{% for g in range(gts|length) %} {% endfor %}

(Labeled) Ground truth motif
Label	Logo	performance coefficient-g
G{{ gts_indices[g] }}

Dataset:

This is data {{jaspars}} from the JASPAR database.

Performance coefficients:

Let $G_i=G_i^f\cup G_i^b$ denote the set of base positions of the $i$th ground truth motif occured, where $G_i^b$ is the reverse complement of $G_i^f$, and $D_j$ be the set of base positions of the $j$th discoverd motif returned from the algorithm

The $j$th entry of performance-coefficients-g is defined as $|G_i \cap D_j| / |G_i|$

This measures the extent of ground truth $G_i$ is captured by $D_j$
The entry NC is the quantity $ |\bigcap_j (G_i \setminus D_j)| / |G_i| $; this measures how much the ground truth $G_i$ is not captured by any $D_j$

The $ith$ entry of performance-coefficient-d is defined as $|G_i \cap D_j| / |D_j|$

This measures how capable the learned motif $D_j$ can capture $G_i$
The entry BG is the quantity $ |D_j \cap B| / |D_j| $ where $B$ is the set of background base positions; this measures how much $D_j$ is from the background

For JASPAR dataset, since the ground truth is labeled, we use the following metrics:

Ratio of labeled ground truth being covered: $ \sum_i\sum_j |G_i\cap D_j| / |\bigcup_i G_i| $
Ratio of labeled ground truth being not being covered: $ 1-\sum_i\sum_j |G_i\cap D_j| / |\bigcup_i G_i| $
Ratio of the dicovered motifs inside the labeled ground truth: $ \sum_i\sum_j |G_i\cap D_j| / |\bigcup_j D_j| $
Ratio of the dicovered motifs outside the labeled ground truth: $ 1-\sum_i\sum_j |G_i\cap D_j| / |\bigcup_j D_j| $

Likelihood ratios 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, $B[\alpha]=1/4,\,\forall \alpha$.

{% for i in range(discovered[1]|length) %} {% endfor %} {% for d in range(discovered|length) %} {% for i in range(discovered[d]|length) %} {% endfor %} {% endfor %}

Discovered motif
Label	Logo	performance coefficient-d
D{{ d_indices[d][i] }}	Learned PWM

Ratio of labeled ground truth being covered: {{gt_cover}}
Ratio of labeled ground truth being not being covered: {{gt_n_cover}}
Ratio of the dicovered motifs inside the labeled ground truth: {{a_cover}}
Ratio of the dicovered motifs outside the labeled ground truth: {{false_cover}}

Likelihood ratio scores: