3 the nal score is the sum of all prediction scores

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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 l-valued 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 cross-validation (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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