from typing import Any, Dict, Hashable, List, Optional, Set, Tuple, Union
import networkx as nx
import numpy as np
import pandas as pd
from scipy.stats import multivariate_normal
from sklearn.linear_model import LinearRegression
from pgmpy.base import DAG
from pgmpy.factors.continuous import LinearGaussianCPD
from pgmpy.global_vars import logger
[docs]
class LinearGaussianBayesianNetwork(DAG):
"""
A Linear Gaussian Bayesian Network is a Bayesian Network whose
variables are all continuous, and whose CPDs are linear Gaussians.
An important result is that Linear Gaussian Bayesian Networks
are an alternative representation for the class of multivariate
Gaussian distributions.
"""
def __init__(
self,
ebunch: Optional[List[Tuple[Hashable, Hashable]]] = None,
latents: Set[Hashable] = set(),
lavaan_str: Optional[str] = None,
dagitty_str: Optional[str] = None,
) -> None:
super(LinearGaussianBayesianNetwork, self).__init__(
ebunch=ebunch,
latents=latents,
)
self.cpds = []
[docs]
def add_cpds(self, *cpds: LinearGaussianCPD) -> None:
"""
Add Linear Gaussian CPDs (Conditional Probability Distributions)
to the Bayesian Network.
Parameters
----------
cpds : instances of LinearGaussianCPD
LinearGaussianCPDs which will be associated with the model.
Examples
--------
>>> from pgmpy.models import LinearGaussianBayesianNetwork
>>> from pgmpy.factors.continuous import LinearGaussianCPD
>>> model = LinearGaussianBayesianNetwork([("x1", "x2"), ("x2", "x3")])
>>> cpd1 = LinearGaussianCPD("x1", [1], 4)
>>> cpd2 = LinearGaussianCPD("x2", [-5, 0.5], 4, ["x1"])
>>> cpd3 = LinearGaussianCPD("x3", [4, -1], 3, ["x2"])
>>> model.add_cpds(cpd1, cpd2, cpd3)
>>> for cpd in model.cpds:
... print(cpd)
...
P(x1) = N(1; 4)
P(x2 | x1) = N(-5 + 0.5*x1; 4)
P(x3 | x2) = N(4 + -1*x2; 3)
"""
for cpd in cpds:
if not isinstance(cpd, LinearGaussianCPD):
raise ValueError("Only LinearGaussianCPD can be added.")
if set(cpd.variables) - set(cpd.variables).intersection(set(self.nodes())):
raise ValueError("CPD defined on variable not in the model", cpd)
for prev_cpd_index in range(len(self.cpds)):
if self.cpds[prev_cpd_index].variable == cpd.variable:
logger.warning(f"Replacing existing CPD for {cpd.variable}")
self.cpds[prev_cpd_index] = cpd
break
else:
self.cpds.append(cpd)
[docs]
def get_cpds(
self, node: Optional[Hashable] = None
) -> Union[LinearGaussianCPD, List[LinearGaussianCPD]]:
"""
Returns the CPD of the specified node. If node is not specified, returns all CPDs
that have been added so far to the graph.
Parameters
----------
node: any hashable python object (optional)
The node whose CPD we want. If node not specified returns all the
CPDs added to the model.
Returns
-------
list[LinearGaussianCPD] or LinearGaussianCPD
A CPD or list of Linear Gaussian CPDs.
Examples
--------
>>> from pgmpy.models import LinearGaussianBayesianNetwork
>>> from pgmpy.factors.continuous import LinearGaussianCPD
>>> model = LinearGaussianBayesianNetwork([("x1", "x2"), ("x2", "x3")])
>>> cpd1 = LinearGaussianCPD("x1", [1], 4)
>>> cpd2 = LinearGaussianCPD("x2", [-5, 0.5], 4, ["x1"])
>>> cpd3 = LinearGaussianCPD("x3", [4, -1], 3, ["x2"])
>>> model.add_cpds(cpd1, cpd2, cpd3)
>>> model.get_cpds()
[P(x1) = N(1; 4), P(x2 | x1) = N(-5 + 0.5*x1; 4), P(x3 | x2) = N(4 + -1*x2; 3)]
"""
if node is not None:
if node not in self.nodes():
raise ValueError("Node not present in the Directed Graph")
else:
for cpd in self.cpds:
if cpd.variable == node:
return cpd
else:
return self.cpds
[docs]
def remove_cpds(self, *cpds: LinearGaussianCPD) -> None:
"""
Removes the CPDs provided in the arguments.
