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I have this simple code to do a regression on a list of points very close to a parabole. It is purely anecdotal that I happen to know the exact underlying trend, the idea is just to have simple/nice synthetic data. The eventual goal is to do regressions with data whose underlying trend is not known.

   Table[x -> {x, x^2 + RandomReal[{-0.9, 0.9}]}, {x, -5., 5., 0.5}];

net = NetChain[{20, Tanh, 2}];

trained = NetTrain[net, data, BatchSize -> 20]

Show[ListPlot[{Flatten[Table[trained@{x}, {x, -4., 4., 0.25}], 1], 
   data[[All, 2]]}], 
 Plot[x^2, {x, -4., 4.}, PlotStyle -> Darker[Green]]]

Is there a more compact / advisable way to do something equivalent using ports? I ask this because that seems the way to go to include weights (https://reference.wolframcloud.com/language/tutorial/NeuralNetworksExampleWeighting.html.en)

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  • $\begingroup$ If you just want to do a simple (or even a complicated) regression, then just try data = Table[{x, x^2 + RandomReal[{-0.9, 0.9}]}, {x, -5., 5., 0.5}]; lmf = LinearModelFit[data, {x, x^2}, x]. That will give you the ability to look at goodness-of-fit statistics. $\endgroup$
    – JimB
    Commented Sep 5 at 16:56
  • $\begingroup$ Sure, colleagues and I have a lengthy MCMC of our own that would do this, the point is to explore the capabilities of machine learning for forecasts. I am using data for which I now the curve to which they fit just to see at a glance the goodness of fit. But I want to move forward to do regressions of which I do not know the underlying trend (cosmology stuff). I will edit the question thus. $\endgroup$
    – Ruth Lazkoz
    Commented Sep 5 at 17:01
  • $\begingroup$ Machine learning can certainly be useful but with a little thought might not be necessary or even appropriate for small amounts of data like your example. You might consider Mathematica's FindFormula function when you want to find a general fit that describes the data rather than explaining the data. $\endgroup$
    – JimB
    Commented Sep 5 at 17:09
  • $\begingroup$ The real peoblem has 2000 data with uncertainty. I could use my own mcmc.My question is concerned with mathematica syntax, not with best regresión approaches in general. I could also code a Gaussiana processes test. I will wsit the question again to make.it clearer. $\endgroup$
    – Ruth Lazkoz
    Commented Sep 5 at 17:42

1 Answer 1

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This is an answer to my question:

data = Flatten@
   Table[x -> {x, x^2 + RandomReal[{-0.9, 0.9}]}, {x, -5., 5., 0.5}];

net = NetChain[{20, Tanh, 2}];

dataset = <|"Input" -> #[[All, 1]], "Output" -> #[[All, 2]]|> &;

trained = NetTrain[net, dataset[data], BatchSize -> 20]

Show[ListPlot[{Flatten[Table[trained@{x}, {x, -4., 4., 0.25}], 1], 
   data[[All, 2]]}], 
 Plot[x^2, {x, -4., 4.}, PlotStyle -> Darker[Green]]]
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