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

James Rice

Papers from arXiv.org

Abstract: I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach, termed Stochastic Latent Differential Inference (SLDI), embeds an It\^o SDE in the latent space of a variational autoencoder, allowing for flexible, continuous-time modeling of uncertainty while preserving a principled mathematical foundation. The drift and diffusion terms of the SDE are parameterized by neural networks, enabling data-driven inference and generalizing classical time series models to handle irregular sampling and complex dynamic structure. A central theoretical contribution is the co-parameterization of the adjoint state with a dedicated neural network, forming a coupled forward-backward system that captures not only latent evolution but also gradient dynamics. I introduce a pathwise-regularized adjoint loss and analyze variance-reduced gradient flows through the lens of stochastic calculus, offering new tools for improving training stability in deep latent SDEs. My paper unifies and extends variational inference, continuous-time generative modeling, and control-theoretic optimization, providing a rigorous foundation for future developments in stochastic probabilistic machine learning.

Date: 2026-01
References: Add references at CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2601.05227 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2601.05227

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().