Stochastic Deep Learning: A Probabilistic Framework for Modeling Uncertainty in Structured Temporal Data

Advancements in Uncertainty Quantification with Stochastic Deep Learning Framework

A novel framework known as Stochastic Latent Differential Inference (SLDI) has been proposed to enhance uncertainty quantification in machine learning applications involving structured temporal data. By integrating stochastic differential equations (SDEs) with deep generative models, this approach offers a new method for continuous-time uncertainty modeling.

The framework embeds an Itô SDE within the latent space of a variational autoencoder, allowing for flexible uncertainty modeling. The core components of the SDE—the drift and diffusion terms—are parameterized using neural networks, enabling the SLDI model to generalize classical time series models and effectively handle irregular sampling.

Theoretical Contributions

A significant advancement is the co-parameterization of the adjoint state with a specialized neural network, creating a coupled forward-backward system that captures both latent evolution and gradient dynamics. Additionally, the introduction of a pathwise-regularized adjoint loss enhances training stability in deep latent SDEs, making SLDI a noteworthy development in stochastic probabilistic machine learning.