Parameters
----------
*cpds: LinearGaussianCPD
LinearGaussianCPD objects (or their variable names) to remove.
Examples
--------
>>> from pgmpy.models import LinearGaussianBayesianNetwork
>>> from pgmpy.factors.continuous import LinearGaussianCPD
>>> model = LinearGaussianBayesianNetwork([("x1", "x2"), ("x2", "x3")])
>>> cpd1 = LinearGaussianCPD("x1", [1], 4)
>>> cpd2 = LinearGaussianCPD("x2", [-5, 0.5], 4, ["x1"])
>>> cpd3 = LinearGaussianCPD("x3", [4, -1], 3, ["x2"])
>>> model.add_cpds(cpd1, cpd2, cpd3)
>>> for cpd in model.get_cpds():
... print(cpd)
...
P(x1) = N(1; 4)
P(x2 | x1) = N(-5 + 0.5*x1; 4)
P(x3 | x2) = N(4 + -1*x2; 3)
>>> model.remove_cpds(cpd2, cpd3)
>>> for cpd in model.get_cpds():
... print(cpd)
...
P(x1) = N(1; 4)
"""
for cpd in cpds:
if isinstance(cpd, (str, int)):
cpd = self.get_cpds(cpd)
self.cpds.remove(cpd)
[docs]
def get_random_cpds(
self,
loc: float = 0,
scale: float = 1,
inplace: bool = False,
seed: Optional[int] = None,
) -> Union[None, List[LinearGaussianCPD]]:
"""
Generates random Linear Gaussian CPDs for the model. The coefficients
are sampled from a normal distribution with mean `loc` and standard
deviation `scale`.
Parameters
----------
loc: float
Mean of the normal from which coefficients are sampled.
scale: float
Std dev of the normal from which coefficients are sampled.
inplace: bool (default: False)
If True, adds the generated LinearGaussianCPDs to the model;
otherwise returns them.
seed: int (optional)
Seed for the random number generator.
Examples
--------
>>> from pgmpy.models import LinearGaussianBayesianNetwork
>>> model = LinearGaussianBayesianNetwork([("x1", "x2"), ("x2", "x3")])
>>> model.get_random_cpds(loc=0, scale=1, seed=42)
"""
# We want a different seed for each CPD; increment an integer seed in the loop.
# We want to provide a different seed for each cpd, therefore we force it to be integer and increment in a loop.
seed = seed if seed else 42
cpds = []
for i, var in enumerate(self.nodes()):
parents = self.get_parents(var)
cpds.append(
LinearGaussianCPD.get_random(
variable=var,
evidence=parents,
loc=loc,
scale=scale,
seed=(seed + i),
)
)
if inplace:
self.add_cpds(*cpds)
else:
return cpds
[docs]
def to_joint_gaussian(self) -> Tuple[np.ndarray, np.ndarray]:
"""
Represents the Linear Gaussian Bayesian Network as a joint
Linear Gaussian Bayesian Networks can be represented using a joint
Gaussian distribution over all the variables. This method gives
the mean and covariance of this equivalent joint gaussian distribution.
Returns
-------
mean, cov: np.ndarray, np.ndarray
Mean vector and covariance matrix of the joint Gaussian.
The mean and the covariance matrix of the joint gaussian distribution.
Examples
--------
>>> mean, cov = model.to_joint_gaussian()
>>> from pgmpy.models import LinearGaussianBayesianNetwork
>>> from pgmpy.factors.continuous import LinearGaussianCPD
>>> model = LinearGaussianBayesianNetwork([("x1", "x2"), ("x2", "x3")])
>>> cpd1 = LinearGaussianCPD("x1", [1], 4)
>>> cpd2 = LinearGaussianCPD("x2", [-5, 0.5], 4, ["x1"])
>>> cpd3 = LinearGaussianCPD("x3", [4, -1], 3, ["x2"])
>>> model.add_cpds(cpd1, cpd2, cpd3)
>>> mean
array([ 1. , -4.5, 8.5])
>>> cov
array([[ 16., 8., -8.],
[ 8., 20., -20.],
[ -8., -20., 29.]])
