  We introduce a new machine-learning-based approach, which we call the
Independent Classifier networks (InClass nets) technique, for the
nonparameteric estimation of conditional independence mixture models (CIMMs).
We approach the estimation of a CIMM as a multi-class classification problem,
since dividing the dataset into different categories naturally leads to the
estimation of the mixture model. InClass nets consist of multiple independent
classifier neural networks (NNs), each of which handles one of the variates of
the CIMM. Fitting the CIMM to the data is performed by simultaneously training
the individual NNs using suitable cost functions. The ability of NNs to
approximate arbitrary functions makes our technique nonparametric. Further
leveraging the power of NNs, we allow the conditionally independent variates of
the model to be individually high-dimensional, which is the main advantage of
our technique over existing non-machine-learning-based approaches. We derive
some new results on the nonparametric identifiability of bivariate CIMMs, in
the form of a necessary and a (different) sufficient condition for a bivariate
CIMM to be identifiable. We provide a public implementation of InClass nets as
a Python package called RainDancesVI and validate our InClass nets technique
with several worked out examples. Our method also has applications in
unsupervised and semi-supervised classification problems.
