機器學習介紹 (Machine learning introduction)

• $X$: feature domain (input), $Y$ range (output)

• $f: X \rightarrow Y$, 將資料由feature轉換到classification (如果$Y \in \mathbb{R}$為regression)的函數，其解析形式未知，只有部份資料集合$D$被觀測到。

• 假設資料集合$D$的特徵$\{ x_1, x_2, \cdots, X_N\}$的定態(stationary)機率分佈為$P$。

• 訓練資料的由未知的資料分佈$P$隨機抽取樣本而產生$\mathbf{x} = \{x_1, x_2, \cdots, x_N\}$，然後$\mathbf{x}$及其目標值$y$被提供給學習器，學習器在學習目標函數$f$時的定義域為假設集合$H$ (set of function)。

• 在觀察了一系列訓練資料$\mathbf{x}$後，學習器需要從假設集合$H$中得到最終的假設(函數)$g$，這是對資料集合$D$未知分佈的目標函數$f$的理想估計函數。

• 最後，我們通過訓練出來的假設$g$對$X$中新的資料的性能來評估訓練器(leave-one-out, K-fold cross-validation or other unobserved samples)。

Example: 核定信用卡問題

• 以下為某個使用者的個人信用資料，請問是否應核準其信用卡的申請?

• 因此input $x = \lbrace 23, female, 1000000, 1 year, 3 year, 200000 \rbrace$.
  • output $y = 1$：核準， $y=0$：拒絕。
  • unknown target function $f: x \rightarrow y$.
  • hypothesis: $g: x \rightarrow y$.
  • 目標是使機器學習模型的函數 $h$逼近未知的真正目標函數 $f$.

Machine learning and data mining

• ML: use data to compute hypothesis that approximates target f.

• DM: use (huge) data to find property that is interesting.

• If "interesting property" == "hypothesis that approximate target"

  • then ML == DM

Machine learning and artificial intelligence

• AI: compute something that shows intelligent behavior.

• g approximates f is something that shows intelligent behavior

  • ML can realize AI, among other routes.
  • eg. chess playing.

Machine learning and statistics

• statistics: use data to make inference about an unknown process.

• g is an inference outcome;

  • f is something unknown
  • statistics can be used to achieve ML
  • traditional statistics also fcous on provable results with math assumptions, and care less about computation.