"""
variables = list(nx.topological_sort(self))
var_to_index = {var: i for i, var in enumerate(variables)}
n_nodes = len(self.nodes())
# Step 1: Compute the mean for each variable.
mean = {}
for var in variables:
cpd = self.get_cpds(node=var)
mean[var] = (
cpd.beta * (np.array([1] + [mean[u] for u in cpd.evidence]))
).sum()
mean = np.array([mean[u] for u in variables])
# Step 2: Populate the adjacency matrix, and variance matrix
B = np.zeros((n_nodes, n_nodes))
omega = np.zeros((n_nodes, n_nodes))
for var in variables:
cpd = self.get_cpds(node=var)
for i, evidence_var in enumerate(cpd.evidence):
B[var_to_index[evidence_var], var_to_index[var]] = cpd.beta[i + 1]
omega[var_to_index[var], var_to_index[var]] = (cpd.std) ** 2
# Step 3: Compute the implied covariance matrix
identity_matrix = np.eye(n_nodes)
inv = np.linalg.inv((identity_matrix - B))
implied_cov = inv.T @ omega @ inv
# Round because numerical errors can lead to non-symmetric cov matrix.
return mean.round(decimals=8), implied_cov.round(decimals=8)
[docs]
def log_likelihood(self, data: pd.DataFrame) -> float:
"""
Computes the log-likelihood of the given dataset under the current
Linear Gaussian Bayesian Network.
Parameters
----------
data : pandas.DataFrame
Observations for all variables (columns must match model variables).
Returns
-------
float
Total log-likelihood of the data under the model.
Examples
--------
>>> import numpy as np
>>> import pandas as pd
>>> from pgmpy.models import LinearGaussianBayesianNetwork
>>> from pgmpy.factors.continuous import LinearGaussianCPD
>>> model = LinearGaussianBayesianNetwork([("x1", "x2"), ("x2", "x3")])
>>> cpd1 = LinearGaussianCPD("x1", [1], 4)
>>> cpd2 = LinearGaussianCPD("x2", [-5, 0.5], 4, ["x1"])
>>> cpd3 = LinearGaussianCPD("x3", [4, -1], 3, ["x2"])
>>> model.add_cpds(cpd1, cpd2, cpd3)
>>> df = pd.DataFrame(
... np.random.normal(0, 1, size=(100, 3)), columns=["x1", "x2", "x3"]
... )
>>> model.log_likelihood(df)
-1128.66
"""
ordering = list(nx.topological_sort(self))
missing = set(ordering) - set(data.columns)
if missing:
raise ValueError(f"Missing required columns in DataFrame: {missing}")
data = data[ordering].values
mean, cov = self.to_joint_gaussian()
return np.sum(multivariate_normal.logpdf(data, mean=mean, cov=cov))
[docs]
def copy(self):
"""
Returns a copy of the model.
Returns
-------
Model's copy: pgmpy.models.LinearGaussianBayesianNetwork
Copy of the model on which the method was called.
Examples
--------
>>> from pgmpy.models import LinearGaussianBayesianNetwork
>>> from pgmpy.factors.continuous import LinearGaussianCPD
>>> model = LinearGaussianBayesianNetwork([("A", "B"), ("B", "C")])
>>> cpd_a = LinearGaussianCPD(variable="A", beta=[1], std=4)
>>> cpd_b = LinearGaussianCPD(
... variable="B", beta=[-5, 0.5], std=4, evidence=["A"]
... )
>>> cpd_c = LinearGaussianCPD(
... variable="C", beta=[4, -1], std=3, evidence=["x2"]
... )
>>> model.add_cpds(cpd_a, cpd_b, cpd_c)
>>> copy_model = model.copy()
>>> copy_model.nodes()
NodeView(('A', 'B', 'C'))
>>> copy_model.edges()
OutEdgeView([('A', 'B'), ('B', 'C')])
>>> len(copy_model.get_cpds())
3
"""
model_copy = LinearGaussianBayesianNetwork()
model_copy.add_nodes_from(self.nodes())
model_copy.add_edges_from(self.edges())
if self.cpds:
model_copy.add_cpds(*[cpd.copy() for cpd in self.cpds])
return model_copy
[docs]
def simulate(
self,
n_samples: int = 1000,
do: Optional[Dict[str, float]] = None,
evidence: Optional[Dict[str, float]] = None,
virtual_intervention: Optional[List[LinearGaussianCPD]] = None,
include_latents: bool = False,
seed: Optional[int] = None,
) -> pd.DataFrame:
"""
Simulates data from the model.
