In gbonte/gbcode: Code from the handbook "Statistical foundations of machine learning"

Shiny dashboard "Statistical foundations of machine learning"

Conditional independence

From marginal dependence to conditional independence

The first tab visualizes the relation between two random variables $x$ and $y$ where

$$y=az+w_y$$ and $$x=bz+w_x$$ where $w_z$ and $w_y$ are Gaussian independent noise terms. The two variables are strongly correlated (then dependent) as shown by the slope of the black line.

Once we condition on $z$ instead, we focus on the red points (satisfying the condition on $z$) only and the two variables become conditionally independent (slope close to zero).

From marginal independence to conditional dependence

The first tab visualizes the relation between two independent random variables $x$ and $y$ as shown by the horizontal black line. Let $$ z =a x +b y +w_z $$ a third random variable.

If we condition on a value of $z=\bar{z}$ (focus on red points satisfying the condition on $z$ ) we see that we create a strong correlation between $x$ and $y$ as illustrated by the red line (slope different from zero).

gbonte/gbcode documentation built on Feb. 27, 2024, 7:38 a.m.