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

BMC Bioinformatics

Table 2 The four-gene network example: 12 data points, white noise and drift noise

Strength of drift noise (γ)	Algorithms	ε _M		ε _S		ε _F
		Mean	STD	Mean	STD	Mean	STD
2.0	LS	9.18	3.63	0.47	0.10	41.38	14.19
	TLS	29.25	178.08	0.57	0.15	237.51	2995.95
	CTLS	8.37	3.95	0.51	0.12	40.28	20.33
1.0	LS	6.31	2.07	0.42	0.07	29.24	8.25
	TLS	8.21	5.02	0.48	0.11	41.76	28.25
	CTLS	5.01	2.00	0.43	0.09	24.67	9.62
0.1	LS	5.14	1.59	0.40	0.06	25.02	6.61
	TLS	6.21	2.38	0.45	0.09	32.87	15.91
	CTLS	3.79	1.40	0.40	0.05	19.71	6.89
0.05	LS	5.18	1.66	0.40	0.06	25.16	6.57
	TLS	6.20	2.39	0.45	0.09	32.29	15.30
	CTLS	3.79	1.46	0.40	0.06	19.56	6.80

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 12. All conditions are the same as in Table 1 with only the drift noise being added. ε_Mis the sum of two tems, i.e (1/N₁) Σ |α_{i j}| and (1/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_Sis given by (1/n²) Σ |sign ( $\hat{f}$ _{i j}) - sign(f_{i j})|, i.e. the average sign differences, where $\hat{f}$ _{i j}and f_{i j}are the (i-th row, j-th column) elements of the estimated and the true Jacobian, respectively. ε_Fis the Frobenius norm of the difference between the estimated and the true Jacobian, i.e. || $\hat{F}$ - F||_F.

ISSN: 1471-2105