# Stochastic Gradient Descent Meets Distribution Regression

arXiv: https://arxiv.org/abs/2010.12842 · HTML: https://mlsanity.com/paper/2010.12842/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2020.

## Built on by (most cited first, 5 of 5)

- [Distribution Regression with Sliced Wasserstein Kernels](https://mlsanity.com/paper/2202.03926/) (2022)
- [Robust Kernel-based Distribution Regression](https://mlsanity.com/paper/2104.10637/) (2021)
- [Learning Theory of Distribution Regression with Neural Networks](https://mlsanity.com/paper/2307.03487/) (2023)
- [Coefficient-based Regularized Distribution Regression](https://mlsanity.com/paper/2208.12427/) (2022)
- [Statistical Learning Theory for Distributional Classification](https://mlsanity.com/paper/2601.14818/) (2026)

## Abstract (arXiv)

Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from probability measures to real-valued responses. Secondly, we sample bags from these distributions for utilizing them to solve the overall regression problem. Recently, DR has been tackled by applying kernel ridge regression and the learning properties of this approach are well understood. However, nothing is known about the learning properties of SGD for two stage sampling problems. We fill this gap and provide theoretical guarantees for the performance of SGD for DR. Our bounds are optimal in a mini-max sense under standard assumptions.