Simulating Data From Bayesian Networks

pgmpy implements the BayesianNetwork.simulate method to allow users to simulate data from a fully defined Bayesian Network under various conditions. These conditions can be any combination of: 1. Virtual Evidence 2. Hard Evidence 3. Virtual Intervention 4. Hard Intervention

Lastly, users can also provide data corresponding to some of the variables in the model (partial samples) to the simulation method. This allows users to fix the values of those variables to the specified value.

# A helper function to compute probability distributions from simulated samples.
def get_distribution(samples, variables=None):
    """
    For marginal distribution, P(A): get_distribution(samples, variables=['A'])
    For joint distribution, P(A, B): get_distribution(samples, variables=['A', 'B'])
    """
    if variables is None:
        raise ValueError("variables must be specified")

    return samples.groupby(variables).size() / samples.shape[0]

# Do not print warnings
import logging
from pgmpy.global_vars import logger
logger.setLevel(logging.ERROR)

# Specify the model to simulate data from.
from pgmpy.factors.discrete import TabularCPD
from pgmpy.utils import get_example_model

alarm = get_example_model("alarm")

1. Standard simulation

Without any specified conditions for simulation, the simulate method draws samples from the joint distribution of the model.

samples = alarm.simulate(n_samples=int(1e4))
samples.head()

	TPR	PAP	MINVOL	HREKG	EXPCO2	DISCONNECT	VENTMACH	VENTLUNG	LVEDVOLUME	HR	...	SHUNT	VENTTUBE	MINVOLSET	LVFAILURE	ERRLOWOUTPUT	HRBP	FIO2	BP	HISTORY	STROKEVOLUME
0	LOW	NORMAL	ZERO	NORMAL	LOW	FALSE	NORMAL	ZERO	NORMAL	HIGH	...	NORMAL	LOW	NORMAL	FALSE	FALSE	HIGH	NORMAL	LOW	FALSE	NORMAL
1	HIGH	NORMAL	ZERO	HIGH	LOW	TRUE	NORMAL	ZERO	NORMAL	HIGH	...	NORMAL	ZERO	NORMAL	FALSE	FALSE	HIGH	NORMAL	HIGH	FALSE	NORMAL
2	LOW	NORMAL	ZERO	HIGH	LOW	FALSE	NORMAL	ZERO	NORMAL	HIGH	...	NORMAL	LOW	NORMAL	FALSE	FALSE	HIGH	NORMAL	LOW	FALSE	NORMAL
3	LOW	NORMAL	ZERO	HIGH	LOW	FALSE	NORMAL	ZERO	NORMAL	HIGH	...	NORMAL	LOW	NORMAL	FALSE	FALSE	HIGH	NORMAL	LOW	FALSE	NORMAL
4	NORMAL	HIGH	ZERO	HIGH	LOW	FALSE	NORMAL	ZERO	NORMAL	HIGH	...	NORMAL	LOW	NORMAL	FALSE	FALSE	HIGH	NORMAL	NORMAL	FALSE	NORMAL

5 rows × 37 columns

2. Simulation under specified evidence

Specifying hard evidence for some variables fixes their values to the specified evidence value during simulation.

evidence = {"CVP": "NORMAL", "HR": "HIGH"}
samples = alarm.simulate(n_samples=int(1e4), evidence=evidence)
samples.head()

	TPR	PAP	MINVOL	HREKG	EXPCO2	DISCONNECT	VENTMACH	VENTLUNG	LVEDVOLUME	HR	...	SHUNT	VENTTUBE	MINVOLSET	LVFAILURE	ERRLOWOUTPUT	HRBP	FIO2	BP	HISTORY	STROKEVOLUME
0	NORMAL	NORMAL	ZERO	HIGH	LOW	FALSE	NORMAL	ZERO	NORMAL	HIGH	...	NORMAL	LOW	NORMAL	FALSE	FALSE	HIGH	NORMAL	LOW	FALSE	LOW
1	LOW	NORMAL	ZERO	HIGH	LOW	FALSE	NORMAL	ZERO	NORMAL	HIGH	...	NORMAL	LOW	NORMAL	FALSE	FALSE	HIGH	NORMAL	LOW	FALSE	LOW
2	LOW	NORMAL	ZERO	HIGH	LOW	FALSE	NORMAL	ZERO	NORMAL	HIGH	...	NORMAL	LOW	NORMAL	FALSE	FALSE	HIGH	LOW	LOW	FALSE	NORMAL
3	LOW	NORMAL	ZERO	HIGH	LOW	FALSE	NORMAL	ZERO	NORMAL	HIGH	...	NORMAL	LOW	NORMAL	FALSE	FALSE	HIGH	NORMAL	LOW	FALSE	NORMAL
4	LOW	NORMAL	NORMAL	NORMAL	LOW	FALSE	NORMAL	ZERO	NORMAL	HIGH	...	HIGH	LOW	NORMAL	FALSE	FALSE	HIGH	NORMAL	LOW	FALSE	NORMAL

