Semi-supervised Conditional Density Estimation with Wasserstein Laplacian Regularisation

Conditional Density Estimation (CDE) has wide-reaching applicability to various real-world problems, such as spatial density estimation and environmental modelling. CDE estimates the probability of a random variable rather than single value can thus model uncertainty inverse problems. This task is inherently more complex regression, many algorithms suffer from overfitting, particularly when modelled with few labelled data points. For applications where unlabelled abundant but scarce, we propose Wasserstein Laplacian Regularisation, semi-supervised learning framework that allows leverage these data. The minimises an objective function which ensures learned smooth along manifold underlying data, measured by distance. When applying our Mixture Networks, resulting algorithm achieve similar performance supervised up three times points on baseline datasets. We additionally apply technique problem remote sensing for chlorophyll-a in inland waters.