anytime algorithms for learning anytime classifiers saher ... - Technion
anytime algorithms for learning anytime classifiers saher ... - Technion
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 />
Procedure Choose-Node(T, E, A)<br />
Foreach node ∈ T<br />
rnode ← Next-R(node)<br />
costnode ← Expected-Cost(T, node)<br />
max-cost ← Expected-Cost(T, root)<br />
If (costnode/max-cost) > g<br />
Tnode ← Subtree(node)<br />
∆q ← Expected-Benefit(Tnode)<br />
unode ← ∆q/costnode<br />
best ← node that maximizes unode<br />
Return 〈best, rbest〉<br />
Figure 3.14: Choosing a node <strong>for</strong> reconstruction in IIDT<br />
Granularity. Considering the cost and benefit approximations described above,<br />
the selection procedure would prefer deep nodes (that are expected to have low<br />
costs) with large subtrees (that are expected to yield large benefits). When<br />
no such large subtrees exist, our algorithm may repeatedly attempt to improve<br />
smaller trees rooted at deep nodes because these trees have low associated costs.<br />
In the short term, this behavior would indeed be beneficial but can be harmful<br />
in the long term. This is because when the algorithm later improves subtrees in<br />
upper levels, the resources spent on deeper nodes will have been wasted. Had the<br />
algorithm first selected the upper level trees, this waste would have been avoided,<br />
but the time gaps between potential improvements would have increased.<br />
To control the tradeoff between efficient resource use and <strong>anytime</strong> per<strong>for</strong>mance<br />
flexibility, we add a granularity parameter 0 ≤ g ≤ 1. This parameter<br />
serves as a threshold <strong>for</strong> the minimal time allocation <strong>for</strong> an improvement phase.<br />
A node can be selected <strong>for</strong> improvement only if its normalized expected cost is<br />
above g. To compute the normalized expected cost, we divide the expected cost<br />
by the expected cost of the root node. Note that it is possible to have nodes<br />
with a cost that is higher than the cost of the root node, since the expected cost<br />
doubles the cost of the last improvement of the node. There<strong>for</strong>e, the normalized<br />
expected cost can be higher than 1. Such nodes, however, will never be selected<br />
<strong>for</strong> improvement, because their expected benefit is necessarily lower than the expected<br />
benefit of the root node. Hence, when g = 1, IIDT is <strong>for</strong>ced to choose<br />
the root node and its behavior becomes identical to that of the sequencing algorithm<br />
described in Section 3.6.1. Observe that IIDT does not determine g but<br />
expects the user to provide this value according to her needs: more frequent small<br />
improvements or faster overall progress.<br />
Figure 3.14 <strong>for</strong>malizes the procedure <strong>for</strong> choosing a node <strong>for</strong> reconstruction.<br />
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