Is probability verifiable?
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16-01-2014, 08:46 AM
RE: Is probability verifiable?
Well, all of reality is probabilistic on a fine scale. So there's that.

It seems to me your question is really more about the validity of modelling approaches?

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16-01-2014, 10:03 AM
RE: Is probability verifiable?
The basics of probability are made on explicit assumptions, for example the birthday problem is based on a specific flat statistical distribution of birthdays. When you ask how much the result would be affected if that assumption was incorrect in various ways then you are getting into sensitivity analysis[1] or are getting into a more complex mathematical model of the problem that will come out with different numbers. How different? It depends on the problem.

Local optima in neural network training are a pretty different class of problems. Instead of a simple well-behaved statistical function you're dealing with a many-dimensional optimisation problem. That heads into the territory of operations research[2] and other forms of optimisation. The reason we approach the training of networks in the way that we do is because the problem space is so large. We have to approach it heuristically and it's no wonder we can't tell if our optimum is local or global. All we can deal with is the question of whether our optimum is good enough to solve the engineering problem at hand.

[1] http://en.wikipedia.org/wiki/Sensitivity_analysis
[2] http://en.wikipedia.org/wiki/Operations_research

Give me your argument in the form of a published paper, and then we can start to talk.
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17-01-2014, 11:25 AM
RE: Is probability verifiable?
(16-01-2014 08:46 AM)cjlr Wrote:  Well, all of reality is probabilistic on a fine scale. So there's that.

It seems to me your question is really more about the validity of modelling approaches?

Yes. I think I haven't found a proper way to formulate my question, I need to think more clearly.
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