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Monte Carlo accelerator and residual approximator with k-nearest neighbors

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LearnAsYouGoEmulator

Python implementation of the k-nearest neighbors Monte Carlo accelerator published in http://arxiv.org/abs/arXiv:1506.01079.

The basic usage of the emulator code should be something like this:

@emulator def loglike(x): if x.ndim!=1: loglist = [] for x0 in x: loglist.append(-np.dot(x0,x0)) return np.array(loglist) else: return np.array(-np.dot(x,x))

This decorates any Python scalar function and loglike is now an instance of the emulator class, where the call(x) function acts similarly to the loglike(x) function definition above. However, it now has the ability to train a k--nearest neighbors emulator using loglike.train(...), which makes a separate emulation routine that will be called first anytime loglike(x) is evaluated.

We learn both the output of loglike(x) and the difference between the emulator and the true value of loglike(x) so that we can make a prediction for the error residuals. We then put a cutoff on the amount of absolute (or fractional) error that one will allow for any local evaluation of the target function. Any call to the emulator(x) that has a too-large error will be discarded and the actual function loglike(x) defined above will be evaluated instead.

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