Conditional Sampling via Wasserstein Autoencoders and Triangular Transport
This provides a novel method for conditional sampling in machine learning, addressing a specific bottleneck in simulation tasks.
The paper tackles conditional simulation by introducing Conditional Wasserstein Autoencoders (CWAEs), which modify Wasserstein autoencoders with triangular decoders and latent independence assumptions to exploit low-dimensional structure. The result shows that CWAE variants achieve substantial reductions in approximation error compared to the low-rank ensemble Kalman filter, especially in problems with low-dimensional conditional measure supports.
We present Conditional Wasserstein Autoencoders (CWAEs), a framework for conditional simulation that exploits low-dimensional structure in both the conditioned and the conditioning variables. The key idea is to modify a Wasserstein autoencoder to use a (block-) triangular decoder and impose an appropriate independence assumption on the latent variables. We show that the resulting model gives an autoencoder that can exploit low-dimensional structure while simultaneously the decoder can be used for conditional simulation. We explore various theoretical properties of CWAEs, including their connections to conditional optimal transport (OT) problems. We also present alternative formulations that lead to three architectural variants forming the foundation of our algorithms. We present a series of numerical experiments that demonstrate that our different CWAE variants achieve substantial reductions in approximation error relative to the low-rank ensemble Kalman filter (LREnKF), particularly in problems where the support of the conditional measures is truly low-dimensional.