How can I evaluate the complexity of a model taking trinomial variables as input and a binary variable as output?
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If I have an input of let's say 3 variables. They can either be 1 (win), 0 (draw) and -1 (loss) and fed to a model M produce some binary output 0 (predicts loss) or 1 (predicts win). How can I go about assessing the complexity of model M? I thought about representing all inputs and their produced output of a given model as a tree structure and then using that tree to assess the complexity. For example, a strategy that is compensatory will say 1 after the first variable is a 1 and does not evaluate the other variables any more. A simple counting strategy would say 1 after the first two variables were a 1 as the third one does not matter any more. For a logistic regression, I would predict all outputs for all possible input combinations, build a tree and again assess the complexity. How can I get the complexity for any given model in that case? There surely has to be a better way than using the suggested tree approach...
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Answer:
I'm trying to get an idea of what you're actually trying to do. If you only have inputs win, draw, or lose and are trying to predict wins... what's the context? Are those wins, draw or lose in the past? Under the exact same circumstances? If not, why are you not listing the other inputs? Why are you not including draws in the prediction? As to any given model, the actual complexity depends on the model, the implementation, and the data. There is no generic way to judge complexity (that I am aware of) without comparing all of these together. If you would care to update your question or comment, I can see if I can update my answer.
Justin Veenstra at Quora Visit the source
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