Likelihood ratio scores:
Let \(P_j\) be the position frequency matrix estimated from the \(j\)th learned motif and \(N_j\) be the number of sequences used in the estimation of \(P_j\).
The
likelihood ratio score of the \(j\)th learned motif of length \(L\) is
$$ \sum_{n=1}^{N_j}\sum_{\ell=1}^L \sum_{\alpha} \unicode{x1D7D9}\left[s_n[\ell]=\alpha\right] \, P_j[\alpha,\ell]\, \ln \frac{P_j[\alpha,\ell]}{B[\alpha]}$$
where \(B[\alpha]\) is the background frequency of nucleotide \(\alpha\), \(s_n\) the \(n\)th substring used in estimating \(P_j\),
and \(\unicode{x1D7D9}[\cdot]\) is the indicator function. In this experiment, \(B[\alpha]=1/4,\,\forall \alpha\).
- count: The number of sequences used in the MSA to estimate the PWM. This is \(N_j\) as in the definition of Likelihood ratio scores.
- LRS: Likelihood ratio score.