# Coefficient-based Regularized Distribution Regression

arXiv: https://arxiv.org/abs/2208.12427 · HTML: https://mlsanity.com/paper/2208.12427/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 26 Aug 2022.

## Builds on (most cited first, 11 of 11)

- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Learning Theory for Distribution Regression](https://mlsanity.com/paper/1411.2066/) (2014)
- [Distributed learning with regularized least squares](https://mlsanity.com/paper/1608.03339/) (2016)
- [Learning with SGD and Random Features](https://mlsanity.com/paper/1807.06343/) (2018)
- [Distribution-Free Distribution Regression](https://mlsanity.com/paper/1302.0082/) (2013)
- [Hilbert Space Embeddings of Predictive State Representations](https://mlsanity.com/paper/1309.6819/) (2013)
- [Differentially Private Database Release via Kernel Mean Embeddings](https://mlsanity.com/paper/1710.01641/) (2017)
- [Robust Kernel-based Distribution Regression](https://mlsanity.com/paper/2104.10637/) (2021)
- [Fast Distribution To Real Regression](https://mlsanity.com/paper/1311.2236/) (2013)
- [Stochastic Gradient Descent Meets Distribution Regression](https://mlsanity.com/paper/2010.12842/) (2020)

## Built on by (most cited first, 2 of 2)

- [Statistical Optimality of Divide and Conquer Kernel-based Functional Linear Regression](https://mlsanity.com/paper/2211.10968/) (2022)
- [LearnedWMP: Workload Memory Prediction Using Distribution of Query Templates](https://mlsanity.com/paper/2401.12103/) (2024)

## Abstract (arXiv)

In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on the coefficients and kernels are assumed to be indefinite. The algorithm involves two stages of sampling, the first stage sample consists of distributions and the second stage sample is obtained from these distributions. Asymptotic behaviors of the algorithm in different regularity ranges of the regression function are comprehensively studied and learning rates are derived via integral operator techniques. We get the optimal rates under some mild conditions, which matches the one-stage sampled minimax optimal rate. Compared with the kernel methods for distribution regression in the literature, the algorithm under consideration does not require the kernel to be symmetric and positive semi-definite and hence provides a simple paradigm for designing indefinite kernel methods, which enriches the theme of the distribution regression. To the best of our knowledge, this is the first result for distribution regression with indefinite kernels, and our algorithm can improve the saturation effect.