Deep density estimation via invertible block-triangular mapping

Abstract

ABSTRACT: In this work, we develop an invertible transport map, called KRnet, for density estimation by coupling the Knothe–Rosenblatt (KR) rearrangement and the flow-based generative model, which generalizes the real-valued non-volume preserving (real NVP) model (arX-iv:1605.08803v3). The triangular structure of the KR rearrangement breaks the symmetry of the real NVP in terms of the exchange of information between dimensions, which not only accelerates the training process but also improves the accuracy significantly. We have also introduced several new layers into the generative model to improve both robustness and effectiveness, including a reformulated affine coupling layer, a rotation layer and a component-wise nonlinear invertible layer. The KRnet can be used for both density estimation and sample generation especially when the dimensionality is relatively high. Numerical experiments have been presented to demonstrate the performance of KRnet.

Keywords

• Deep learning
• Density estimation
• Optimal transport
• Uncertainty quantification