mars.tensor.random.dirichlet#

mars.tensor.random.dirichlet(alpha, size=None, chunk_size=None, gpu=None, dtype=None)[source]#

Draw samples from the Dirichlet distribution.

Draw size samples of dimension k from a Dirichlet distribution. A Dirichlet-distributed random variable can be seen as a multivariate generalization of a Beta distribution. Dirichlet pdf is the conjugate prior of a multinomial in Bayesian inference.

Parameters

  • alpha (array) – Parameter of the distribution (k dimension for sample of dimension k).

  • size (int or tuple of ints, optional) – Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. Default is None, in which case a single value is returned.

  • chunk_size (int or tuple of int or tuple of ints, optional) – Desired chunk size on each dimension

  • gpu (bool, optional) – Allocate the tensor on GPU if True, False as default

  • dtype (data-type, optional) – Data-type of the returned tensor.

Returns

samples – The drawn samples, of shape (size, alpha.ndim).

Return type

Tensor

Raises

ValueError – If any value in alpha is less than or equal to zero

Notes

\[X \approx \prod_{i=1}^{k}{x^{\alpha_i-1}_i}\]

Uses the following property for computation: for each dimension, draw a random sample y_i from a standard gamma generator of shape alpha_i, then \(X = \frac{1}{\sum_{i=1}^k{y_i}} (y_1, \ldots, y_n)\) is Dirichlet distributed.

References

1

David McKay, “Information Theory, Inference and Learning Algorithms,” chapter 23, http://www.inference.phy.cam.ac.uk/mackay/

2

Wikipedia, “Dirichlet distribution”, http://en.wikipedia.org/wiki/Dirichlet_distribution

Examples

Taking an example cited in Wikipedia, this distribution can be used if one wanted to cut strings (each of initial length 1.0) into K pieces with different lengths, where each piece had, on average, a designated average length, but allowing some variation in the relative sizes of the pieces.

>>> import mars.tensor as mt

>>> s = mt.random.dirichlet((10, 5, 3), 20).transpose()

>>> import matplotlib.pyplot as plt

>>> plt.barh(range(20), s[0].execute())
>>> plt.barh(range(20), s[1].execute(), left=s[0].execute(), color='g')
>>> plt.barh(range(20), s[2].execute(), left=(s[0]+s[1]).execute(), color='r')
>>> plt.title("Lengths of Strings")