(7 The function which has been minimized is as follows: mathop sum limits_{i = 1}^{N} mathop sum limits_{j = 1}^{M} times left[ {X_{{{text{c}}_{i,j} }} - g(t_{i,j},k_{1},k_{2},C_{{{text{A}}0_{i} }},M_{i} )} right]^{2}, (8 where (X_{{{text{c}}_{i,j} }}): values obtained experimentally and predicted through ANN, M: number of data points and N: number of molar ratios.
The dimensions of E, A and P are (N × M), (N × L) and (L × M), respectively, where N is the number of genes in the network, M is the number of data points or experiments conducted, and L is the number of transcription factors used in the study.
The dimensions of E, A and P are (N × M), (N × L) and (L × M), respectively, where N is the number of genes in the network, M is the number of data points or experiments conducted, and L is the number of transcription factors used in the analysis.
In addition to the data, the model parameters should also be encoded which in turn requires κ 2 log ( m ) bits where κ is the number of independent parameters to be encoded in the model and m is the number of data points.k Thus, the two-part MDL selects the model that minimizes the whole required code length which is given by [139]: − log p y | θ ̂ ML + κ 2 log ( m ) (65).
Parameters N and M are the number of data points and dimension of each data point, respectively.
Based on the log-likelihood scores, we compute the perplexity of the entire dataset as (text {perplexity}=exp left (-sum _{i=1}^{M} frac {log p(boldsymbol {x}_{i})}{M}right)), where M is the number of data points.
end{aligned} (4 where (S_j x)) is the transfer function as a function of the frequency x on an interval ([x_j, x_{j+1}], x_j) is the jth frequency at which the calibration data are available, (a_j, b_j, c_j), and (d_j) are the coefficients of the polynomials obtained by the cubic spline interpolation, and M is the number of data points of the calibration table.
We denote the number of genes by M and the number of data points in the two groups D A and D B by N A and N B respectively.
It is known that least squares fitting for a linear system can be done in O mp + p) time where m is the number of data points and p is the number of parameters.
