Continuous¶
Canonical Factor¶
The intermediate factors in a Gaussian network can be described compactly using a simple parametric representation called the canonical form. This representation is closed under the basic operations used in inference: factor product, factor division, factor reduction, and marginalization. Thus, we define this CanonicalDistribution class that allows the inference process to be performed on joint Gaussian networks.
A canonical form C (X; K,h,g) is defined as
C (X; K,h,g) = exp( ((-1/2) * X.T * K * X) + (h.T * X) + g)
References
Probabilistic Graphical Models, Principles and Techniques, Daphne Koller and Nir Friedman, Section 14.2, Chapter 14.
Continuous Factor¶
- class pgmpy.factors.continuous.ContinuousFactor.ContinuousFactor(variables, pdf, *args, **kwargs)[source]¶
Base class for factors representing various multivariate representations.
- assignment(*args)[source]¶
Returns a list of pdf assignments for the corresponding values.
- Parameters
*args (values) – Values whose assignment is to be computed.
Examples
>>> from pgmpy.factors.continuous import ContinuousFactor >>> from scipy.stats import multivariate_normal >>> normal_pdf = lambda x1, x2: multivariate_normal.pdf((x1, x2), [0, 0], [[1, 0], [0, 1]]) >>> phi = ContinuousFactor(['x1', 'x2'], normal_pdf) >>> phi.assignment(1, 2) 0.013064233284684921
- copy()[source]¶
Return a copy of the distribution.
- Returns
ContinuousFactor object
- Return type
copy of the distribution
Examples
>>> import numpy as np >>> from scipy.special import beta >>> from pgmpy.factors.continuous import ContinuousFactor # Two variable dirichlet distribution with alpha = (1,2) >>> def dirichlet_pdf(x, y): ... return (np.power(x, 1) * np.power(y, 2)) / beta(x, y) >>> dirichlet_factor = ContinuousFactor(['x', 'y'], dirichlet_pdf) >>> dirichlet_factor.variables ['x', 'y'] >>> copy_factor = dirichlet_factor.copy() >>> copy_factor.variables ['x', 'y']
- discretize(method, *args, **kwargs)[source]¶
Discretizes the continuous distribution into discrete probability masses using various methods.
- Parameters
method (A Discretizer Class from pgmpy.discretize) –
*args – The parameters to be given to the Discretizer Class.
**kwargs – The parameters to be given to the Discretizer Class.
- Returns
An n-D array or a DiscreteFactor object according to the discretiztion
method used.
Examples
>>> import numpy as np >>> from scipy.special import beta >>> from pgmpy.factors.continuous import ContinuousFactor >>> from pgmpy.factors.continuous import RoundingDiscretizer >>> def dirichlet_pdf(x, y): ... return (np.power(x, 1) * np.power(y, 2)) / beta(x, y) >>> dirichlet_factor = ContinuousFactor(['x', 'y'], dirichlet_pdf) >>> dirichlet_factor.discretize(RoundingDiscretizer, low=1, high=2, cardinality=5) # TODO: finish this
- divide(other, inplace=True)[source]¶
Gives the ContinuousFactor divide with the other factor.
- Parameters
other (ContinuousFactor) – The ContinuousFactor to be divided.
- Returns
if inplace=True (default) returns None if inplace=False returns a new ContinuousFactor instance.
- Return type
Examples
>>> from pgmpy.factors.continuous import ContinuousFactor >>> from scipy.stats import multivariate_normal >>> sn_pdf1 = lambda x: multivariate_normal.pdf([x], [0], [[1]]) >>> sn_pdf2 = lambda x1,x2: multivariate_normal.pdf([x1, x2], [0, 0], [[1, 0], [0, 1]]) >>> sn1 = ContinuousFactor(['x2'], sn_pdf1) >>> sn2 = ContinuousFactor(['x1', 'x2'], sn_pdf2)
>>> sn4 = sn2.divide(sn1, inplace=False) >>> sn4.assignment(0, 0) 0.3989422804014327
>>> sn4 = sn2 / sn1 >>> sn4.assignment(0, 0) 0.3989422804014327
- marginalize(variables, inplace=True)[source]¶
Marginalize the factor with respect to the given variables.
- Parameters
variables (list, array-like) – List of variables with respect to which factor is to be maximized.
inplace (boolean) – If inplace=True it will modify the factor itself, else would return a new ContinuousFactor instance.
- Returns
DiscreteFactor or None – if inplace=False returns a new ContinuousFactor instance.
- Return type
if inplace=True (default) returns None
Examples
>>> from pgmpy.factors.continuous import ContinuousFactor >>> from scipy.stats import multivariate_normal >>> std_normal_pdf = lambda *x: multivariate_normal.pdf(x, [0, 0], [[1, 0], [0, 1]]) >>> std_normal = ContinuousFactor(['x1', 'x2'], std_normal_pdf) >>> std_normal.scope() ['x1', 'x2'] >>> std_normal.assignment([1, 1]) 0.058549831524319168 >>> std_normal.marginalize(['x2']) >>> std_normal.scope() ['x1'] >>> std_normal.assignment(1)
- normalize(inplace=True)[source]¶
Normalizes the pdf of the continuous factor so that it integrates to 1 over all the variables.
