Stochastic Deep Learning: A Probabilistic Framework for Modeling Uncertainty in Structured Temporal Data
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 Itô 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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equations
Accurate forecasting of spatiotemporal data remains challenging due to complex spatial dependencies and temporal dynamics. The inherent uncertainty and variability in such data often render deterministic models insuffici…
DenoisingTime SeriesTime Series ForecastingProTerrain: Probabilistic Physics-Informed Rough Terrain World Modeling
Uncertainty-aware robot motion prediction is crucial for downstream traversability estimation and safe autonomous navigation in unstructured, off-road environments, where terrain is heterogeneous and perceptual uncertain…
Trajectory ForecastingTrajectory PredictionA Semiparametric Framework for Stochastic Fundamental Diagram Modeling
The stochastic fundamental diagram (SFD) provides a probabilistic description of the relationship between traffic density and flow or speed, enabling uncertainty-aware traffic modeling. However, existing stochastic model…
Merging Two Cultures: Deep and Statistical Learning
Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning …
Dimensionality ReductionFeature EngineeringUncertainty QuantificationVocal Bursts Valence PredictionDiffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations
We introduce a novel framework for uncertainty quantification of solution operators associated with stochastic partial differential equations (SPDEs). Although SPDEs play a central role in modeling complex physical syste…