bnlearn contains several examples within the library that can be used to practice with the functionalities of bnlearn.structure_learning(), bnlearn.parameter_learning() and bnlearn.inference().

Start with RAW data

Lets demonstrate by example how to process your own dataset containing mixed variables. I will demonstrate this by the titanic case. This dataset contains both continues as well as categorical variables and can easily imported using bnlearn.bnlearn.import_example(). With the function bnlearn.bnlearn.df2onehot() it can help to convert the mixed dataset towards a one-hot matrix. The settings are adjustable, but by default the unique non-zero values must be above 80% per variable, and the minimal number of samples must be at least 10 per variable.

import bnlearn as bn
# Load titanic dataset containing mixed variables

df_raw = bn.import_example(data='titanic')

# Pre-processing of the input dataset
dfhot, dfnum = bn.df2onehot(df_raw)

# Structure learning
DAG = bn.structure_learning.fit(dfnum)

# Plot
G = bn.plot(DAG)
_images/fig_titanic.png

From this point we can learn the parameters using the DAG and input dataframe.

# Parameter learning
model = bn.parameter_learning.fit(DAG, dfnum)

Finally, we can start making inferences. Note that the variable and evidence names should exactly match the input data (case sensitive).

# Print CPDs
CPDs = bn.print_CPD(model)
# Make inference
q = bn.inference.fit(model, variables=['Survived'], evidence={'Sex':0, 'Pclass':1})

print(q.df)
print(q._str())

Survived

phi(Survived)

Survived(0)

0.3312

Survived(1)

0.6688

Structure learning

A different, but quite straightforward approach to build a DAG from data is to identify independencies in the data set using hypothesis tests, such as chi2 test statistic. The p_value of the test, and a heuristic flag that indicates if the sample size was sufficient. The p_value is the probability of observing the computed chi2 statistic (or an even higher chi2 value), given the null hypothesis that X and Y are independent given Zs. This can be used to make independence judgements, at a given level of significance.

Example (1)

import bnlearn as bn
# Load dataframe
df = bn.import_example()
# Learn structure
model = bn.structure_learning.fit(df)
# adjacency matrix:
model['adjmat']

# print
print(model['adjmat'])

Reading the table from left to right we see that Cloudy is connected to Sprinkler and also to Rain in a directed manner. Sprinkler is connect to Wet_grass. Rain is connected to Wet_grass. Wet_grass is connected to nothing.

Cloudy

Sprinkler

Rain

Wet_Grass

Cloudy

False

True

True

False

Sprinkler

False

False

False

True

Rain

False

False

False

True

Wet_Grass

False

False

False

False

Example (2)

For this example, we will be investigating the sprinkler data set. This is a very simple data set with 4 variables and each variable can contain value [1] or [0]. The question we can ask: What are the relationships and dependencies across the variables? Note that his data set is already pre-processed and no missing values are present.

Let’s bring in our dataset.

import bnlearn as bn
df = bn.import_example()
df.head()

Cloudy

Sprinkler

Rain

Wet_Grass

0

1

0

1

1

1

1

1

1

0

1

1

0

0

0

0

1

0

0

0

1

0

1

1

From the bnlearn library, we’ll need the fit for this exercise:

import bnlearn as bn
 model = bn.structure_learning.fit(df)
 G = bn.plot(model)
Learned structure on the Sprinkler data set.

logo3

We can specificy the method and scoring type. As described previously, some methods are more expensive to run then others. Make the decision on the number of variables, hardware in your machine, time you are willing to wait etc

Method types:

  • hillclimbsearch or hc (greedy local search if many more nodes are involved)

  • exhaustivesearch or ex (exhaustive search for very small networks)

  • constraintsearch or cs (Constraint-based Structure Learning by first identifing independencies in the data set using hypothesis test, chi2)

Scoring types:

  • bic

  • k2

  • bdeu

import bnlearn as bn
model_hc_bic  = bn.structure_learning.fit(df, methodtype='hc', scoretype='bic')
model_hc_k2   = bn.structure_learning.fit(df, methodtype='hc', scoretype='k2')
model_hc_bdeu = bn.structure_learning.fit(df, methodtype='hc', scoretype='bdeu')
model_ex_bic  = bn.structure_learning.fit(df, methodtype='ex', scoretype='bic')
model_ex_k2   = bn.structure_learning.fit(df, methodtype='ex', scoretype='k2')
model_ex_bdeu = bn.structure_learning.fit(df, methodtype='ex', scoretype='bdeu')

Example (3)

Lets learn the structure of a more complex data set and compare it to another one.

import bnlearn as bn
# Load asia DAG
model_true = bn.import_DAG('asia')
# plot ground truth
G = bn.plot(model_true)
_images/fig2a_asia_groundtruth.png

True DAG of the Asia data set.

