# 5.3 Accumulated Local Effects (ALE) Plot
## M-Plots
* 條件機率
* 參雜其他相關變數的效果
## ALE Plots
* 依照觀察變數的範圍，切成N段(Intervals)
* 將每個instances的變數值帶入所在區間的最大值和最小值，求其差
* 除以區間內的樣本數 --> 中心化 --> 相加
## ALE plots for 變數間的交互作用項
* Second-order effect : 只考慮交互作用項帶來的額外效果
## ALE plots for 類別變數
* 計算每個class之間的similarity --> 得到Distance Matrix --> 再利用MDS(Multi-Dimensional Scaling)將所有資料點降至一維
* 如何計算Similarity:
* 類別 vs 連續 ：ECDF (Empirical Cumulative Distribution Function)
* 什麼是ECDF: https://medium.com/ai反斗城/exploratory-data-analysis-探索資料-ecdf-7fa350c32897
* Kolmogorov-Smirnov distance

* 類別 vs 類別 ：relative frequency tables 列連表

## Differences
* Partial Dependence Plots: “Let me show you what the model predicts on average when each data instance has the value v for that feature. I ignore whether the value v makes sense for all data instances.”
* M-Plots: “Let me show you what the model predicts on average for data instances that have values close to v for that feature. The effect could be due to that feature, but also due to correlated features.”
* ALE plots: “Let me show you how the model predictions change in a small”window" of the feature around v for data instances in that window."
## Advantages
* 可以處理有關聯性的變數
* 計算速度較PDP快
* 解讀較易懂，由於ALE plots集中在0,條件機率下因子的變化較為明顯
## Disadvantages
* ALE plots can become a bit shaky (many small ups and downs) with a high number of intervals.
* 無法看到每一個因子異質性的影響效果
* Second-order ALE 在不同feature 隔窗的穩定性差異大，因為每一的隔窗的資料是不同的
* Second-order effect plots can be a bit annoying to interpret
* implementation of ALE plots is much more complex也較PDP不直覺

Use ALE instead of PDP.

## 參考資料
* https://www.yanxishe.com/TextTranslation/1627
* https://zhuanlan.zhihu.com/p/90217007
* https://medium.com/the-die-is-forecast/shining-a-light-on-the-black-box-of-machine-learning-2b49fe471cee
* https://kknews.cc/zh-tw/tech/3q3mz93.html
## Python Code
* https://github.com/blent-ai/ALEPython

###### tags: `重點摘要`