A PWM is a compact probabilistic model with important assumptions.

highlighted = computed this step

PWM columns are independent

A PWM treats positions as independent, so it ignores correlations between columns. It also assumes the alignment is already given.

PWM score=product of column terms\text{PWM score}=\text{product of column terms}
PWM model boundaryThe table separates what the PWM captures from what it leaves out.PWM capturesStill a modelling choiceposition frequenciesposition-independence assumptiongiven aligned columnsfinding the motif is hardexact countspseudocounts for zero cellsproduct scorelog-odds against background

Small data need careful modelling

Small N can overfit, zero counts need pseudocounts, and real motif scoring often uses log-odds against a background model. A PWM is a compact model, not the full biology of regulation.

model scorecomplete regulatory meaning\text{model score} \ne \text{complete regulatory meaning}
PWM model boundaryThe table separates what the PWM captures from what it leaves out.PWM capturesStill a modelling choiceposition frequenciesposition-independence assumptiongiven aligned columnsfinding the motif is hardexact countspseudocounts for zero cellsproduct scorelog-odds against background