Worry less about the algorithm, more about the sequence of events

Background: Many algorithms exist for learning network structure and parameters from data. Some of these algorithms include Grow Shrink, Incremental Association Markov Blanket, IAMB, Fast IAMB, and Interleaved IAMB, Hill Climbing, Restricted Maximization and Maximum-Minimum Hill Climbing. These algorithms optimize the fit to the data, while ignoring the order of occurrences of the variables in the network structure. Objective: This paper examines if sequence information (i.e., one variable occurs before another) can make algorithms for learning directed acyclical graph networks more accurate. Methods: A 13- variable network was simulated, where information on sequence of occurrence of some of the variables was assumed to be known. In each simulation 10,000 observations were generated. These observations were used by 4 conditional dependency and 4 search and score algorithms to discover the network from the simulated data. Partial sequence was used to prohibit a directed arc from a later variable to an earlier one. The Area under the Receiver Operating Curve (AROC) was used to compare the accuracy of the sequence-constrained and unconstrained algorithms in predicting the last node in the network. In addition, we examined the performance of sequence constrained algorithms in a real data set. We analyzed 1.3 million disability assessments done on 296,051 residents in Veterans Affairs nursing homes; where the sequence of occurrence of variables was inferred from the average age of occurrence of disabilities. We constructed three networks using Grow-Shrink algorithm, one without and the other two use two permutation of the observed sequence. The fit of these three models to data was examined using Bayesian Information Criterion (BIC). Results: In simulated data, algorithms that used sequenced constraints (AROC = 0.94, confidence intervals, C.I. = 0.86 to 1) were significantly more accurate than the same algorithm without use of sequence constraints (AROC = 0.74, C.I. = 0.65 to 0.83). The agreement between discovered and observed networks improved from range of 0.54 to 0.97 to range of 0.88 to 1. In the real data set, the Bayesian network constructed with use of sequence had 6% lower BIC scores. Conclusions: Sequence information improved accuracy of all eight learning algorithms and should be routinely examined in learning network structure from data.