Parameters
----------
n_samples: int
Number of samples to draw.
The number of samples to draw from the model.
do: dict (default: None)
The interventions to apply to the model. dict should be of the form
{variable_name: value}
evidence: dict (default: None)
Observed evidence to apply to the model. dict should be of the form
{variable_name: value}
virtual_intervention: list
Also known as soft intervention. `virtual_intervention` should be a list
of `pgmpy.factors.discrete.LinearGaussianCPD` objects specifying the virtual/soft
intervention probabilities.
include_latents: boolean
Whether to include the latent variable values in the generated samples.
seed: int (default: None)
Seed for the random number generator.
Returns
-------
pandas.DataFrame
pandas.DataFrame: generated samples
A pandas data frame with the generated samples.
Examples
--------
>>> model.simulate(n_samples=3, seed=42)
>>> from pgmpy.models import LinearGaussianBayesianNetwork
>>> from pgmpy.factors.continuous import LinearGaussianCPD
>>> model = LinearGaussianBayesianNetwork([("x1", "x2"), ("x2", "x3")])
>>> cpd1 = LinearGaussianCPD("x1", [1], 4)
>>> cpd2 = LinearGaussianCPD("x2", [-5, 0.5], 4, ["x1"])
>>> cpd3 = LinearGaussianCPD("x3", [4, -1], 3, ["x2"])
>>> model.add_cpds(cpd1, cpd2, cpd3)
Simple forward sampling
>>> model.simulate(n_samples=3, seed=42, do={"x2": 0.0})
Sampling with intervention (do)
>>> model.simulate(n_samples=3, seed=42, evidence={"x1": 2.0})
Sampling with evidence
>>> model.simulate(n_samples=3, seed=42, do={"x2": 1.0}, evidence={"x1": 0.0})
Sampling with both intervention and evidence
"""
# Step 1: Check if all arguments are specified and valid
evidence = {} if evidence is None else evidence
do = {} if do is None else do
virtual_intervention = (
[] if virtual_intervention is None else virtual_intervention
)
do_nodes = list(do.keys())
evidence_nodes = list(evidence.keys())
rng = np.random.default_rng(seed=seed)
invalid_nodes = set(do_nodes) - set(self.nodes())
if not set(do_nodes).issubset(set(self.nodes())):
raise ValueError(
f"The following do-nodes are not present in the model: {invalid_nodes}. "
f"do argument contains: {do_nodes}"
)
invalid_nodes = set(evidence_nodes) - set(self.nodes())
if not set(evidence_nodes).issubset(set(self.nodes())):
raise ValueError(
f"The following evidence-nodes are not present in the model: {invalid_nodes}. "
f"evidence argument contains: {evidence_nodes}"
)
self.check_model()
model = self.copy()
if common_vars := set(do.keys()) & set(evidence.keys()):
raise ValueError(
f"Variable(s) can't be in both do and evidence: {', '.join(common_vars)}"
)
if virtual_intervention != []:
for cpd in virtual_intervention:
var = cpd.variable
if var not in self.nodes():
raise ValueError(
f"Virtual intervention provided for variable which is not in the model: {var}"
f"The following nodes are present in the model: {self.nodes()}"
)
# Step 2: If do is specified, modify the network structure.
if do != {}:
for var, val in do.items():
