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Well a random variable is a function, from event space to the real line. We return to a single measure by taking its expectation. We dont model `Y = f(X)`. Thi
by mjburgess 5y ago
Well a random variable is a function, from event space to the real line. We return to a single measure by taking its expectation. We dont model `Y = f(X)`.
This doesn't play well with the universal theorem in the article. NNs can only be said to model expectations of random variables.
- thfuran 5y ago>We return to a single measure by taking its expectation Only if you want to throw away most of the information in your model.
- deleted 5y ago[deleted]
- mjburgess 5y agoWell, indeed. One then needs to explain how a NN being a "universal fn approximator" helps at all in this context. One models RVs generativey using distributions (and so on), the actual model (eg., of house prices) isnt a function, it's often an infinity of them.
- thfuran 5y ago>One then needs to explain how a NN being a "universal fn approximator" helps at all in this context. Given that I can't tell why you don't think it does, I don't think I can explain it to you. From the other contexts you've talked about here, you seem to be implying that the only thing that is potentially useful is an AGI which either carries out or merely designs experiments. But that's patently absurd.
- mjburgess 5y agoI'm happy to hear the very narrow case on this. Can a NN learn geometric Brownian motion?