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Table 3 The four-gene network example: 21 data points, white noise and drift noise

From: Least-squares methods for identifying biochemical regulatory networks from noisy measurements

Strength of drift noise (γ) Algorithms ε M ε S ε F
   Mean STD Mean STD Mean STD
2.0 LS 6.32 2.59 0.43 0.08 28.32 10.61
  TLS 19.57 179.54 0.50 0.12 111.66 949.78
  CTLS 5.81 3.10 0.47 0.10 28.62 17.56
1.0 LS 4.46 1.51 0.39 0.05 21.21 6.61
  TLS 4.83 2.15 0.43 0.08 26.42 14.98
  CTLS 3.17 1.24 0.41 0.06 16.08 7.20
0.1 LS 3.68 1.05 0.38 0.02 17.93 4.34
  TLS 3.58 1.27 0.40 0.05 19.90 8.33
  CTLS 2.18 0.68 0.38 0.02 11.16 2.91
0.05 LS 3.68 1.04 0.38 0.02 17.92 4.10
  TLS 3.63 1.35 0.40 0.06 19.88 8.16
  CTLS 2.18 0.69 0.38 0.02 11.14 2.93
  1. The table shows the error comparisons in terms of the mean and the standard deviation (STD) for different strengths of drift noise for each method based on 1000 Monte-Carlo simulations. The number of measurements per experiment is fixed at 21. All conditions are the same as the ones for Table 1 with only the drift noise being added. ε M is the sum of two tems, i.e (1/N1) Σ |α i j | and (l/N2) Σ |β i j |, where β i j and β i j are the relative magnitude errors in the non-zero and zero elements of the true Jacobian, respectively, and N1 and N2 are the number of non-zero and zero elements in the true Jacobian, respectively. ε S is given by (1/n2) Σ |sign( f ^ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGMbGzgaqcaaaa@2E11@ i j ) - sign(f i j )|, i.e. the average sign differences, where f ^ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGMbGzgaqcaaaa@2E11@ i j and f i j are the (i-th row, j-th column) element of the estimated and the true Jacobian, respectively. ε F is the Frobenius norm of the difference between the estimated and the true Jacobian, i.e. || F ^ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGgbGrgaqcaaaa@2DD1@ - F|| F .