  Machine learning techniques typically rely on large datasets to create
accurate classifiers. However, there are situations when data is scarce and
expensive to acquire. This is the case of studies that rely on state-of-the-art
computational models which typically take days to run, thus hindering the
potential of machine learning tools. In this work, we present a novel
classifier that takes advantage of lower fidelity models and inexpensive
approximations to predict the binary output of expensive computer simulations.
We postulate an autoregressive model between the different levels of fidelity
with Gaussian process priors. We adopt a fully Bayesian treatment for the
hyper-parameters and use Markov Chain Mont Carlo samplers. We take advantage of
the probabilistic nature of the classifier to implement active learning
strategies. We also introduce a sparse approximation to enhance the ability of
themulti-fidelity classifier to handle large datasets. We test these
multi-fidelity classifiers against their single-fidelity counterpart with
synthetic data, showing a median computational cost reduction of 23% for a
target accuracy of 90%. In an application to cardiac electrophysiology, the
multi-fidelity classifier achieves an F1 score, the harmonic mean of precision
and recall, of 99.6% compared to 74.1% of a single-fidelity classifier when
both are trained with 50 samples. In general, our results show that the
multi-fidelity classifiers outperform their single-fidelity counterpart in
terms of accuracy in all cases. We envision that this new tool will enable
researchers to study classification problems that would otherwise be
prohibitively expensive. Source code is available at
https://github.com/fsahli/MFclass.