- Parameters
inplace (boolean) – If inplace=True it will modify the factor itself, else would return a new factor.
- Returns
if inplace=True (default) returns None if inplace=False returns a new ContinuousFactor instance.
- Return type
Examples
>>> from pgmpy.factors.continuous import ContinuousFactor >>> from scipy.stats import multivariate_normal >>> std_normal_pdf = lambda x: 2 * multivariate_normal.pdf(x, [0, 0], [[1, 0], [0, 1]]) >>> std_normal = ContinuousFactor(['x1', 'x2'], std_normal_pdf) >>> std_normal.assignment(1, 1) 0.117099663049 >>> std_normal.normalize() >>> std_normal.assignment(1, 1) 0.0585498315243
- property pdf¶
Returns the pdf of the ContinuousFactor.
- product(other, inplace=True)[source]¶
Gives the ContinuousFactor product with the other factor.
- Parameters
other (ContinuousFactor) – The ContinuousFactor to be multiplied.
- Returns
if inplace=True (default) returns None if inplace=False returns a new ContinuousFactor instance.
- Return type
Examples
>>> from pgmpy.factors.continuous import ContinuousFactor >>> from scipy.stats import multivariate_normal >>> sn_pdf1 = lambda x: multivariate_normal.pdf([x], [0], [[1]]) >>> sn_pdf2 = lambda x1,x2: multivariate_normal.pdf([x1, x2], [0, 0], [[1, 0], [0, 1]]) >>> sn1 = ContinuousFactor(['x2'], sn_pdf1) >>> sn2 = ContinuousFactor(['x1', 'x2'], sn_pdf2)
>>> sn3 = sn1.product(sn2, inplace=False) >>> sn3.assignment(0, 0) 0.063493635934240983
>>> sn3 = sn1 * sn2 >>> sn3.assignment(0, 0) 0.063493635934240983
- reduce(values, inplace=True)[source]¶
Reduces the factor to the context of the given variable values.
- Parameters
values (list, array-like) – A list of tuples of the form (variable_name, variable_value).
inplace (boolean) – If inplace=True it will modify the factor itself, else would return a new ContinuousFactor object.
- Returns
ContinuousFactor or None – if inplace=False returns a new ContinuousFactor instance.
- Return type
if inplace=True (default) returns None
Examples
>>> import numpy as np >>> from scipy.special import beta >>> from pgmpy.factors.continuous import ContinuousFactor >>> def custom_pdf(x, y, z): ... return z*(np.power(x, 1) * np.power(y, 2)) / beta(x, y) >>> custom_factor = ContinuousFactor(['x', 'y', 'z'], custom_pdf) >>> custom_factor.variables ['x', 'y', 'z'] >>> custom_factor.assignment(1, 2, 3) 24.0
>>> custom_factor.reduce([('y', 2)]) >>> custom_factor.variables ['x', 'z'] >>> custom_factor.assignment(1, 3) 24.0
- scope()[source]¶
Returns the scope of the factor.
- Returns
list
- Return type
List of variable names in the scope of the factor.
Examples
>>> from pgmpy.factors.continuous import ContinuousFactor >>> from scipy.stats import multivariate_normal >>> normal_pdf = lambda x: multivariate_normal(x, [0, 0], [[1, 0], [0, 1]]) >>> phi = ContinuousFactor(['x1', 'x2'], normal_pdf) >>> phi.scope() ['x1', 'x2']
Linear Gaussian CPD¶
- class pgmpy.factors.continuous.LinearGaussianCPD.LinearGaussianCPD(variable, evidence_mean, evidence_variance, evidence=[], beta=None)[source]¶
For, X -> Y the Linear Gaussian model assumes that the mean of Y is a linear function of mean of X and the variance of Y does not depend on X.
For example,
Here,
is the mean of the variable 
.Let
be a continuous variable with continuous parents
. We say that has a linear Gaussian CPD
if there are parameters 
and 
such that,In vector notation,
References
- copy()[source]¶
Returns a copy of the distribution.
- Returns
LinearGaussianCPD
- Return type
copy of the distribution
Examples
>>> from pgmpy.factors.continuous import LinearGaussianCPD >>> cpd = LinearGaussianCPD('Y', [0.2, -2, 3, 7], 9.6, ['X1', 'X2', 'X3']) >>> copy_cpd = cpd.copy() >>> copy_cpd.variable 'Y' >>> copy_cpd.evidence ['X1', 'X2', 'X3']
- fit(data, states, estimator=None, complete_samples_only=True, **kwargs)[source]¶
Determine βs from data
- Parameters
data (pandas.DataFrame) – Dataframe containing samples from the conditional distribution, p(Y|X) estimator: ‘MLE’ or ‘MAP’
completely_samples_only (boolean (True or False)) – Are they downsampled or complete? Defaults to True
- maximum_likelihood_estimator(data, states)[source]¶
Fit using MLE method.
- Parameters
data (pandas.DataFrame or 2D array) – Dataframe of values containing samples from the conditional distribution, (Y|X) and corresponding X values.
states (All the input states that are jointly gaussian.) –
- Returns
beta, variance (tuple)
- Return type
Returns estimated betas and the variance.