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Old 01-12-2013, 10:52 AM
DaveS DaveS is offline
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Join Date: Jan 2013
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Default How to handle ambiguous target function, f

There are many occasions in engineering when the unknown target function f is being designed while a system to predict f is also being designed.

Let me give a concrete example. Suppose I am building a robotic system that builds widgets. I will deploy a machine vision system on my widget machine to classify different widgets as they are being built. I plan to use supervised learning to take features derived from possible widgets and learn a target function that will predict which widget the machine vision system is looking at. Unfortunately, my machine vision system isn't the highest priority part of the widget system. The systems engineer thinks there may be some shadows that I will have to contend with, and there may exist some bizarre lighting, which he has hasn't really nailed down yet. In other words, I'm not yet able to generate training data from the true f (which would be the final system that my systems engineer decides on). Still, my systems engineer wants me to tell him what an optimal f would be. That is, if I could choose an f to maximize the chances that my g approximates f really well, what should that f look like? (Let's assume that learning is necessary -- that is, no matter what we do f will not be something we can easily pin down mathematically)

So what do I do? Suppose that I go into the lab and build some mock-up machine vision systems. This is like constructing an f_possible that anticipates the true f. I generate samples from the mock-up, learn a g, and report back how well my g approximates f_possible. How can I take the results of this process to inform what f should be? It seems like this is the inverse problem from supervised learning. That is, I want to design my f so that g will approximate it very well.

I'm thinking out loud a bit here -- I'm trying to map this problem to the learning diagram and understand where it fits in. I appreciate any insight that might help clarify my thinking.
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