mindspore.nn.probability.distribution.Normal

class mindspore.nn.probability.distribution.Normal(mean=None, sd=None, seed=None, dtype=mstype.float32, name='Normal')[source]

Normal distribution. A Normal distributio is a continuous distribution with the range \((-\inf, \inf)\) and the probability density function:

\[f(x, \mu, \sigma) = 1 / \sigma\sqrt{2\pi} \exp(-(x - \mu)^2 / 2\sigma^2).\]

where \(\mu, \sigma\) are the mean and the standard deviation of the normal distribution respectively.

Parameters

mean (int, float, list, numpy.ndarray, Tensor) – The mean of the Normal distribution. Default: None.
sd (int, float, list, numpy.ndarray, Tensor) – The standard deviation of the Normal distribution. Default: None.
seed (int) – The seed used in sampling. The global seed is used if it is None. Default: None.
dtype (mindspore.dtype) – The type of the event samples. Default: mstype.float32.
name (str) – The name of the distribution. Default: ‘Normal’.

Inputs and Outputs of APIs:

The accessible APIs of the Normal distribution are defined in the base class, including:

prob, log_prob, cdf, log_cdf, survival_function, and log_survival
mean, sd, mode, var, and entropy
kl_loss and cross_entropy
sample

For more details of all APIs, including the inputs and outputs of all APIs of the Normal distribution, please refer to mindspore.nn.probability.distribution.Distribution, and examples below.

Supported Platforms:

Ascend GPU

Note

sd must be greater than zero. dist_spec_args are mean and sd. dtype must be a float type because Normal distributions are continuous.

Raises

ValueError – When sd <= 0.
TypeError – When the input dtype is not a subclass of float.

Examples

>>> import mindspore
>>> import mindspore.nn as nn
>>> import mindspore.nn.probability.distribution as msd
>>> from mindspore import Tensor
>>> # To initialize a Normal distribution of the mean 3.0 and the standard deviation 4.0.
>>> n1 = msd.Normal(3.0, 4.0, dtype=mindspore.float32)
>>> # A Normal distribution can be initialized without arguments.
>>> # In this case, `mean` and `sd` must be passed in through arguments.
>>> n2 = msd.Normal(dtype=mindspore.float32)
>>> # Here are some tensors used below for testing
>>> value = Tensor([1.0, 2.0, 3.0], dtype=mindspore.float32)
>>> mean_a = Tensor([2.0], dtype=mindspore.float32)
>>> sd_a = Tensor([2.0, 2.0, 2.0], dtype=mindspore.float32)
>>> mean_b = Tensor([1.0], dtype=mindspore.float32)
>>> sd_b = Tensor([1.0, 1.5, 2.0], dtype=mindspore.float32)
>>> # Private interfaces of probability functions corresponding to public interfaces, including
>>> # `prob`, `log_prob`, `cdf`, `log_cdf`, `survival_function`, and `log_survival`,
>>> # have the same arguments as follows.
>>> # Args:
>>> #     value (Tensor): the value to be evaluated.
>>> #     mean (Tensor): the mean of the distribution. Default: self._mean_value.
>>> #     sd (Tensor): the standard deviation of the distribution. Default: self._sd_value.
>>> # Examples of `prob`.
>>> # Similar calls can be made to other probability functions
>>> # by replacing 'prob' by the name of the function
>>> ans = n1.prob(value)
>>> print(ans.shape)
(3,)
>>> # Evaluate with respect to the distribution b.
>>> ans = n1.prob(value, mean_b, sd_b)
>>> print(ans.shape)
(3,)
>>> # `mean` and `sd` must be passed in during function calls
>>> ans = n2.prob(value, mean_a, sd_a)
>>> print(ans.shape)
(3,)
>>> # Functions `mean`, `sd`, `var`, and `entropy` have the same arguments.
>>> # Args:
>>> #     mean (Tensor): the mean of the distribution. Default: self._mean_value.
>>> #     sd (Tensor): the standard deviation of the distribution. Default: self._sd_value.
>>> # Example of `mean`. `sd`, `var`, and `entropy` are similar.
>>> ans = n1.mean() # return 0.0
>>> print(ans.shape)
()
>>> ans = n1.mean(mean_b, sd_b) # return mean_b
>>> print(ans.shape)
(3,)
>>> # `mean` and `sd` must be passed in during function calls.
>>> ans = n2.mean(mean_a, sd_a)
>>> print(ans.shape)
(3,)
>>> # Interfaces of 'kl_loss' and 'cross_entropy' are the same:
>>> # Args:
>>> #     dist (str): the type of the distributions. Only "Normal" is supported.
>>> #     mean_b (Tensor): the mean of distribution b.
>>> #     sd_b (Tensor): the standard deviation of distribution b.
>>> #     mean_a (Tensor): the mean of distribution a. Default: self._mean_value.
>>> #     sd_a (Tensor): the standard deviation of distribution a. Default: self._sd_value.
>>> # Examples of `kl_loss`. `cross_entropy` is similar.
>>> ans = n1.kl_loss('Normal', mean_b, sd_b)
>>> print(ans.shape)
(3,)
>>> ans = n1.kl_loss('Normal', mean_b, sd_b, mean_a, sd_a)
>>> print(ans.shape)
(3,)
>>> # Additional `mean` and `sd` must be passed in.
>>> ans = n2.kl_loss('Normal', mean_b, sd_b, mean_a, sd_a)
>>> print(ans.shape)
(3,)
>>> # Examples of `sample`.
>>> # Args:
>>> #     shape (tuple): the shape of the sample. Default: ()
>>> #     mean (Tensor): the mean of the distribution. Default: self._mean_value.
>>> #     sd (Tensor): the standard deviation of the distribution. Default: self._sd_value.
>>> ans = n1.sample()
>>> print(ans.shape)
()
>>> ans = n1.sample((2,3))
>>> print(ans.shape)
(2, 3)
>>> ans = n1.sample((2,3), mean_b, sd_b)
>>> print(ans.shape)
(2, 3, 3)
>>> ans = n2.sample((2,3), mean_a, sd_a)
>>> print(ans.shape)
(2, 3, 3)

property mean

Return the mean of the distribution.

Returns

Tensor, the mean of the distribution.

property sd

Return the standard deviation of the distribution.

Returns

Tensor, the standard deviation of the distribution.

cdf(value, mean, sd)

Compute the cumulatuve distribution function(CDF) of the given value.

Parameters

value (Tensor) - the value to compute.
mean (Tensor) - the mean of the distribution. Default value: None.
sd (Tensor) - the standard deviation of the distribution. Default value: None.

Returns

Tensor, the value of the cumulatuve distribution function for the given input.

cross_entropy(dist, mean_b, sd_b, mean, sd)

Compute the cross entropy of two distribution

Parameters

dist (str) - the type of the other distribution.
mean_b (Tensor) - the mean of the other distribution.
sd_b (Tensor) - the standard deviation of the other distribution.
mean (Tensor) - the mean of the distribution. Default value: None.
sd (Tensor) - the standard deviation of the distribution. Default value: None.

Returns

Tensor, the value of the cross entropy.

entropy(mean, sd)

Compute the value of the entropy.

Parameters

mean (Tensor) - the mean of the distribution. Default value: None.
sd (Tensor) - the standard deviation of the distribution. Default value: None.

Returns

Tensor, the value of the entropy.

kl_loss(dist, mean_b, sd_b, mean, sd)

Compute the value of the K-L loss between two distribution, namely KL(a||b).

Parameters

dist (str) - the type of the other distribution.
mean_b (Tensor) - the mean of the other distribution.
sd_b (Tensor) - the standard deviation of the other distribution.
mean (Tensor) - the mean of the distribution. Default value: None.
sd (Tensor) - the standard deviation of the distribution. Default value: None.

Returns

Tensor, the value of the K-L loss.

log_cdf(value, mean, sd)

Compute the log value of the cumulatuve distribution function.

Parameters

value (Tensor) - the value to compute.
mean (Tensor) - the mean of the distribution. Default value: None.
sd (Tensor) - the standard deviation of the distribution. Default value: None.

Returns

Tensor, the log value of the cumulatuve distribution function.

log_prob(value, mean, sd)

the log value of the probability.

Parameters

value (Tensor) - the value to compute.
mean (Tensor) - the mean of the distribution. Default value: None.
sd (Tensor) - the standard deviation of the distribution. Default value: None.

Returns

Tensor, the log value of the probability.

log_survival(value, mean, sd)

Compute the log value of the survival function.

Parameters

value (Tensor) - the value to compute.
mean (Tensor) - the mean of the distribution. Default value: None.
sd (Tensor) - the standard deviation of the distribution. Default value: None.

Returns

Tensor, the value of the K-L loss.

mode(mean, sd)

Compute the mode value of the distribution.

Parameters

mean (Tensor) - the mean of the distribution. Default value: None.
sd (Tensor) - the standard deviation of the distribution. Default value: None.

Returns

Tensor, the mode of the distribution.

prob(value, mean, sd)

The probability of the given value. For the continuous distribution, it is the probability density function.

Parameters

value (Tensor) - the value to compute.
mean (Tensor) - the mean of the distribution. Default value: None.
sd (Tensor) - the standard deviation of the distribution. Default value: None.

Returns

Tensor, the value of the probability.

sample(shape, mean, sd)

Generate samples.

Parameters

shape (tuple) - the shape of the sample.
mean (Tensor) - the mean of the distribution. Default value: None.
sd (Tensor) - the standard deviation of the distribution. Default value: None.

Returns

Tensor, the sample following the distribution.

survival_function(value, mean, sd)

Compute the value of the survival function.

Parameters

value (Tensor) - the value to compute.
mean (Tensor) - the mean of the distribution. Default value: None.
sd (Tensor) - the standard deviation of the distribution. Default value: None.

Returns

Tensor, the value of the survival function.

var(mean, sd)

Compute the variance of the distribution.

Parameters

mean (Tensor) - the mean of the distribution. Default value: None.
sd (Tensor) - the standard deviation of the distribution. Default value: None.

Returns

Tensor, the variance of the distribution.