Biology Reference
In-Depth Information
+
main = paste("tabu(..., iss = ", iss, ")",
+
sep = "")
+
sub = paste(narcs(bn), "arcs")
+
graphviz.plot(bn, main = main, sub = sub)
+}
(b) The length of the tabu list does have a significant impact on structure learning,
for two reasons. First of all, it does increase the number of network structures
that are by
tabu
, and therefore structure learning requires more time. This is
especially relevant for score functions that are expensive to compute, such as
BGe. Furthermore, the score of network structure consistently increases with
the length of the tabu list; getting stuck into a local maximum becomes more
and more unlikely as the tabu list grows.
> par(mfrow = c(1, 5))
> for (n in c(10, 15, 20, 50, 100)) {
+
bn = tabu(alarm, score = "bde", tabu = n)
+
bde = score(bn, alarm, type = "bde")
+
main = paste("tabu(..., tabu = ", n, ")",
+
sep = "")
+
sub = paste(ntests(bn), "steps, score", bde)
+
graphviz.plot(bn, main = main, sub = sub)
+}
(c) The BIC score is asymptotically equivalent to BDe, so the networks learned
using these two scores become more similar as sample size increases. At small
sample sizes, BIC penalizes dense networks more heavily than BDe and there-
fore results in much fewer arcs being included and in much lower execution
time.
> par(mfrow = c(2, 6))
> for (n in c(100, 200, 500, 1000, 2000, 5000)) {
+
bn.bde = hc(alarm[1:n, ], score = "bde")
+
bn.bic = hc(alarm[1:n, ], score = "bic")
+
bde = score(bn.bde, alarm, type = "bde")
+
bic = score(bn.bic, alarm, type = "bic")
+
main = paste("BDe, sample size", n)
+
sub = paste(ntests(bn.bde), "steps, score", bde)
+
graphviz.plot(bn.bde, main = main, sub = sub)
+
main = paste("BIC, sample size", n)
+
sub = paste(ntests(bn.bic), "steps, score", bic)
+
graphviz.plot(bn.bic, main = main, sub = sub)
+}
2.6
Consider the observational data set from
Sachs et al.
(
2005
)usedin
Sect.
2.5.1
(the original data set, not the discretized one).
(a) Evaluate the networks learned by hill-climbing with BIC and BGe using
cross-validation and the log-likelihood loss function.
Search WWH ::
Custom Search