Winner-takes-all Learners Are Geometry-Aware Conditional Density Estimators

Winner-takes-all training is a simple learning paradigm, which handlesambiguous tasks by predicting a set of plausible hypotheses. Recently, aconnection was established between Winner-takes-all training and centroidalVoronoi tessellations, showing that, once trained, hypotheses should quantizeoptimally the shape of the conditional distribution to predict. However, thebest use of these hypotheses for uncertainty quantification is still an openquestion.In this work, we show how to leverage the appealing geometricproperties of the Winner-takes-all learners for conditional density estimation,without modifying its original training scheme. We theoretically establish theadvantages of our novel estimator both in terms of quantization and densityestimation, and we demonstrate its competitiveness on synthetic and real-worlddatasets, including audio data.