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

Technion - Computer Science Department - Ph.D. Thesis PHD-2008-12 - 2008
|SID3|=3
|SID3|=4
a
|SID3|=6
Figure 3.7: Attribute evaluation using LSID3. The estimated subtree size for a is
min(4, 3) + min(2, 6) = 5.
we have
|SID3|=2
Procedure LSID3-Choose-Attribute(E, A, r)
If r = 0
Return ID3-Choose-Attribute(E, A)
Foreach a ∈ A
Foreach vi ∈ domain(a)
Ei ← {e ∈ E | a(e) = vi}
mini ← ∞
Repeat r times
mini ← min (mini, |SID3(Ei, A − {a})|)
mini
Return a for which totala is minimal
totala ← � |domain(a)|
i=1
Figure 3.8: Attribute selection in LSID3
�n−1
r · (n − i) · O(m · (n − i)) =
i=0
n�
O(r · m · i 2 ) = O(r · m · n 3 ). (3.2)
i=1
According to the above analysis, the run-time of LSID3 grows at most linearly
with r (under the assumption that increasing r does not result in larger trees).
29