Impact of Laplace smoothing on likelihood in Naive Bayes When 1 is added to word count in Laplace Smoothing in Naive Bayes, the new probabilities either increase or decrease as shown below.
Though the problem of "zero" probability has been solved.
Does the smoothing represents the true picture of probability?
Denominator of Old P(w/c) is 15.
Denominator of New P(w/c) is 21.




Word (w)
Count (word)
Old P(w/c)
Count + 1
New P(w/c)
New P(w/c) - Old P(w/c)




w0
0
0.000
1
0.048
0.048


w1
1
0.067
2
0.095
0.029


w2
2
0.133
3
0.143
0.010


w3
3
0.200
4
0.190
-0.010


w4
4
0.267
5
0.238
-0.029


w5
5
0.333
6
0.286
-0.048





Does the smoothing represents the true picture of probability?

You are using a Bayesian estimator, that besides data considers a prior, so the estimate is biased. In this sense, it is not “true”. But on another hand, are the observed zero counts true zeros? Are those values really impossible? Likely not, so your empirical probabilities were not “true” as well. Laplace smoothing is a trick for overcoming a specific problem, we accept the bias because helps us to solve the bigger problem of dealing with zeros.
