[問題] 一題CTR 條件機率期望的問題
有遇到一題條件機率的預估問題
但不是很確定我的想法有無問題
題目有點長 懇請大家幫忙了
謝謝
A pair of items (s,t) where s represents the source and t represents the
target item.
ctr(s,t):= P(user will click on t when the target next to s)
In order help the company to estimate the CTR pairs, to create a heuristic
fucntion H(s,t), which return a number between 0 and 100 for any ordinal
pair of items.
Goal:
to estimate the following functions:
E(v):= E(ctr(s,t)|H(s,t) = v)
Var(ctr(s,t)|H(s,t) = v)
p.s
1.E(v) and Var(v) are piecewise constant functions and suppose to collect
the historical impressions and click counts for various values of v.
2.Definition of CTR = number of clicks / number of impressions
想法：
利用beta-binomial distribution的特性 去預估E(v) & Var(v)
但我不是很懂 在這邊要怎麼處理heuristic function H(s,t)
我可以假設 f(ctr(s,t) , h(s,t)) 服從beta-binomial distribution嗎？
之後再去分別算the estimation of E(v) & Var(v)
謝謝
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