Quantum Bayesian Networks

April 30, 2017

I don’t use plates to eat Bayesian networks

Filed under: Uncategorized — rrtucci @ 2:02 am

I am referring here to the “plates” used by some to draw Bayesian networks. Here is why I don’t like them. Consider this diagram given as an example by the Wikipedia article on plate notation. In this diagram, I would replace
\theta by \theta^{M}, z by z^{NM}, and w by w^{NM}. F*** (forget) the plates.

This aversion of mine to plates is related to the following idiosyncratic notation of mine.

In computer code, I like to use x\_ for a random variable x and vx for a vector of N observations x. (In a latex document I might use \underline{x} for a random variable and \underline{x}^N for the N observations.)

A vector of x measurements vx is like a primitive version of the random variable x\_. In fact, from vx one can get an empirical distribution P_{emp}(x) which approximates the true distribution P(x) which defines the random variable x\_. That’s why when I see a statement like x\_ \sim P(x), I think of this as an ordinary equivalence relation. In fact,

x\_ \sim vx \sim P_{emp}(x) \sim  P(x)

are all equivalent in the limit of a large number of observations.

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