# On Mitigating the Utility-Loss in Differentially Private Learning: A new Perspective by a Geometrically Inspired Kernel Approach

arXiv: https://arxiv.org/abs/2304.01300 · HTML: https://mlsanity.com/paper/2304.01300/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 3 Apr 2023.

## Builds on (most cited first, 12 of 12)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [To understand deep learning we need to understand kernel learning](https://mlsanity.com/paper/1802.01396/) (2018)
- [FALKON: An Optimal Large Scale Kernel Method](https://mlsanity.com/paper/1705.10958/) (2017)
- [Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nystr"om Method, and Use of Kernels in Machine Learning: Tutorial and Survey](https://mlsanity.com/paper/2106.08443/) (2021)
- [Variational Bayes In Private Settings (VIPS)](https://mlsanity.com/paper/1611.00340/) (2016)
- [Optimal Noise-Adding Mechanism in Additive Differential Privacy](https://mlsanity.com/paper/1809.10224/) (2018)
- [Membership-Mappings for Data Representation Learning: Measure Theoretic Conceptualization](https://mlsanity.com/paper/2104.07060/) (2021)
- [Differentially Private Transferrable Deep Learning with Membership-Mappings](https://mlsanity.com/paper/2105.04615/) (2021)
- [The Deep Kernelized Autoencoder](https://mlsanity.com/paper/1807.07868/) (2018)
- [Membership-Mappings for Practical Secure Distributed Deep Learning](https://mlsanity.com/paper/2204.05765/) (2022)

## Built on by (most cited first, 3 of 3)

- [Geometrically Inspired Kernel Machines for Collaborative Learning Beyond Gradient Descent](https://mlsanity.com/paper/2407.04335/) (2024)
- [Operator-Theoretic Framework for Gradient-Free Federated Learning](https://mlsanity.com/paper/2512.01025/) (2025)
- [Kernel Affine Hull Machines as Compute-Efficient Encoders for Frozen Semantic Spaces](https://mlsanity.com/paper/2605.02950/) (2026)

## Abstract (arXiv)

Privacy-utility tradeoff remains as one of the fundamental issues of differentially private machine learning. This paper introduces a geometrically inspired kernel-based approach to mitigate the accuracy-loss issue in classification. In this approach, a representation of the affine hull of given data points is learned in Reproducing Kernel Hilbert Spaces (RKHS). This leads to a novel distance measure that hides privacy-sensitive information about individual data points and improves the privacy-utility tradeoff via significantly reducing the risk of membership inference attacks. The effectiveness of the approach is demonstrated through experiments on MNIST dataset, Freiburg groceries dataset, and a real biomedical dataset. It is verified that the approach remains computationally practical. The application of the approach to federated learning is considered and it is observed that the accuracy-loss due to data being distributed is either marginal or not significantly high.