Audio note: this article contains 65 uses of latex notation, so the narration may be difficult to follow. There's a link to the original text in the episode description.

Suppose two Bayesian agents are presented with the same spreadsheet - IID samples of data in each row, a feature in each column. Each agent develops a generative model of the data distribution. We'll assume the two converge to the same predictive distribution, but may have different generative models containing different latent variables. We'll also assume that the two agents develop their models independently, i.e. their models and latents don't have anything to do with each other informationally except via the data. Under what conditions can a latent variable in one agent's model be faithfully expressed in terms of the other agent's latents?

Let's put some math on that question.

The n “features” in the data are random [...]

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Outline:

(02:37) The Main Argument

(05:27) Approximation

(06:47) Why Is This Interesting?

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

The original text contained 5 images which were described by AI.

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First published:

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Narrated by TYPE III AUDIO.

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