This is one of my favorite posts because it gives me tools that I expect to use.
A little while ago, John described his natural latent result to me. It seemed cool, but I didn’t really understand how to use it and didn’t take the time to work through it properly. I played around with similar math in the following weeks though; I was after a similar goal, which was better ways to think about abstract variables.
More recently, John worked through the natural latent proof on a whiteboard at a conference. At this point I felt like I got it, including the motivation. A couple of weeks later I tried to prove it as an exercise for myself (with the challenge being that I had to do it from memory, rigorously, and including approximation). This took me two or three days, and the version I ended up with used a slightly different version of the same assumptions, and got weaker approximation results. I used the graphoid axioms, which are the standard (but slow and difficult) way of formally manipulating independence relationships (and I didn’t have previous experience using them).
This experience caused me to particularly appreciate this post. It turns lots of work into relatively little work.
This is one of my favorite posts because it gives me tools that I expect to use.
A little while ago, John described his natural latent result to me. It seemed cool, but I didn’t really understand how to use it and didn’t take the time to work through it properly. I played around with similar math in the following weeks though; I was after a similar goal, which was better ways to think about abstract variables.
More recently, John worked through the natural latent proof on a whiteboard at a conference. At this point I felt like I got it, including the motivation. A couple of weeks later I tried to prove it as an exercise for myself (with the challenge being that I had to do it from memory, rigorously, and including approximation). This took me two or three days, and the version I ended up with used a slightly different version of the same assumptions, and got weaker approximation results. I used the graphoid axioms, which are the standard (but slow and difficult) way of formally manipulating independence relationships (and I didn’t have previous experience using them).
This experience caused me to particularly appreciate this post. It turns lots of work into relatively little work.