# Step 2.1: Remove incoming edges to the intervened
# node as well as remove the CPD's of the intervened nodes.
for parent in list(model.get_parents(var)):
model.remove_edge(parent, var)
model.remove_cpds(model.get_cpds(var))
# Step 2.2 : For each child of an intervened node, change its CPD to remove
# the parent (intervened node) from the evidence and update its intercept accordingly
for child in model.get_children(var):
child_cpd = model.get_cpds(child)
new_evidence = list(child_cpd.evidence)
new_beta = list(child_cpd.beta)
parent_idx = child_cpd.evidence.index(var)
new_beta[0] += new_beta[parent_idx + 1] * val
del new_evidence[parent_idx]
del new_beta[parent_idx + 1]
new_cpd = LinearGaussianCPD(
variable=child_cpd.variable,
beta=new_beta,
std=child_cpd.std,
evidence=new_evidence,
)
model.remove_cpds(child_cpd)
model.add_cpds(new_cpd)
model.remove_node(var)
# Step 3: If virtual_interventions are specified, change the CPD's of intervened variables
# to specified ones and remove the incoming nodes
for cpd in virtual_intervention:
var = cpd.variable
old_cpd = model.get_cpds(var)
model.remove_cpds(old_cpd)
model.add_cpds(cpd)
for parent in list(model.get_parents(var)):
model.remove_edge(parent, var)
mean, cov = model.to_joint_gaussian()
variables = list(nx.topological_sort(model))
# Step 4: Sample according to evidence
if len(evidence) == 0:
df = pd.DataFrame(
rng.multivariate_normal(mean=mean, cov=cov, size=n_samples),
columns=variables,
)
else:
df_evidence = pd.DataFrame([evidence])
missing_vars, mean_cond, cov_cond = model.predict(data=df_evidence)
sorted_indices = np.argsort(missing_vars)
missing_vars = [missing_vars[i] for i in sorted_indices]
mean_cond = mean_cond[:, sorted_indices]
cov_cond = cov_cond[sorted_indices][:, sorted_indices]
samples_missing = rng.multivariate_normal(
mean=mean_cond[0], cov=cov_cond, size=n_samples
)
df_missing = pd.DataFrame(samples_missing, columns=missing_vars)
df = pd.DataFrame(index=range(n_samples), columns=variables)
for ev_var, ev_val in evidence.items():
df[ev_var] = ev_val
for mv in missing_vars:
df[mv] = df_missing[mv].values
df = df[variables]
# Step 5: Add do variables to the final dataframe
for do_var, do_val in do.items():
df[do_var] = do_val
# Step 6: Remove latent variables if specified
if not include_latents:
df = df.drop(columns=self.latents)
return df
[docs]
def check_model(self) -> bool:
"""
Checks the model for structural/parameter consistency.
Currently checks:
* Each CPD's listed parents match the graph's parents.
Returns
-------
bool
True if all checks pass; raises ValueError otherwise.
"""
for node in self.nodes():
cpd = self.get_cpds(node=node)
if isinstance(cpd, LinearGaussianCPD):
if set(cpd.evidence) != set(self.get_parents(node)):
raise ValueError(
"CPD associated with %s doesn't have "
"proper parents associated with it." % node
)
return True
[docs]
def get_cardinality(self, node: Any) -> None:
"""
Cardinality is not defined for continuous variables.
"""
raise ValueError("Cardinality is not defined for continuous variables.")
[docs]
def fit(
self,
data: pd.DataFrame,
estimator: str = "mle",
std_estimator: str = "unbiased",
) -> "LinearGaussianBayesianNetwork":
"""
Estimates (fits) the Linear Gaussian CPDs from data.
Parameters
----------
data: pd.DataFrame
Continuous-valued data containing all model variables.
A pandas DataFrame with the data to which to fit the model
structure. All variables must be continuously valued.
Currently only 'mle' (OLS) supported.
The estimator to use for estimating the parameters. Currently, MLE via OLS is the
only supported method.
'mle' uses ddof=0; 'unbiased' uses ddof = 1 + number_of_parents.
Whether to use maximum likelihood estimate (MLE) or unbiased estimate for standard
deviation. If 'mle', then ddof=0 is used while calculating standard deviation. If
unbiased, ddof = 1 + number of parents.
Returns
-------
self
None: The estimated LinearGaussianCPDs are added to the model. They can
be accessed using `model.cpds`.
