# Obstructing Classification via Projection

arXiv: https://arxiv.org/abs/2105.09047 · HTML: https://mlsanity.com/paper/2105.09047/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 28 references that are in the map.
- First posted on arXiv 19 May 2021.

## Builds on (most cited first, 17 of 17)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Semantics derived automatically from language corpora contain human-like biases](https://mlsanity.com/paper/1608.07187/) (2016)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Identifying and Reducing Gender Bias in Word-Level Language Models](https://mlsanity.com/paper/1904.03035/) (2019)
- [Censoring Representations with an Adversary](https://mlsanity.com/paper/1511.05897/) (2015)
- [Learning Gender-Neutral Word Embeddings](https://mlsanity.com/paper/1809.01496/) (2018)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [On Measuring and Mitigating Biased Inferences of Word Embeddings](https://mlsanity.com/paper/1908.09369/) (2019)
- [Understanding the Origins of Bias in Word Embeddings](https://mlsanity.com/paper/1810.03611/) (2018)
- [Attenuating Bias in Word Vectors](https://mlsanity.com/paper/1901.07656/) (2019)
- [Fairness in representation: quantifying stereotyping as a representational harm](https://mlsanity.com/paper/1901.09565/) (2019)
- [The Rainbow at the End of the Line --- A PPAD Formulation of the Colorful Carath'eodory Theorem with Applications](https://mlsanity.com/paper/1608.01921/) (2016)

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

- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [Emergent and Predictable Memorization in Large Language Models](https://mlsanity.com/paper/2304.11158/) (2023)
- [Linear Adversarial Concept Erasure](https://mlsanity.com/paper/2201.12091/) (2022)
- [Efficient fair PCA for fair representation learning](https://mlsanity.com/paper/2302.13319/) (2023)
- [Better Hit the Nail on the Head than Beat around the Bush: Removing Protected Attributes with a Single Projection](https://mlsanity.com/paper/2212.04273/) (2022)

## Abstract (arXiv)

Machine learning and data mining techniques are effective tools to classify large amounts of data. But they tend to preserve any inherent bias in the data, for example, with regards to gender or race. Removing such bias from data or the learned representations is quite challenging. In this paper we study a geometric problem which models a possible approach for bias removal. Our input is a set of points P in Euclidean space R^d and each point is labeled with k binary-valued properties. A priori we assume that it is "easy" to classify the data according to each property. Our goal is to obstruct the classification according to one property by a suitable projection to a lower-dimensional Euclidean space R^m (m < d), while classification according to all other properties remains easy. What it means for classification to be easy depends on the classification model used. We first consider classification by linear separability as employed by support vector machines. We use Kirchberger's Theorem to show that, under certain conditions, a simple projection to R^(d-1) suffices to eliminate the linear separability of one of the properties whilst maintaining the linear separability of the other properties. We also study the problem of maximizing the linear "inseparability" of the chosen property. Second, we consider more complex forms of separability and prove a connection between the number of projections required to obstruct classification and the Helly-type properties of such separabilities.