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anytime algorithms for learning anytime classifiers saher ... - Technion

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<strong>Technion</strong> - Computer Science Department - Ph.D. Thesis PHD-2008-12 - 2008<br />

Average Size<br />

Average Accuracy<br />

180<br />

160<br />

140<br />

120<br />

100<br />

80<br />

60<br />

40<br />

20<br />

IIDT(0.1)<br />

Skewing<br />

Sequential Skewing<br />

0<br />

0 1 2 3 4 5 6 7<br />

100<br />

90<br />

80<br />

70<br />

60<br />

50<br />

Time [sec]<br />

IIDT(0.1)<br />

Skewing<br />

Sequential Skewing<br />

Bagging-ID3<br />

Bagging-LSID3<br />

0 1 2 3 4 5 6 7<br />

Time [sec]<br />

Figure 3.34: Anytime behavior of modern learners on the Multiplexer-20 dataset<br />

its results separately later in this section.<br />

The graphs <strong>for</strong> the first 2 problems, which are known to be hard, show that<br />

IIDT clearly outper<strong>for</strong>ms the other methods both in terms of tree size and accuracy.<br />

In both cases IIDT reaches almost perfect accuracy (99%), while bagging-<br />

ID3 and skewing topped at 55% <strong>for</strong> the first problem and 75% <strong>for</strong> the second.<br />

The inferior per<strong>for</strong>mance of bagging-ID3 on the XOR-5 and Multiplexer-20<br />

tasks is not surprising. The trees that <strong>for</strong>m the committee were induced greedily<br />

and hence could not discover these difficult concepts, even when they were combined.<br />

Similar results were obtained when running bagging over C4.5 and RTG.<br />

However, when our LSID3(r = 1) was used as a base learner, per<strong>for</strong>mance was<br />

significantly better than that of the greedy committees. Still, IIDT per<strong>for</strong>med<br />

significantly better than bagging-LSID3, indicating that <strong>for</strong> difficult concepts, it<br />

is better to invest more resources <strong>for</strong> improving a single tree than <strong>for</strong> adding more<br />

trees of lower quality to the committee.<br />

67

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