Mixture density networks for the indirect estimation of reference intervals

BMC Bioinformatics

Table 2 Average integrated squared error as the average difference between predicted value and data-generating process

Setting		EM	BFGS_α		BFGS_α(x)		ADAM
α	n	EM	Random	Custom	Random	Custom	Random	Custom
Average \(\text {ISE}({\hat{\alpha }}_1)\)
Dep.	10000	0.0139	0.0135	0.0137	0.0045	0.0057	0.0067	0.0078
Dep.	5000	0.0149	0.0145	0.0143	0.0073	0.0099	0.0092	0.0125
Indep.	10000	0.0021	0.0019	0.0019	0.0049	0.0065	0.0049	0.0071
Indep.	5000	0.0032	0.0042	0.0037	0.0079	0.0109	0.0087	0.0096
Average \(\text {ISE}({\hat{\mu }}_1)\)
Dep.	10000	1.2292	1.4308	1.4921	0.6809	0.8533	1.2838	0.8794
Dep.	5000	1.6960	1.8426	2.1324	1.3833	1.8223	1.9156	1.7716
Indep.	10000	0.3875	0.4078	0.4649	0.6731	0.9459	1.2989	0.8172
Indep.	5000	0.8185	0.8941	0.9648	1.3963	1.9779	2.0296	1.5842
Average \(\text {ISE}({\hat{\sigma }}_1)\)
Dep.	10000	0.4588	0.4583	0.5003	0.2780	0.3837	0.2672	0.3645
Dep.	5000	0.6584	0.6347	0.7312	0.4800	0.7890	0.3657	0.6859
Indep.	10000	0.1992	0.1813	0.2173	0.2741	0.4116	0.2797	0.3574
Indep.	5000	0.3370	0.3286	0.4086	0.4686	0.7624	0.4462	0.5760
Average \(\text {ISE}({\hat{Q}}_{0.95,1})\)
Dep.	10000	4.4896	4.9129	5.1704	2.4881	3.3152	2.8388	3.0161
Dep.	5000	6.1319	6.3538	7.2327	4.6173	6.8189	4.0797	6.2077
Indep.	10000	1.5022	1.4790	1.6823	2.4710	3.5811	2.9686	2.8411
Indep.	5000	2.7713	2.9091	3.2766	4.5883	7.0449	4.9499	5.2115

Bold numbers denote the smallest value comparing EM to \(\text {BFGS}_{\alpha }\) and \(\text {BFGS}_{\alpha (x)}\) to ADAM in each setting. Runs with location crossing or failing to identify two components are excluded for the corresponding algorithms

ISSN: 1471-2105