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I have trained an SVM Regression model using training data, $x_1,x_2,\dots,x_N$.

I want to perform active learning to improve the model; i.e., I want to add more samples to the training data and relearn a better model, and to choose these new samples in such a way as to maximize the resulting model performance.

For an SVM classifier, a useful heuristic for active learning is to choose samples that fall close to the decision boundary; i.e., for a particular sample, the 'confidence' (c) can be computed using the SVM. Samples that have small |c| are more likely to improve the decision boundary in the retrained SVM.

Any suggestions on how to do this for SVM regression?

(I can generate samples at will, but it is costly to label them, so I want to know if I can use the 'already-trained' regression-SVM to help me decide which ones to label)

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Active learning requires a compromise between exploration and exploitation. If the model you have so far is bad, if you exploit this model to determine the best place to label mode data, it will probably suggest bad places to label the data as your current hypothesis is poor. It is a good idea to do some random exploration as well, as that is about the best way to ensure that eventually you will label the data that shows the current hypothesis to be incorrect.

For regression models, I would suggest that Gaussian Process regression is a better bet for active learning, as it gives you predictive error bars, so you can query the labels for points where the model is most uncertain. See for example this paper looks an interesting place to start.

I have worked on active learning in classification, and the results have been rather mixed for all strategies. Often just picking points randomly (i.e. all exploration, no exploitation) works best. I am looking into active learning for regression problems at the moment and intending to tse GPs, I'll add to my answer if I find out anything that seems to work better than exploration only.

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I have worked on active learning in classification and in SVM, that problem was same for me, if the boundary you found out by first model isn't that good the probability to have a good label for new points will decrease. If you have any other method to labelize your new generated points rather than using the boundary that can be a good way and your accuracy for the new generated boundary will be better.

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