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I have been evaluation various regression techniques over a regression dataset . I am surprised by the fact that cross-validated RMSE of Lasso is better than SVM and Random Forest in my case.

Can this happen? I believed that a non-linear modelling technique like random forest or SVM would do better than a linear model like Lasso.

Is that really possible!?

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    $\begingroup$ Could you please add "on one example" to the title, and give some details on it ? $\endgroup$
    – denis
    Commented Apr 26, 2012 at 17:05
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    $\begingroup$ The explanation for this is called "no free lunch theorem" (for machine learning). :) $\endgroup$
    – alfa
    Commented Apr 26, 2012 at 21:18
  • $\begingroup$ @whuber: It says "Lasso" not "Loess" as in your comment! $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jan 4, 2017 at 23:54
  • $\begingroup$ @kjetil check out the edit history! $\endgroup$
    – whuber ♦
    Commented Jan 5, 2017 at 1:30
  • $\begingroup$ @whuber: will do ... must learn to do it first $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jan 5, 2017 at 1:31

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There is no perfect algorithm. I believe Loess, at least as implemented in R, is limited to ~4 features. Given so few features, the overhead of RandomForests or SVM-regression is likely wasted. It might be that the intrinsic scaling of the data is important and the RandomForest loses that in it's trees. For the SVM it could easily be the difficulty in properly tuning it or choosing the right kernel. If the relationship is simple enough, you don't need to expand in the faux-infinite dimensions of kernel space to understand it.

Having said that, just because Loess is better in this particular training set via cross-validation, that doesn't mean it will always be better. All models are just approximations.

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  • $\begingroup$ My bad--- It is Lasso and not Loess. Please give your views on a Lasso vs SVM- setting, instead of Loess. Apologies. $\endgroup$
    – qlinck
    Commented Apr 26, 2012 at 12:47
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    $\begingroup$ Times when Lasso would be better: Many of the features are meaningless (Lasso does more feature selection than SVM or RandomForest). The relationships really are close to linear (RandomForest will struggle to approximate a linear releationship and SVMs will at least get all squiggly) There aren't any strong interactions (RF and SVM will waste resources looking for things that don't exist)... $\endgroup$
    – Shea Parkes
    Commented Apr 26, 2012 at 13:22
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A summary from this useful discussion at MetaOptimize regarding the general issue of L1 versus L2 regularization:

  • L1 (e.g. Lasso): choose for a sparse model / feature selection as Shea Parkes mentions above, especially when n >> m
  • L2 (e.g. SVM): choose when seeking rotational invariance and there are plenty of samples
  • L1+L2 (e.g. elastic-net): if you want to combine both
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Non-linear models are not necessarily better than linear models, in my work experience, generally non-linear models do better job in interpolation, linear models can do better job in extrapolation. Complex models can lead to overfitting issues. Anyway, you should choose your model based on your cross validation scores.

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