5 rows × 37 columns

# All values of HR and CVP should be set to HIGH and NORMAL respectively.
print(all(samples.HR == "HIGH"))
print(all(samples.CVP == "NORMAL"))

True
True

3. Simulation under soft/virtual evidence

Unlike hard evidence where the value of the specified variables is fixed to the specified evidence, virtual evidence allows users to set the marginal distribution of variables.

# The virtual evidence is specified using TabularCPDs. Here, P(CVP=NORMAL) = 0.2, P(CVP=LOW) = 0.3, and P(CPV=HIGH) = 0.5
cvp_evidence = TabularCPD(variable="CVP",
                          variable_card=3,
                          values=[[0.2], [0.3], [0.5]],
                          state_names={"CVP": ["LOW", "NORMAL", "HIGH"]})
samples = alarm.simulate(n_samples=int(1e4), virtual_evidence=[cvp_evidence])

# Check the marginal distribution of CVP
get_distribution(samples, variables=['CVP'])

CVP
HIGH      0.2414
LOW       0.0692
NORMAL    0.6894
dtype: float64

4. Simulation under specified intervention

Using the do argument, users can specify interventions to the model. The value of the intervened variables are set to the specified value and all incoming edges to these variables are removed in the model.

samples = alarm.simulate(n_samples=int(1e4), do={"CVP": "NORMAL", "HR": "HIGH"})
samples.head()

	TPR	PAP	MINVOL	HREKG	EXPCO2	DISCONNECT	VENTMACH	VENTLUNG	LVEDVOLUME	HR	...	SHUNT	VENTTUBE	MINVOLSET	LVFAILURE	ERRLOWOUTPUT	HRBP	FIO2	BP	HISTORY	STROKEVOLUME
0	HIGH	NORMAL	ZERO	HIGH	LOW	FALSE	NORMAL	ZERO	LOW	HIGH	...	NORMAL	LOW	NORMAL	FALSE	FALSE	NORMAL	NORMAL	HIGH	FALSE	NORMAL
1	NORMAL	NORMAL	ZERO	HIGH	LOW	FALSE	NORMAL	ZERO	LOW	HIGH	...	NORMAL	LOW	NORMAL	TRUE	FALSE	HIGH	NORMAL	LOW	FALSE	LOW
2	NORMAL	NORMAL	ZERO	HIGH	LOW	FALSE	NORMAL	ZERO	LOW	HIGH	...	NORMAL	LOW	NORMAL	TRUE	FALSE	HIGH	NORMAL	LOW	TRUE	LOW
3	LOW	NORMAL	ZERO	HIGH	LOW	FALSE	NORMAL	ZERO	NORMAL	HIGH	...	NORMAL	LOW	NORMAL	FALSE	FALSE	HIGH	LOW	LOW	FALSE	NORMAL
4	NORMAL	NORMAL	ZERO	HIGH	HIGH	FALSE	NORMAL	ZERO	HIGH	HIGH	...	NORMAL	LOW	NORMAL	FALSE	FALSE	HIGH	NORMAL	NORMAL	FALSE	LOW

5 rows × 37 columns

5. Simulation under soft/virtual intervention

Similar to virtual evidence, users can specify virtual intervention as well.

cvp_intervention = TabularCPD(variable="CVP",
                              variable_card=3,
                              values=[[0.2], [0.3], [0.5]],
                              state_names={"CVP": ["LOW", "NORMAL", "HIGH"]})
samples = alarm.simulate(n_samples=int(1e4), virtual_intervention=[cvp_intervention])
get_distribution(samples, variables=["CVP"])  # P(HISTORY)

CVP
HIGH      0.3814
LOW       0.2110
NORMAL    0.4076
dtype: float64

6. Partial samples

Lastly, users can also pass already generated data for some variables (for example, from some other simulation) to the simulation. This is equivalent to separately specifying evidence for each sample that is generate.

# Generate some data on CVP.
partial_cvp = pd.DataFrame(np.random.choice(["LOW", "NORMAL", "HIGH"], int(1e4)), columns=['CVP'])
samples = alarm.simulate(n_samples=int(1e4), partial_samples=partial_cvp)

samples.CVP == partial_cvp