# Empirical risk minimization algorithm for multiclass classification of S.D.E. paths

arXiv: https://arxiv.org/abs/2503.14045 · HTML: https://mlsanity.com/paper/2503.14045/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 10 of 10)

- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Dynamic Sparse Network for Time Series Classification: Learning What to "see''](https://mlsanity.com/paper/2212.09840/) (2022)
- [scikit-fda: A Python Package for Functional Data Analysis](https://mlsanity.com/paper/2211.02566/) (2022)
- [Depth for curve data and applications](https://mlsanity.com/paper/1901.00180/) (2019)
- [Nonparametric plug-in classifier for multiclass classification of S.D.E. paths](https://mlsanity.com/paper/2212.10259/) (2022)
- [Fast DD-classification of functional data](https://mlsanity.com/paper/1403.1158/) (2014)

## Built on by (most cited first, 1 of 1)

- [Plug-In Classification of Drift Functions in Diffusion Processes Using Neural Networks](https://mlsanity.com/paper/2602.02791/) (2026)

## Abstract (arXiv)

We address the multiclass classification problem for stochastic diffusion paths, assuming that the classes are distinguished by their drift functions, while the diffusion coefficient remains common across all classes. In this setting, we propose a classification algorithm that relies on the minimization of the L 2 risk. We establish rates of convergence for the resulting predictor. Notably, we introduce a margin assumption under which we show that our procedure can achieve fast rates of convergence. Finally, a simulation study highlights the numerical performance of our classification algorithm.