Pointwise mutual information (m i).
Since mutual information (M I) is defined as a quantity representing dependent relationship between two random variables, M I between positions in a protein, which is obtained from the distribution of amino acids in multiple sequence alignments for its homologous proteins, is useful for predicting interacting residues.
Then, mutual information m ij between two positions i in protein A and j in RNA B is defined by (1) m i j = ∑ a ∈ Σ a ∑ b ∈ Σ b P i j (a, b ) log P i j (a, b ) P i (a ) P j (b ).
In this section, we propose a probabilistic model for protein-protein and domain-domain interactions using conditional random fields [ 6, 7] because it can be considered that two domains D m and D n do not always interact even if the mutual information M mn is large.
We can construct an adjacency matrix of the connectivity graph as follows: g i, j =1 if MI i, j ≥ mMI c or otherwise 0, where MI i, j is mutual information between m i and m j, and m MI c is a threshold value.
Given that R(m) is the set of neighboring reactions, then average mutual information I m for metabolite m is defined as in Equation (8).
We also showed how the proposed universal decoder is very similar to both Oosterwijk et al.'s decoder h and an approximation of Moulin's empirical mutual information decoder m for 0≪p≪1 by begin{array}{*{20}l} c cdot g x,y,p) sim h x,y,p) sim n cdot m x,y,p), end{array}.
We consider statistical significance testing for the mutual information measurement M (X, Y), where X and Y represent the random variables associated to the considered two gene expressions.
The relationship between the miRNA expression level (miR) and that of its (t) was computed using mutual information: (1) M I miR, t = ∑ d ∈ miR ∑ r ∈ t p (d, r ) log p (d, r ) p (d ) p (r ) p d, r) is the joint probability density function pdf) of miR and t, and P d) and p(r) are the marginal pdf's of miRand t respectively.
With this approximation, the significance of any given data point can be estimated by treating it as a chi-square statistic with value (2 ln 2) Im, where I is the calculated mutual information and m is the number of independent data points supporting it.
We here introduce mutual information between domains M = { M mn} as given conditional data in order to combine it with the probabilistic model.
