Audio note: this article contains 32 uses of latex notation, so the narration may be difficult to follow. There's a link to the original text in the episode description.

This post is a comment on Natural Latents: Latent Variables Stable Across Ontologies by John Wentworth and David Lorell. It assumes some familiarity with that work and does not attempt to explain it. Instead, I present an alternative proof that was developed as an exercise to aid my own understanding. While the original theorem and proof are written in the language of graphical models, mine instead uses the language of information theory. My proof has the advantage of being algebraically succinct, while theirs has the advantage of developing the machinery to work directly with causal structures. Very often, seeing multiple explanations of a fact helps us understand it, so I hope someone finds this post useful.

Specifically, we [...]

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Outline:

(01:55) New Theorem 1 (deterministic latents)

(02:38) Proof

(03:12) Old Theorem 1 (stochastic latents)

(03:59) Proof

The original text contained 1 footnote which was omitted from this narration.

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Narrated by TYPE III AUDIO.