# Sampling
df = bn.sampling(model_true, n=10000)
# Structure learning of sampled dataset
model_learned = bn.structure_learning.fit(df, methodtype='hc', scoretype='bic')
_images/fig2b_asia_structurelearning.png

Learned DAG based on data set.

# Plot based on structure learning of sampled data
bn.plot(model_learned, pos=G['pos'])
# Compare networks and make plot
bn.compare_networks(model_true, model_learned, pos=G['pos'])
_images/fig2c_asia_comparion.png
_images/fig2d_confmatrix.png

Comparison True vs. learned DAG.

Parameter learning

Extracting adjacency matrix after Parameter learning:

import bnlearn as bn
# Load dataframe
df = bnlearn.import_example()
# Import DAG
DAG = bnlearn.import_DAG('sprinkler', CPD=False)
# Learn parameters
model = bnlearn.parameter_learning.fit(DAG, df)
# adjacency matrix:
model['adjmat']

# print
print(model['adjmat'])

Cloudy

Sprinkler

Rain

Wet_Grass

Cloudy

False

True

True

False

Sprinkler

False

False

False

True

Rain

False

False

False

True

Wet_Grass

False

False

False

False

Create a Bayesian Network, learn its parameters from data and perform the inference

Lets make an example were we have data with many measurements, and we have expert information of the relations between nodes. Our goal is to create DAG on the expert knowledge and learn the CPDs. To showcase this, I will use the sprinkler example.

Import example dataset of the sprinkler dataset.

import bnlearn as bn
df = bn.import_example('sprinkler')
print(tabulate(df.head(), tablefmt="grid", headers="keys"))

Cloudy

Sprinkler

Rain

Wet_Grass

0

0

0

0

0

1

1

0

1

1

2

0

1

0

1

3

1

1

1

1

4

1

1

1

1

Define the network structure. This can be based on expert knowledge.

edges = [('Cloudy', 'Sprinkler'),
         ('Cloudy', 'Rain'),
         ('Sprinkler', 'Wet_Grass'),
         ('Rain', 'Wet_Grass')]

Make the actual Bayesian DAG

import bnlearn as bn
DAG = bn.make_DAG(edges)
# [BNLEARN] Bayesian DAG created.

# Print the CPDs
CPDs = bn.print_CPD(DAG)
# [BNLEARN.print_CPD] No CPDs to print. Use bnlearn.plot(DAG) to make a plot.

Plot the DAG

bnlearn.plot(DAG)
_images/DAG_sprinkler.png

Parameter learning on the user-defined DAG and input data using maximumlikelihood.

DAG = bn.parameter_learning.fit(DAG, df, methodtype='maximumlikelihood')

Lets print the learned CPDs:

CPDs = bn.print_CPD(DAG)

# [BNLEARN.print_CPD] Independencies:
# (Cloudy _|_ Wet_Grass | Rain, Sprinkler)
# (Sprinkler _|_ Rain | Cloudy)
# (Rain _|_ Sprinkler | Cloudy)
# (Wet_Grass _|_ Cloudy | Rain, Sprinkler)
# [BNLEARN.print_CPD] Nodes: ['Cloudy', 'Sprinkler', 'Rain', 'Wet_Grass']
# [BNLEARN.print_CPD] Edges: [('Cloudy', 'Sprinkler'), ('Cloudy', 'Rain'), ('Sprinkler', 'Wet_Grass'), ('Rain', 'Wet_Grass')]
CPD of Cloudy:

Cloudy(0)

0.494

Cloudy(1)

0.506

CPD of Sprinkler:

Cloudy

Cloudy(0)

Cloudy(1)

Sprinkler(0)

0.4807692307692308

0.7075098814229249

Sprinkler(1)

0.5192307692307693

0.2924901185770751

CPD of Rain:

Cloudy

Cloudy(0)

Cloudy(1)

Rain(0)

0.6518218623481782

0.33695652173913043

Rain(1)

0.3481781376518219

0.6630434782608695

CPD of Wet_Grass:

Rain

Rain(0)

Rain(0)

Rain(1)

Rain(1)

Sprinkler

Sprinkler(0)

Sprinkler(1)

Sprinkler(0)

Sprinkler(1)

Wet_Grass(0)

0.7553816046966731

0.33755274261603374

0.25588235294117645

0.37910447761194027

Wet_Grass(1)

0.2446183953033268

0.6624472573839663

0.7441176470588236

0.6208955223880597

Lets make an inference:

q1 = bn.inference.fit(DAG, variables=['Wet_Grass'], evidence={'Rain':1, 'Sprinkler':0, 'Cloudy':1})

+--------------+------------------+
| Wet_Grass    |   phi(Wet_Grass) |
+==============+==================+
| Wet_Grass(0) |           0.2559 |
+--------------+------------------+
| Wet_Grass(1) |           0.7441 |
+--------------+------------------+

Print the values:

print(q1.df)
# array([0.25588235, 0.74411765])