Here is the function below :

import numpy as np

from sklearn.naive$\_$bayes import GaussianNB

def CBN$($X$,$ Y$)$:

# Calculate the class means $($barycenters$)$

class$\_$means $=\{$label: np$.$mean$($X$[$Y $==$ label$],$ axis$=0)$ for label in np$.$unique$($Y$)\}$

# Calculate the class prior probabilities P$($wk$)$

class$\_$priors $=\{$label: np$.$sum$($Y $==$ label$)/$ len$($Y$)$ for label in np$.$unique$($Y$)\}$

def calculate$\_$conditional$\_$probability$($data$\_$point, class$\_$label$)$:

# Calculate the conditional probability P$($xi$/$wk$)$ for each variable

probabilities $=[$

np$.$exp$(-$np$.$sum$(($data$\_$point $-$ class$\_$means$[$class$\_$label$][$i$])**2)/(2*$ np$.$var$($X$[$:$,$ i$])))$

$/$ np$.$sqrt$(2*$ np$.$pi $*$ np$.$var$($X$[$:$,$ i$]))$

for i in range$($X$.$shape$[1])$

$]$

return np$.$prod$($probabilities$)$

def predict$\_$single$($data$\_$point$)$:

# Predict the most likely class for a single data point

class$\_$probabilities $=\{$

label: calculate$\_$conditional$\_$probability$($data$\_$point, label$)*$ class$\_$priors$[$label$]$

for label in np$.$unique$($Y$)$

$\}$

return max$($class$\_$probabilities, key$=$class$\_$probabilities.get$)$

# Apply the prediction function to each data point

predicted$\_$labels $=[$predict$\_$single$($data$\_$point$)$ for data$\_$point in X$]$

return predicted$\_$labels

# Example usage:

# Assuming X is your feature matrix and Y is your target labels

# predicted$\_$labels $=$ CBN$($X$,$ Y$)$