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If you have a large number of correlated response variables, each with its own set of predictors, but you think the relationship of the response to the predictors is the same for all predictors, what neural network architecture should be used? This differs from the case where all responses have the same inputs.

For example, if for 1000 stocks over 5 years you predict monthly returns each month using the 12-month return of each stock and the price/earnings ratio of each stock, you have 5*12 = 60 observations. Each observation has 1000 responses with 2 predictors for each response. Stock returns are positively correlated to each other, so the responses cannot be assumed independent.

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  • $\begingroup$ From your exemple, i can't see why you would assume that "the relationship of the response to the predictors is the same for all predictors". If you are going to do stock analysis may I suggest you to try some more basic time series analysis ? Quantitative finance is a field in itself (and even has it own stack exchange website). $\endgroup$ – lcrmorin Jan 5 at 9:26
  • $\begingroup$ In the example I gave, using the same model for all stocks results in a factor of 1000 fewer parameters, so imposing this constraint is a form of regularization. $\endgroup$ – Fortranner Jan 6 at 11:17
  • $\begingroup$ Do you mean that the relationship of the response to the predictors is the same for all stocks ? $\endgroup$ – lcrmorin Jan 6 at 15:16
  • $\begingroup$ Yes, I am willing to assume that the "relationship of the response to the predictors is the same for all stocks". One could test out-of-sample whether this works better than fitting a different model for each stock. $\endgroup$ – Fortranner Jan 6 at 18:57

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