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Table 1 The kinetic ODE and both the conjugate gradient and LARS optimization algorithms obtain the best fit to the 0 to 15 minutes data, with good leave-out-last predictions

From: Predictive network modeling of the high-resolution dynamic plant transcriptome in response to nitrate

    Best hyperparameters (with respect to SNR on leave-1 training dataset) Performed on training set: Performed on test set:
Dynamics Normalization Optimization Gamma (state-space coefficient) Tau (kinetic time constant) Lambda (regularization parameter) SNR (in dB) on leave-1 training dataset percentage of correct signs on leave-1 test dataset
Kinetic MAS5 Gradient 1 3 0.0001 32.4 68%
Kinetic MAS5 LARS 0.1 3 0.1 32.4 74%
Kinetic MAS5 Elastic Nets 0.1 7 0.05 32.2 71%
Brownian MAS5 Gradient 0.1 NA 0.0001 32.1 65%
Brownian MAS5 LARS 0 NA 0.05 32.1 63%
Brownian MAS5 Elastic Nets 0 NA 0.05 32.1 63%
Naïve trend prediction MAS5   NA NA NA NA 52%
  1. Each line in the table represents the type of ODE for the dynamical model of transcription factor-gene regulation (either kinetic, with mRNA degradation, or 'Brownian motion', without mRNA degradation), the type of microarray data normalization, and the optimization algorithm for learning the parameters of the dynamical model. For each of these, we selected the best hyperparameters, namely the state-space coefficient gamma, the kinetic time constant (in minutes) and the parameter regularization coefficient lambda, based on the quality of fit to the training data (from 0 to 15 minutes), as measured by the signal-to-noise ratio (SNR), in dB. We then performed a leave-out-last (leave-1) prediction and counted the number of times the sign of the mRNA change between 15 minutes and 20 minutes was correct. We compared these results to a naïve extrapolation (based on the trend between 12 and 15 minutes) and obtained statistically significant results at P = 0.0145.