PMC:1540429 / 3969-8382 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/1540429","sourcedb":"PMC","sourceid":"1540429","source_url":"https://www.ncbi.nlm.nih.gov/pmc/1540429","text":"Log likelihood ratio\nThis ratio and its associated forms are used by most alignment-driven algorithms to assess the significance of motif candidates. When the candidates are of different lengths, the p-value of the ratio is used. A method to compute the p-value is described in [3]. The log likelihood ratio of the predicted motif m is\nwhere X is the set of sequences in the dataset, Pr(X|φ, Z) is the likelihood of the sequences X given the motif model φ and its binding sites Z, and Pr(X|p0) gives the likelihood of the sequences assuming the background model p0.\nMEME [4] carries out an EM-based procedure to search for a model that maximizes the likelihood ratio. The local optimum can sometimes be avoided by rerunning the program with different initializations. Figure 1 depicts, for each dataset from [1], the scores (the p-values of the log likelihood ratio in the negative logarithm scale) of MEME's predictions and the planted binding sites. For most datasets, the predictions of MEME have higher scores than the planted motifs. We conclude that even an algorithm guaranteeing the global optimal solution for the log likelihood ratio function will miss the true binding sites in these datasets, because this objective function does not accurately capture the nature of the binding sites.\nFigure 1 Objective function: p-Value of log likelihood ratio in negative logarithm scale. The figure exhibits the comparison of the p-value of the log likelihood ratio between the planted motifs (\"TFBS\" in the legend) and that of MEME's predictions for selected datasets from [1]: we use only \"Generic\" and \"Markov\" among the three types of datasets (see [1]), because in \"Real\" type datasets the predictions are possibly genuine binding sites of some unannotated transcription factor other than the ones planted. The datasets are sorted in ascending order of TFBS scores for clarity. For each dataset, there are two scores: the score of TFBS and the score of MEME's prediction. Points on the x-axis correspond to the datasets for which MEME didn't make any prediction. Now, consider one dataset in detail. The dataset is an example for which the planted motif has a higher log likelihood ratio score than MEME's prediction, yet we argue that log likelihood ratio still doesn't work well as an objective function in this case.\nIn a way, the motif-searching problem is a classification problem: all the words of a certain length appearing in the sequences should be partitioned into two classes: the binding sites, and all the others. Training the optimal classifier equates to searching for the optimal candidate motif model. When the log likelihood ratio is applied as the objective function, the ultimate classifier would be a threshold of the log likelihood ratio score so that all the binding sites are above the threshold, and all the others are below it. A classifier corresponding to a good prediction can achieve a decent balance between the false positives and false negatives of the classification. Vice versa, if no threshold is satisfactory enough to classify the words, no good prediction can be found under this motif model.\nTo test the classifiability of this dataset, we calculated the log likelihood ratio scores of all the words in it, including the true binding sites, and tried out various threshold values to classify the words. Among those having scores above the threshold, the numbers of words are counted which belong to binding sites and which belong to the background sequences. Figure 2 indicates that no matter what threshold we choose to identify the binding sites of the motif, we won't be able to find a value to achieve an acceptable balance between the sensitivity and the specificity of the classification. For example, to correctly classify all 11 true binding sites, the threshold must be chosen so low that 130 false positives are classified as binding sites of the motif.\nFigure 2 Classifiability using log likelihood ratios as thresholds. Each bar stands for a value of the cut-off threshold to distinguish the binding sites of the motif from background. The pair of numbers on the top of each bar indicate the number of false positives(FP) and the number of false negatives(FN) resulting from the classification. It is therefore fair to say that log likelihood ratio alone will not be able to separate the true motif from the background noise. 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