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 distribution 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’.
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.
- Supported Platforms:
Ascend
GPU
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.