# An Efficient Difference-of-Convex Solver for Privacy Funnel

arXiv: https://arxiv.org/abs/2403.04778 · HTML: https://mlsanity.com/paper/2403.04778/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 2 Mar 2024.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Algorithms for Fitting the Constrained Lasso](https://mlsanity.com/paper/1611.01511/) (2016)
- [A Variational Approach to Privacy and Fairness](https://mlsanity.com/paper/2006.06332/) (2020)
- [Bottleneck Problems: Information and Estimation-Theoretic View](https://mlsanity.com/paper/2011.06208/) (2020)
- [Variational Laplace Autoencoders](https://mlsanity.com/paper/2211.17267/) (2022)
- [Rate-Distortion Theory for Secrecy Systems](https://mlsanity.com/paper/1305.3905/) (2013)
- [A Linearly Convergent Douglas-Rachford Splitting Solver for Markovian Information-Theoretic Optimization Problems](https://mlsanity.com/paper/2203.07527/) (2022)
- [Deep Variational Privacy Funnel: General Modeling with Applications in Face Recognition](https://mlsanity.com/paper/2401.14792/) (2024)
- [The Wyner Variational Autoencoder for Unsupervised Multi-Layer Wireless Fingerprinting](https://mlsanity.com/paper/2303.15860/) (2023)
- [Efficient Alternating Minimization Solvers for Wyner Multi-View Unsupervised Learning](https://mlsanity.com/paper/2303.15866/) (2023)

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

- [Fundamental Limits of Perfect Concept Erasure](https://mlsanity.com/paper/2503.20098/) (2025)
- [Deep Privacy Funnel Model: From a Discriminative to a Generative Approach with an Application to Face Recognition](https://mlsanity.com/paper/2404.02696/) (2024)

## Abstract (arXiv)

We propose an efficient solver for the privacy funnel (PF) method, leveraging its difference-of-convex (DC) structure. The proposed DC separation results in a closed-form update equation, which allows straightforward application to both known and unknown distribution settings. For known distribution case, we prove the convergence (local stationary points) of the proposed non-greedy solver, and empirically show that it outperforms the state-of-the-art approaches in characterizing the privacy-utility trade-off. The insights of our DC approach apply to unknown distribution settings where labeled empirical samples are available instead. Leveraging the insights, our alternating minimization solver satisfies the fundamental Markov relation of PF in contrast to previous variational inference-based solvers. Empirically, we evaluate the proposed solver with MNIST and Fashion-MNIST datasets. Our results show that under a comparable reconstruction quality, an adversary suffers from higher prediction error from clustering our compressed codes than that with the compared methods. Most importantly, our solver is independent to private information in inference phase contrary to the baselines.