# Lautum Information¶

The lautum information [PVerdu08] is, in a sense, the mutual information in reverse (lautum is mutual backwards):

$\L{X_{0:n}} = \DKL{X_0 \cdot X_1 \cdot \ldots \cdot X_n || X_{0:n}}$

## API¶

lautum_information(dist, rvs=None, crvs=None, rv_mode=None)[source]

Computes the lautum information.

Parameters
• dist (Distribution) – The distribution from which the lautum information is calculated.

• rvs (list, None) – A list of lists. Each inner list specifies the indexes of the random variables used to calculate the lautum information. If None, then the lautum information is calculated over all random variables, which is equivalent to passing rvs=dist.rvs.

• crvs (list, None) – A single list of indexes specifying the random variables to condition on. If None, then no variables are conditioned on.

• rv_mode (str, None) – Specifies how to interpret rvs and crvs. Valid options are: {‘indices’, ‘names’}. If equal to ‘indices’, then the elements of crvs and rvs are interpreted as random variable indices. If equal to ‘names’, the the elements are interpreted as random variable names. If None, then the value of dist._rv_mode is consulted, which defaults to ‘indices’.

Returns

L – The lautum information.

Return type

float

Examples

>>> outcomes = ['000', '001', '010', '011', '100', '101', '110', '111']
>>> pmf = [3/16, 1/16, 1/16, 3/16, 1/16, 3/16, 3/16, 1/16]
>>> d = dit.Distribution(outcomes, pmf)
>>> dit.other.lautum_information(d)
0.20751874963942196
>>> dit.other.lautum_information(d, rvs=[, ])
0.0

Raises

ditException – Raised if dist is not a joint distribution or if rvs or crvs contain non-existent random variables.