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

BMC Bioinformatics

Table 1 The four-gene network example: white noise

Samplings per Experiment	Algorithms	ε _M		ε _S		ε _F
		Mean	STD	Mean	STD	Mean	STD
3	LS	94.36	36.54	0.95	0.20	368.06	123.08
	TLS	94.36	36.54	0.95	0.20	368.06	123.08
	CTLS	94.36	36.54	0.95	0.20	368.06	123.08
6	LS	16.35	5.11	0.59	0.14	71.10	17.84
	TLS	196.04	2239.78	0.74	0.20	1778.75	24252.19
	CTLS	14.96	5.63	0.63	0.16	64.29	21.34
9	LS	7.87	2.42	0.46	0.09	35.73	9.03
	TLS	11.96	9.68	0.54	0.13	67.47	118.27
	CTLS	6.61	2.74	0.47	0.10	31.57	12.05
12	LS	5.19	1.64	0.40	0.06	24.98	6.47
	TLS	6.20	2.34	0.45	0.09	32.42	15.33
	CTLS	3.79	1.48	0.40	0.06	19.59	6.74
21	LS	3.74	1.06	0.38	0.02	18.12	4.39
	TLS	3.71	1.36	0.40	0.05	20.40	8.51
	CTLS	2.20	0.68	0.38	0.02	11.29	2.93
30	LS	3.70	0.87	0.41	0.06	17.21	3.62
	TLS	3.45	1.20	0.44	0.07	18.75	7.30
	CTLS	2.31	0.56	0.49	0.03	10.10	1.96
60	LS	3.75	0.66	0.50	0.01	17.05	2.59
	TLS	3.59	1.05	0.52	0.05	16.25	4.74
	CTLS	2.51	0.52	0.50	0.01	10.76	1.45

The table shows the error comparisons in terms of the mean and the standard deviation (STD) for different numbers of data points for each method based on 1000 Monte-Carlo Simulations. ε_Mis the sum of two terms, i.e (l/N₁) Σ |α_ij| and (l/N₂) Σ |β_ij| where α_ijand β_ijare 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 ( $\hat{f}$ _ij) - sign (f_ij)|, i.e. the average sign differences, where $\hat{f}$ _ijand f_ijare 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