A family of heuristic algorithms that aims at finding high scoring directed acyclic graphs

A flexible implementation of multiple greedy search algorithms to find high scoring network (DAG)

Usage

searchHeuristic(score.cache, score = "mlik",
                       num.searches = 1, seed = 42L, start.dag = NULL,
                       max.steps = 100,
                       algo = "hc", tabu.memory = 10, temperature = 0.9,
                       verbose = FALSE, ...)

Arguments

score.cache: output from buildScoreCache().
score: which score should be used to score the network. Possible choices are aic, bic, mdl, mlik.
num.searches: a positive integer giving the number of different search to run, see details.
seed: a non-negative integer which sets the seed.
start.dag: a DAG given as a matrix, see details for format, which can be used to explicity provide a starting point for the structural search.
max.steps: a constant giving the number of search steps per search, see details.
algo: which heuristic algorithm should be used. Possible choices are: hc, tabu, sa.
tabu.memory: a non-negative integer number to set the memory of the tabu search.
temperature: a real number giving the update in temperature for the sa (simulated annealing) search algorithm.
verbose: if TRUE then provides some additional output.
...: further arguments passed to or from other methods.

Value

An object of class abnHeuristic (which extends the class abnLearnd) and contains list with entires:

dags: a list of DAGs
scores: a vector giving the network score for the locally optimal network for each search
detailed.score: a vector giving the evolution of the network score for the all the random restarts
score: a number giving the network score for the locally optimal network
score.cache: the pre-computed cache of scores
num.searches: a numeric giving the number of random restart
max.steps: a numeric giving the maximal number of optimization steps within each search
algorithm: a character for indicating the algorithm used

Details

This function is a flexible implementation of multiple greedy heuristic algorithms, particularly well adapted to the abn framework. It targets multi-random restarts heuristic algorithms. The user can select the num.searches and the maximum number of steps within by max.steps. The optimization algorithm within each search is relatively rudimentary.

The function searchHeuristic is different from the searchHillClimber in the sense that this function is fully written in R, whereas the searchHillClimber is written in C and thus expected to be faster. The function searchHillClimber at each hill-climbing step consider every information from the pre-computed scores cache while the function searchHeuristic performs a local stepwise optimization. This function chooses a structural move (or edge move) and compute the score's change. On this point, it is closer to the MCMCMC algorithm from Madigan and York (1995) and Giudici and Castelo (2003) with a single edge move.

If the user select random, then a random valid DAG is selected. The routine used favourise low density structure. The function implements three algorithm selected with the parameter algo: hc, tabu or sa.

If algo=hc: The Hill-climber algorithm (hc) is a single move algorithm. At each Hill-climbing step within a search an arc is attempted to be added. The new score is computed and compared to the previous network's score.

If algo=tabu: The same algorithm is as with hc is used, but a list of banned moves is computed. The parameter tabu.memory controls the length of the tabu list. The idea is that the classical Hill-climber algorithm is inefficient when it should cross low probability regions to unblock from a local maximum and reaching a higher score peak. By forcing the algorithm to choose some not already used moves, this will force the algorithm to escape the local maximum.

If algo=sa: This variant of the heuristic search algorithm is based on simulated annealing described by Metropolis et al. (1953). Some accepted moves could result in a decrease of the network score. The acceptance rate can be monitored with the parameter temperature.

References

Heckerman, D., Geiger, D. and Chickering, D. M. (1995). Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning, 20, 197-243. Madigan, D. and York, J. (1995) "Bayesian graphical models for discrete data". International Statistical Review, 63:215232. Giudici, P. and Castelo, R. (2003). "Improving Markov chain Monte Carlo model search for data mining". Machine Learning, 50:127158. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). "Equation of state calculations by fast computing machines". The journal of chemical physics, 21(6), 1087-1092.

Examples

if (FALSE) {
##############################################
## example: use built-in simulated data set
##############################################

mydat <- ex1.dag.data ## this data comes with abn see ?ex1.dag.data

## setup distribution list for each node
mydists<-list(b1="binomial", p1="poisson", g1="gaussian", b2="binomial",
              p2="poisson", b3="binomial", g2="gaussian", b4="binomial",
              b5="binomial", g3="gaussian")

mycache <- buildScoreCache(data.df = mydat, data.dists = mydists, max.parents = 2)

## Now peform 10 greedy searches
heur.res <- searchHeuristic(score.cache = mycache, data.dists = mydists,
                            start.dag = "random", num.searches = 10,
                            max.steps = 50)

## Plot (one) dag
plotAbn(heur.res$dags[[1]], data.dists = mydists)
}