvival_function: 1 - cdf at X

log_survival_function(X)

Logarithm of the survival function.

Args:

• X: n dimensional Tensor

Returns:

• log_survival_function: log(1 - cdf) at X

prob(X)

Probability density function

Args:

• X: n dimensional Tensor

Returns:

• pdf: pdf at X
  • n dimensional Tensor

log_prob(X)

Logarithm of the probability density function

Args:

• X: n dimensional Tensor

Returns:

• log_pdf: log_pdf at X
  • n dimensional Tensor

mean(n_samples=1000)

Empirical mean of the distribution.

Args:

• n_samples: number of samples used

Returns:

• empirical mean
  • n dimensional Tensor

variance(n_samples=1000)

Empirical variance of the distribution.

Args:

• n_samples: number of samples used
  • defaults to 1000
• ddof: degrees of freedom
  • defaults to 1

Returns:

• empirical variance
  • n dimensional Tensor

stddev(n_samples=1000)

Empirical standard deviation of the distribution.

Args:

• *args: arguments to be passed to self.variance
• **kwargs: names arguments to be passed to self.variance

Returns:

• empirical standard deviation
  • n dimensional Tensor