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I am using XGBoost for a classification problem. The model has multiple inputs and a probability as output.

For simplicity's sake, let's say the model only has one continous input and the function to be learned is f(x) = x.

I am creating training samples for it using the f(x) = x relationship. Of course, in reality, I cannot create an endless amount of training samples and am restricted by the given data set.

The model output would look something like this:

enter image description here

As can be seen, the model predictions are noisy. As the x variable goes from 0 to 1, the y variable jitters around the true relationship. I would want to reduce / penalize this jitter. For every delta x, I want to to keep the delta y as small as possible but as high as necessary. Are there any model parameters to do this? Of course, I can just smooth the predictions ex post but I'd like to tell it to the model directly to make the smoothness vs. optimal prediction trade-off.

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  • $\begingroup$ You can use regularization, such as lambda in XGBoost, although you will still not get a diagonal line but a step function (if using trees). $\endgroup$ Nov 15, 2023 at 12:11
  • $\begingroup$ I have tried this (sweeped all sensible regularization parameter combinations). Unfortunately, the effect is a 1-1 trade-off with out-of-sample prediction accuracy and therefore not feasible. $\endgroup$
    – Neo
    Nov 15, 2023 at 15:45
  • $\begingroup$ In that case maybe the relationship is not as smooth as you think. If the relationship is truly smooth have you tried using a linear model with appropriate terms? $\endgroup$ Nov 15, 2023 at 15:49
  • $\begingroup$ I am quite sure it is smooth but not linear. A neural network creates a smoother prediction, however, I would prefer a tree based model if possible. $\endgroup$
    – Neo
    Nov 15, 2023 at 15:55
  • $\begingroup$ Trees cannot create smooth functions, it's a feature. If you want smooth you need to look elsewhere. If you know the nature of the relationship, say quadratic, you could add this variable to the model and it might help. $\endgroup$ Nov 15, 2023 at 16:00

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