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I am looking for ways to calculate confidence interval of the prediction given by the following algorithms:

  1. Support Vector Regression
  2. K-Nearest Neighbor Regression
  3. Random Forest Regression
  4. Polynomial Regression (Polynomial Features in scikit-learn followed by Linear Regression)

Just to clarify, suppose $\hat{y}$ is the estimate of $y$, where $y$ is the output variable and $x = [x_1, x_2, x_3,...,x_N]$ is the input variable. I would like to get the confidence interval of $\hat{y}$ from the above algorithms.

So far, I have found the followings:

  1. Bootstrapping confidence interval from a regression prediction
  2. CONFINE & CONFIVE: article can be downloaded here.

I am new to this topic and looking for a comprehensive list of alternatives with pros and cons.

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I am also new to this area, but I would like to share with some results on random forest. You could use Gradientboost in sklearn to generate percentile results. Also forestci could give you the standard deviations of your predictions. It would be nice if someone could answer the related questions for SVR.

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