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For a project, I need to create synthetic categorical data containing specific dependencies between the attributes. This can be done by sampling from a pre-defined Bayesian Network. After some exploration on the internet, I found that Pomegranate is a good package for Bayesian Networks, however - as far as I'm concerned - it seems unpossible to sample from such a pre-defined Bayesian Network. As an example, model.sample() raises a NotImplementedError (despite this solution says so).

Does anyone know if there exists a library which provides a good interface for the construction and sampling of/from a Bayesian network?

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Please use the function from_samples() to build a Bayesian n/w from the data.

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There is an open issue in pomegranate for this in github. In the issue, they mention an ongoing pull request that implements rejections sampling and Gibbs sampling; the last comment in the PR discussion is from 7 days ago (2020, May 17th), so it is not abandoned but actively developed. You could use the version of pomegranate from that PR to sample from your Bayesian Network.

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Just to elucidate the above answers with a concrete example, so that it will be helpful for someone, let's start with the following simple dataset (with 4 variables and 5 data points):

import pandas as pd
df = pd.DataFrame({'A':[0,0,0,1,0], 'B':[0,0,1,0,0], 'C':[1,1,0,0,1], 'D':[0,1,0,1,1]})
df.head()

#   A   B   C   D
#0  0   0   1   0
#1  0   0   1   1
#2  0   1   0   0
#3  1   0   0   1
#4  0   0   1   1 

Now, let's learn the Bayesian Network structure from the above data using the 'exact' algorithm with pomegranate (uses DP/A* to learn the optimal BN structure), using the following code snippet:

import numpy as np
from pomegranate import *
model = BayesianNetwork.from_samples(df.to_numpy(), state_names=df.columns.values, algorithm='exact')
# model.plot()

The BN structure that is learn is shown in the next figure along with the corresponding CPTs:

enter image description here

As can be seen from the above figure, it explains the data exactly. We can compute the log-likelihood of the data with the model as follows:

np.sum(model.log_probability(df.to_numpy()))
# -7.253364813857112

Once the BN structure is learnt, we can sample from the BN as follows:

model.sample()  
# array([[0, 1, 0, 0]], dtype=int64)

As a side note, if we use algorithm='chow-liu' instead (which finds a tree-like structure with fast approximation), we shall obtain the following BN:

enter image description here

The log-likelihood of the data this time is

np.sum(model.log_probability(df.to_numpy()))
# -8.386987635761297

which indicates the algorithm exact finds better estimate.

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