Before smoothing, a zero feature count gives an exact zero likelihood. This side example shows the raw count arithmetic that the add-one policy changes next.

highlighted = computed this step

Start from the raw zero count

Before add-one smoothing, the side feature F3 has raw count 0 inside class A and raw count 1 inside class B.

F3=1:A count 0,B count 1F3=1:\quad A\text{ count }0,\quad B\text{ count }1
Zero count before smoothingRaw count arithmetic only.Zero count before smoothingfeature F3=1; raw counts before add-one smoothingunsmoothed likelihood = feature count / class countclassclass countfeature countraw ratiolikelihoodA400/40B211/21/2A product with the zero factor: 2/3 * 0 = 0smoothing is a declared policy before scoringnot a claim of accuracy, calibration, or generalization

Make the unsmoothed ratios

The unsmoothed likelihood for A is 0/4 = 0. For B it is 1/2 = 1/2.

P(F3=1A)=0/4=0,P(F3=1B)=1/2P(F3=1\mid A)=0/4=0,\quad P(F3=1\mid B)=1/2
Zero count before smoothingRaw count arithmetic only.Zero count before smoothingfeature F3=1; raw counts before add-one smoothingunsmoothed likelihood = feature count / class countclassclass countfeature countraw ratiolikelihoodA400/40B211/21/2A product with the zero factor: 2/3 * 0 = 0smoothing is a declared policy before scoringnot a claim of accuracy, calibration, or generalization

A product with a zero factor is zero

An unsmoothed A product containing that zero factor becomes 0. Smoothing is a declared policy applied before scoring; this zero-count demo is exact count arithmetic only, not a claim of accuracy, calibration, or generalization, and not proof that smoothing is always better.

2/30=02/3\cdot0=0
Zero count before smoothingRaw count arithmetic only.Zero count before smoothingfeature F3=1; raw counts before add-one smoothingunsmoothed likelihood = feature count / class countclassclass countfeature countraw ratiolikelihoodA400/40B211/21/2A product with the zero factor: 2/3 * 0 = 0smoothing is a declared policy before scoringnot a claim of accuracy, calibration, or generalization