A local squared Wasserstein-2 method for efficient reconstruction of models with uncertainty
This addresses uncertainty quantification problems for researchers and practitioners in fields like machine learning and scientific computing, though it appears incremental as it builds on existing Wasserstein-2 methods.
The paper tackles the inverse problem of reconstructing models with uncertain latent variables or parameters without requiring prior distribution information, achieving efficient reconstruction of output distributions based on empirical observation data across tasks like linear regression, neural network training, and ODE reconstruction.
In this paper, we propose a local squared Wasserstein-2 (W_2) method to solve the inverse problem of reconstructing models with uncertain latent variables or parameters. A key advantage of our approach is that it does not require prior information on the distribution of the latent variables or parameters in the underlying models. Instead, our method can efficiently reconstruct the distributions of the output associated with different inputs based on empirical distributions of observation data. We demonstrate the effectiveness of our proposed method across several uncertainty quantification (UQ) tasks, including linear regression with coefficient uncertainty, training neural networks with weight uncertainty, and reconstructing ordinary differential equations (ODEs) with a latent random variable.