LinearGaussianCPD#

class pgmpy.factors.continuous.LinearGaussianCPD(variable, beta, std, evidence=[])[source]#

Bases: BaseFactor

Defines a Linear Gaussian CPD.

The Linear Gaussian CPD makes the following assumptions [1]:

  1. The variable is Gaussian/Normally distributed.

  2. The mean of the variable depends on the values of the parents and the

    intercept term.

  3. The variance is independent of other variables.

For example,

\[p(Y|X) = N(0.9 - 2x; 1)\]

Here, \(0.9 - 2x\) is the mean of the variable \(Y\) and the standard deviation is 1.

In generalized terms, let \(Y\) be a Gaussian variable with parents \(X_1, X_2, \cdots, X_k\). Assuming linear relationship between Y and mathbf{X}, the conditional distribution of Y can be defined as:

\[p(Y |x1, x2, ..., xk) = \mathcal{N}(\beta_0 + x1*\beta_1 + ......... + xk*\beta_k ; \sigma)\]
Parameters:
variable: any hashable python object

The variable whose CPD is defined.

beta: list (array-like)

The coefficients corresponding to each of the evidence variable. The first term of the beta array is the intercept term.

std: float

The standard deviation of variable.

evidence: iterator (array-like)

List of parents/evidence variables of variable. The order in which evidence is specified should match the order of beta.

References

Examples

# To represent the conditional distribution, P(Y| X1, X2, X3) = N(0.2 - 2*x1 + 3*x2 + 7*x3 ; 9.6), we can write:

>>> from pgmpy.factors.continuous import LinearGaussianCPD
>>> cpd = LinearGaussianCPD(
...     variable="Y", beta=[0.2, -2, 3, 7], std=9.6, evidence=["X1", "X2", "X3"]
... )
>>> cpd.variable
'Y'
>>> cpd.evidence
['X1', 'X2', 'X3']
>>> cpd.beta
array([ 0.2, -2. ,  3. ,  7. ])
copy()[source]#

Returns a copy of the distribution.

Returns:
LinearGaussianCPD: copy of the distribution

Examples

>>> from pgmpy.factors.continuous import LinearGaussianCPD
>>> cpd = LinearGaussianCPD(
...     variable="Y", beta=[0.2, -2, 3, 7], std=9.6, evidence=["X1", "X2", "X3"]
... )
>>> copy_cpd = cpd.copy()
>>> copy_cpd.variable
'Y'
>>> copy_cpd.evidence
['X1', 'X2', 'X3']
static get_random(variable, evidence, loc=0.0, scale=1.0, seed=None)[source]#

Generates a LinearGaussianCPD instance with random values on variable with parents/evidence evidence with beta and std sampled from loc and scale

Parameters:
variable: str, int or any hashable python object.

The variable on which to define the TabularCPD.

evidence: list, array-like

A list of variable names which are the parents/evidence of variable.

loc: float

The mean of the normal distribution from which the coefficients are sampled.

scale: float

The standard deviation of the normal distribution from which the coefficients are sampled.

seed: int (default: None)

The seed for the random number generator.

Returns:
Random CPD: pgmpy.factors.continuous.LinearGaussianCPD

A LinearGaussianCPD object on variable with evidence as evidence with random values.

Examples

>>> from pgmpy.factors.continuous import LinearGaussianCPD
>>> LinearGaussianCPD.get_random(
...     variable="Income",
...     evidence=["Age", "Experience"],
...     loc=2.0,
...     scale=0.5,
...     seed=5,
... )
<LinearGaussianCPD: P(Income | Age, Experience) = N(1.338*Age + 1.876*Experience + 1.599; 2.21) at 0x...