A theory of learning from different domains
本文要解決的問題
- 在什麼條件下,由源域訓練的分類器能在目標域上取得很好的效果
- 鑑於目標域中只有少量的標記資料,在訓練過程中,我們應該怎樣利用擁有大量已標記資料的源域使得在測試的時候目標誤差最低。
相關概念
1.域適應(domain adaptation)
域適應模型
我們考慮二分類的域適應問題。
定義領域為分佈D,輸入X,標籤函式f:X→[0,1].源域<DS,fS
源域和目標域誤差估計
在源域上訓練一個分類器,計算這個分類器在目標域上的泛化誤差。
我們用L1來衡量兩個分佈之間的差異d1(D,D′)=2B∈Bsup∣PrD[B]−PrD′[B]∣其中B是D和D′的可測子集。
定理一:對任意假設函式h,ϵT(h)≤ϵS(h)+d1(DS,DT)+min{EDS[∣fS(x)−fT(x)∣],EDT[∣fS(x)−fT(x)∣]}.
證明: 令ϵT(h)=ϵT(h,fT),ϵS(h)=ϵS(h,fS)。記DS和DT的概率密度函式為ϕS和ϕT
ϵT(h)=ϵT(h)+ϵS(h)−ϵS(h)+ϵS(h,fT)−ϵS(h,fT) ≤ϵS(h)+∣ϵS(h)−ϵS(h)∣+∣ϵS(h,fT)−ϵS(h,fT)∣ =ϵS(h)+∣EX∼DS[∣h(x)−fT(x)∣]−EX∼DS[∣h(x)−fS(x)∣]∣+∣∣EX∼DT[∣h(x)−fT(x)∣]−∣EX∼DS[∣h(x)−fT(x)∣]∣ ≤ϵS(h)+EX∼DS[∣fS(x)−fT(x)∣]+∫∣ϕS(x)−ϕT(x)∣∣h(x)−fT(x)∣dx ≤ϵ
本文要解決的問題
在什麼條件下,由源域訓練的分類器能在目標域上取得很好的效果
鑑於目標域中只有少量的標記資料,在訓練過程中,我們應該怎樣利用擁有大量已標記資料的源域使得在測試的時候目標誤差最低。
相關概念
1.域適應(domain adaptation)
域 We sometimes just want to return a couple of elements next to one another from a React functional component, without adding a wrapper component which only
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要想聽懂這一段,先準備一點基礎知識:
Tishby另一個視訊,介紹的更詳細一點。
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2. 假設空間:Hypoth
回看前幾篇筆記發現我剪貼的公式顯示很亂,雖然編輯時調整過了,但是不知道為什麼顯示的和編輯時的不一樣,為方便大家的閱讀,我開始嘗試著採用markdown的形式寫筆記,前幾篇有時間的話再修改。
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author by Yubo Feng.
Intro
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During such trial-and-error processes of sensorimotor learning, a bird remembers not just the best possible command, but a whole suite of possibilities, s A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as
Summary
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