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This is probably a broad question, but I am interested to know if there are any studies that throw some light on this question:

If I have to train regression models (in the least-squared sense), how do various modeling techniques (e.g., OLS, L1/L2 regularised least-squares, neural networks, etc.) compare with respect to each other from a computational speed vs model quality (some measure of out-of-sample prediction error)?

Put another way, for a given data set, CPU resources, how much additional processing time would I need to train a broad class of neural networks to get the same/better performance as a simple OLS/L2 regularised regression?

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  • $\begingroup$ I don't think it's realistic to seek an answer to this question quite the way you've asked it. After all, it's not as if there is a single, standard way to design each type of model -- OLS, NN, etc. To take advantage of the capabilities of each approach, one will want to work on model specification, which might involve transformed variables, interaction terms, penalization, etc. Obtaining good predictive accuracy requires a lot of thought and can seldom be achieved by rote application of tools. In spite of what some users of the SAS or SPSS data mining/modeler tools might say. $\endgroup$
    – rolando2
    Feb 8, 2018 at 19:10
  • $\begingroup$ If we were to abstract out the prediction process to finding a good estimator $f$ that minimises $(y - f(x))^2$, then there can be various model approaches to $f$ (OLS, NN, etc.), each with its own computation and performance tradeoffs. OLS with interaction terms, penalty, etc., can be thought of as a new modeling approach to $f$ that includes a broader class of functions, definitely requiring more computation, possibly with better performance. It is precisely that tradeoff that I would like to understand. $\endgroup$
    – Vimal
    Feb 8, 2018 at 21:09

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