· edit view bookmarks go communicator location: da£tmout:il edu/wmontague/metasearch/metasea...
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4
The Metasearch Problem
Search for: chili peppers
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€
β ∈ 0,1[ ];N strategies (systems)
initial weights w1 ∈ 0,1[ ]N ; wi1
i=1
N
∑ =1
∑=
= N
i
ti
tit
i
w
wp
1
€
lt ∈ 0,1[ ]N tttH lpL ⋅=
tilt
iti ww β⋅=+1
∑ =⋅=
T
ttt
HEDGE lpL1
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β
β
−
+
≤1
ln1ln NLL
SYSTEMBEST
HEDGE
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11
+=
−=
TNONRELEVANRELEVANT
rZ
Zrrrvalue ln1...
111)( ≈+++
+=
rZdlabelrankvaluedlabelsdLOSS sd ln)()()(),( , ⋅≈⋅=
• map ranks to values
total loss vs. total precision vs. average precision
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)(
)(_
,1
1sd
N
s
ts
t
rankvaluew
dvalueaverage
⋅=
=
∑=
−
),(1 sdLOSSts
ts
ttww β⋅=+
)()(),( ,sdtt trankvaluedlabelsdLOSS ⋅=
( ))(_maxarg dvalueaveraged dt =