Examples
--------
>>> import numpy as np
>>> import pandas as pd
>>> from pgmpy.models import LinearGaussianBayesianNetwork
>>> df = pd.DataFrame(
... np.random.normal(0, 1, (100, 3)), columns=["x1", "x2", "x3"]
... )
>>> model = LinearGaussianBayesianNetwork([("x1", "x2"), ("x2", "x3")])
>>> model.fit(df)
>>> model.cpds
[<LinearGaussianCPD: P(x1) = N(-0.114; 0.911) at 0x7eb77d30cec0>,
[<LinearGaussianCPD: P(x1) = N(-0.114; 0.911) at 0x7eb77d30cec0,
<LinearGaussianCPD: P(x2 | x1) = N(0.07*x1 + -0.075; 1.172) at 0x7eb77171fb60,
"""
# Step 1: Check the input
if len(missing_vars := (set(self.nodes()) - set(data.columns))) > 0:
raise ValueError(
f"Following variables are missing in the data: {missing_vars}"
)
if estimator not in {
"mle",
}:
raise ValueError("estimator must be one of {'mle', 'unbiased'}")
if std_estimator not in {"mle", "unbiased"}:
raise ValueError("std_estimator must be one of {'mle', 'unbiased'}")
# Step 2: Estimate the LinearGaussianCPDs
cpds = []
for node in self.nodes():
parents = self.get_parents(node)
# Step 2.1: If node doesn't have any parents (i.e. root node),
# simply take the mean and variance.
if len(parents) == 0:
ddof = 0 if std_estimator == "mle" else 1
cpds.append(
LinearGaussianCPD(
variable=node,
beta=[data.loc[:, node].mean()],
std=data.loc[:, node].std(ddof=ddof),
)
)
# Step 2.2: Else, fit a linear regression model and take the coefficients and intercept.
# Compute error variance using predicted values.
else:
lm = LinearRegression().fit(data.loc[:, parents], data.loc[:, node])
residuals = data.loc[:, node] - lm.predict(data.loc[:, parents])
p = 1 + len(parents) # intercept + coefficients
ddof = 0 if std_estimator == "mle" else p
cpds.append(
LinearGaussianCPD(
variable=node,
beta=np.append([lm.intercept_], lm.coef_),
std=residuals.std(ddof=ddof),
evidence=parents,
)
)
# Step 3: Add the estimated CPDs to the model
self.add_cpds(*cpds)
return self
[docs]
def predict(
self, data: pd.DataFrame, distribution: str = "joint"
) -> Tuple[List[str], np.ndarray, np.ndarray]:
"""
Predicts the conditional distribution of missing variables
Predicts the distribution of the missing variable (i.e. missing
columns) in the given dataset and returns its mean and covariance.
Parameters
----------
data: pandas.DataFrame
DataFrame with a subset of model variables observed.
The dataframe with missing variable which to predict.
Returns
-------
variables: list
Missing variables (order matches returned distribution).
The list of variables on which the returned conditional distribution is defined on.
mu: np.array
The mean array of the conditional joint distribution over
the missing variables corresponding to each row of data.
cov: np.array
The covariance of the conditional joint distribution over the missing variables.
Examples
--------
>>> # Drop a column you want to predict (avoid inplace=True to keep return value)
>>> from pgmpy.utils import get_example_model
>>> model = get_example_model("ecoli70")
>>> df = model.simulate(n_samples=5)
>>> # Drop a column that we want to predict.
>>> df = df.drop(columns=["folK"], axis=1, inplace=True)
>>> model.predict(df)
array([[0.13440001]]))
"""
# Step 0: Check the inputs
missing_vars = list(set(self.nodes()) - set(data.columns))
if len(missing_vars) == 0:
raise ValueError("No missing variables in the data")
# Step 1: Create separate mean and cov matrices for missing and known variables.
mu, cov = self.to_joint_gaussian()
variable_order = list(nx.topological_sort(self))
missing_vars = [var for var in variable_order if var in missing_vars]
observed_vars = [var for var in variable_order if var not in missing_vars]
missing_indexes = [variable_order.index(var) for var in missing_vars]
observed_indexes = [variable_order.index(var) for var in observed_vars]
mu_a = mu[missing_indexes]
mu_b = mu[observed_indexes]
cov_aa = cov[np.ix_(missing_indexes, missing_indexes)] # Full |a|×|a| submatrix
cov_bb = cov[
np.ix_(observed_indexes, observed_indexes)
] # Full |b|×|b| submatrix
cov_ab = cov[
np.ix_(missing_indexes, observed_indexes)
] # Full |a|×|b| submatrix
# Step 2: Compute the conditional distributions
X_b = data.loc[:, observed_vars].values # shape: (n_samples, |observed|)
centered_b = X_b - np.atleast_1d(mu_b) # shape: (n_samples, |observed|).
