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Unformatted text preview: ngle) with its two prediction
nodes (ovals) is introduced. Every test network follows multiple paths in the tree, dictated by the inequalities in the decision nodes (S# refers to a speciﬁc subgraph
count; see Fig. 3). The ﬁnal score is the sum of all prediction scores over all paths, and the class with the highest prediction score wins. • “Subgraph census” – classify each network by exhaustive
search for is sh wn in Fig. 2. A gi subgraphs Dup tpto aaeagivenedsize.re(“Motifs”)
the A T ou uts r lvalued pr iction sco , which is the sum
A n example of an ADT all opossible ven net work’s
subg raph c ounts deter mine paths in the ADT dict ated by
inequalities specified by the decision nodes (rect angles) (subg raphs associated w ith Fig. 2 are shown in Fig. 3). For each class, of all weights over all paths. The class w ith the highest sc ore w ins.
The prediction sc ore y ( c ) for class c is related to the probabilit y
p ( c ) for the tested net work to be in class c by p ( c ) e 2y(c) ( 1
e 2y(c)) (42). (The supporting infor mation gives additional det ails
on the exact learn ing algorithm. Source c ode is available f rom
C.H.W. on request.)
A n advant age of ADTs is that they do not assume a specific
geometr y of the input space; that is, features are not c oordinates
in a metric space (as in support vector machines or k nearestneighbors classifiers), and the classification is thus independent
of nor malization. The algorithm assumes neither independence
nor dependence among subg raph c ounts. The subg raphs reveal
their import ance themselves solely by their abilities to discriminate among dif ferent classes. • Classify each of the 7 mechanisms by raw subgraph counts. Fig. 3. Subgraphs associated with Figs. 2 and 4. Shown is the subset of 51 Results
We per for m crossvalidation (ref. 13 and supporting infor mation) w ith multiclass ADTs, thus deter min ing an empirical
estimate of the generalization error, i.e., the probabilit y of
mislabeling an unseen test datum. Table 1 relates tr uth and
prediction for the test sets. Five of seven classes have nearly
per fect p...
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 Winter '11
 RaissaD'Souza

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