因果推論 (Causal Inference)

This is the sixth post on the series we work our way through “Causal Inference In Statistics” a nice Primer co-authored by Judea Pearl himself.

這是本系列的第六篇文章，我們將通過Judea Pearl本人與他人合著的《引誘統計學中的因果關系》一書進行介紹。

Amazon Affiliate Link 亞馬遜會員鏈接

You can find the previous post here and all the we relevant Python code in the companion GitHub Repository:

您可以在此處找到相關的上一篇文章以及相關的GitHub存儲庫中所有與我們相關的Python代碼：

While I will do my best to introduce the content in a clear and accessible way, I highly recommend that you get the book yourself and follow along. So, without further ado, let’s get started!

盡管我會盡力以清晰易懂的方式介紹內容，但我強烈建議您自己拿書并繼續學習。 因此，事不宜遲，讓我們開始吧！

In the previous post V, we started on Chapter II of the book where Pearl starts to build up the machinery of Causal Inference. In this post we look at Colliders, one of the most powerful ideas in the analysis of graphical models.

在上一篇文章V中 ，我們從書的第二章開始，Pearl開始建立因果推理的機制。 在這篇文章中，我們看一下碰撞器，它是圖形模型分析中最強大的想法之一。

2.3對撞機 (2.3 Colliders)

The third, and perhaps the most important, graph motif that we will cover is known as the Collider and is illustrated in this figure:

我們將介紹的第三個(也許是最重要的)圖形圖案稱為Collider，如下圖所示：

Fig. 2.3 — A simple collider圖2.3 —一個簡單的對撞機

Collider nodes are nodes that receive inputs from 2 or more other variables. Applying the rules we are already familiar with, we can immediately conclude:

對撞機節點是從2個或更多其他變量接收輸入的節點。 應用我們已經熟悉的規則，我們可以立即得出結論：

X and Z are dependent — P(X|Z) ≠ P(X)

X和Z是依賴的 -P(X | Z)≠P(X)

Y and Z are dependent — P(Y|Z) ≠ P(Y)

Y和Z是依賴的 -P(Y | Z)≠P(Y)

X and Y are independent — P(X|Y) =P(X)

X和Y是獨立的 -P(X | Y)= P(X)

X and Y are dependent conditional on Z — P(X|Y, Z) ≠ P(X|Z)

X和Y取決于Z — P(X | Y，Z)≠P(X | Z)

Points 1 and 2 follow directly from Rule 0: Any two variables with a directed edge between them are dependent. Point 3 is obvious from the fact that there is no directed path between X and Y (neither is an ancestor or a descendent of the other).

點1和2直接從規則0得出：在它們之間有向邊的任何兩個變量都是相關的。 從X和Y之間沒有定向路徑的事實可以明顯看出第3點(兩者都不是祖先或后代)。

Point 4 is the most interesting case, but it can be understood with a simple algebraic example. Consider the mathematical expression:

點4是最有趣的情況，但是可以通過一個簡單的代數示例來理解。 考慮一下數學表達式：

This relationship determines the value of Z and is valid for any possible value of X and Y, but as soon as I fix the value of Z, say Z=10 that immediately limits the possible values of X and Y that are now constrained such that, Y = 10-Z (or, graphically, lie on the intersection of the two Z=X+Y and Z=10 planes):

此關系確定Z的值，并且對于X和Y的任何可能值均有效，但是一旦我確定Z的值，則說Z = 10立即限制了現在受約束的X和Y的可能值，從而，Y = 10-Z(或以圖形方式位于兩個Z = X + Y和Z = 10平面的交點上)：

The effect of conditioning on a collider node, Z條件對撞節點Z的影響

This is a simple illustration of the most fundamental definition of conditioning: filtering by the value of the conditioning variable.

這是對調節的最基本定義的簡單說明：通過調節變量的值進行過濾。

The book further illustrates this idea using the example of the well known Monty-Hall problem. For this game, our probability table would be:

本書以著名的蒙蒂·霍爾(Monty-Hall)問題為例進一步說明了這一想法。 對于這個游戲，我們的概率表將是：

Where the 0.0555 values correspond to the fact that we give Monty a 50/50 chance of choosing either goat if I happen to choose the door where the car is.

0.0555的值對應的事實是，如果我碰巧選擇了汽車所在的門，我們給Monty 50/50的機會選擇任一只山羊。

From this table, it’s easy to see that P(Choice|Car)=P(Car), or, in other words:

從此表中，很容易看出P(Choice | Car)= P(Car)，或者換句話說：

Essentially, I’m choosing one of the three doors at random. Now, let’s take a look at P(Choice | Car, Monty):

本質上，我是隨機選擇三個門之一。 現在，讓我們看一下P(Choice | Car，Monty)：

Where it is now clear that depending on the door that Monty has chosen, the value of P(Choice | Car) will change.

現在很明顯，根據Monty選擇的門，P(Choice | Car)的值將改變。

This is also a clear example of a non-causal dependency between two variables, illustrating the point that correlation does not imply causation. Here the relationship between the two variables (Car and Choice) comes about just due to the fact that we limited our space of possibilities by adding the extra information about Monty’s choice. An event that is already familiar to us from our discussion of Bayes Theorem.

這也是兩個變量之間的非因果關系的一個清晰示例，說明了相關性并不意味著因果關系。 在這里，這兩個變量(汽車和選擇)之間的關系恰好是由于我們通過添加有關蒙蒂選擇的額外信息來限制可能性的事實。 通過貝葉斯定理的討論，我們已經很熟悉這一事件。

From these examples, it is easy to extract a new general rule:

從這些示例中，很容易提取出一條新的通用規則：

Rule 3 (Conditional Independence in Colliders): If a variable Z is the collision node between two variables X and Y, and there is only one path between X and Y, then X and Y are unconditionally independent but are dependent conditional on Z and any descendents of Z.

規則3(碰撞者的條件獨立性)：如果變量Z是兩個變量X和Y之間的碰撞節點，并且X和Y之間只有一條路徑，則X和Y是無條件獨立的，但取決于Z和任何其他條件Z的后代。

Congratulations on following along yet another blog post on this series series. I sincerely hope that you continue to enjoy reading them as much as I enjoy writing them.

祝賀您關注本系列文章的另一篇博客文章。 我衷心希望您繼續喜歡閱讀它們，就像我喜歡寫它們一樣。

Just a quick reminder that you can find the code for all the examples above in our GitHub repository:

謹在此提醒您，您可以在我們的GitHub存儲庫中找到上述所有示例的代碼：

And if you would like to be notified when the next post comes out, you can subscribe to the The Sunday Briefing newsletter:

而且，如果您希望在下一篇文章發表時得到通知，可以訂閱《星期日簡報》時事通訊：

翻譯自: https://medium.com/data-for-science/causal-inference-part-vi-colliders-af07301c9a15

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