mu_cond = (
np.atleast_2d(mu_a) + (cov_ab @ np.linalg.solve(cov_bb, centered_b.T)).T
)
cov_cond = cov_aa - cov_ab @ np.linalg.solve(cov_bb, cov_ab.T)
# Step 3: Return values
return (missing_vars, mu_cond, cov_cond)
[docs]
def to_markov_model(self) -> None:
"""
For now, to_markov_model method has not been implemented for LinearGaussianBayesianNetwork.
"""
raise NotImplementedError(
"to_markov_model method has not been implemented for LinearGaussianBayesianNetwork."
)
[docs]
def is_imap(self, JPD: Any) -> None:
"""
For now, is_imap method has not been implemented for LinearGaussianBayesianNetwork.
"""
raise NotImplementedError(
"is_imap method has not been implemented for LinearGaussianBayesianNetwork."
)
[docs]
@staticmethod
def get_random(
n_nodes: int = 5,
edge_prob: float = 0.5,
node_names: Optional[List] = None,
latents: bool = False,
loc: float = 0,
scale: float = 1,
seed: Optional[int] = None,
) -> "LinearGaussianBayesianNetwork":
"""
Returns a randomly generated Linear Gaussian Bayesian Network on `n_nodes`
Returns a randomly generated Linear Gaussian Bayesian Network on `n_nodes` variables
with edge probabiliy of `edge_prob` between variables.
Parameters
----------
n_nodes: int
Number of nodes.
The number of nodes in the randomly generated DAG.
Probability of an edge (consistent with a topological order).
The probability of edge between any two nodes in the topologically
sorted DAG.
node_names: list (default: None)
A list of variables names to use in the random graph.
If None, the node names are integer values starting from 0.
latents: bool (default: False)
loc: float
Mean of normal for coefficients.
The mean of the normal distribution from which the coefficients are
sampled.
Std dev of normal for coefficients.
The standard deviation of the normal distribution from which the
coefficients are sampled.
seed: int
The seed for the random number generator.
Returns
-------
LinearGaussianBayesianNetwork
The randomly generated model.
Examples
--------
>>> from pgmpy.models import LinearGaussianBayesianNetwork
>>> model = LinearGaussianBayesianNetwork.get_random(n_nodes=5)
>>> model.nodes()
NodeView((0, 3, 1, 2, 4))
>>> model.edges()
OutEdgeView([(0, 3), (3, 4), (1, 3), (2, 4)])
>>> model.cpds
[<LinearGaussianCPD: P(0) = N(1.764; 1.613) at 0x2732f41aae0,
<LinearGaussianCPD: P(3 | 0, 1) = N(-0.721*0 + -0.079*1 + 0.943; 0.12) at 0x2732f16db20,
<LinearGaussianCPD: P(1) = N(-0.534; 0.208) at 0x2732f320b30,
<LinearGaussianCPD: P(2) = N(-0.023; 0.166) at 0x2732d8d5f40,
<LinearGaussianCPD: P(4 | 2, 3) = N(-0.24*2 + -0.907*3 + 0.625; 0.48) at 0x2737fecdaf0]
"""
dag = DAG.get_random(
n_nodes=n_nodes, edge_prob=edge_prob, node_names=node_names, latents=latents
)
lgbn_model = LinearGaussianBayesianNetwork(dag.edges(), latents=dag.latents)
lgbn_model.add_nodes_from(dag.nodes())
cpds = lgbn_model.get_random_cpds(loc=loc, scale=scale, seed=seed)
lgbn_model.add_cpds(*cpds)
return lgbn_model
