Efficient and Effective Learning of HMMs Based on Identification of Hidden States

Table 4

Identification results on identifiable HMMs.

Type	Method	# Iters.	Time (s)	select			Para. Dist.	Conv. (%)	Identi. (%)
Pers.	BW	15	1054	Min. AIC	1.67	0.028	0.15	45.56	88.89
				Correct	0.00	0.058	0.02	16.11	66.67
	SCT	4	4	DBI	0.00	0.012	0.00	—	100
Tran.	BW	22	1276	Min. AIC	1.00	0.014	0.08	100	100
				Correct	0.00	0.012	0.01	75.56	100
	SCT	8	5	DBI	0.00	0.011	0.01	—	100
Hybr.	BW	19	891	Min. AIC	1.75	0.008	0.19	88	100
				Correct	0.00	0.007	0.00	36.50	100
	SCT	10	5	DBI	0.00	0.007	0.00	—	100

Iters.: average number of iterations; Conv. : rate of convergence; Identi. : percentage of identification; : unit log-likelihood difference between the true models and the learned model on test-sets; Para. Dist.: parameter distance; Pers.: Persistent; Tran.: Transient-cyclic; Hybr.: Hybrid. Note that, for the BW, when calculating , , and Para. Dist., the learned model is the best one selected from the repeated random models.