Fairness in AI

CSE 849: Deep Learning

Vishnu Boddeti

Progress In Machine Learning

Speech Processing

Image Analysis

Natural Language Processing

Physical Sciences

Key Drivers Data, Compute, Algorithms

State-of-Affairs

(report from the real-world)

"Machine Bias"

May 23, 2016

"Facial recognition is accurate, if you're a white guy"

Feb. 09, 2018

lighter faces: 0.7% error

darker faces: 12.9% error

Boulamwini and Gebru, "Gender Shades:Intersectional Accuracy Disparities in Commercial Gender Classification," FAT 2018

"Black Artists Say A.I. Shows Bias"

July 04, 2023

"How AI reduces the world to stereotypes"

October 10, 2023

"LLMs propagate race-based medicine"

October 20, 2023

Economic Bias

DeVries "Does Object Recognition Work for Everyone?," CVPRW 2020

Real world machine learning systems are effective but,

are biased,

violate user's privacy and

not trustworthy.

Goal

Build ML systems that are fair while retaining utility.

Trade-Offs in Fair Machine Learning

Questions of Interest

What are the trade-offs between fairness and utility?

When do the trade-offs between fairness and utility exist?

How to explicitly characterize the utility-fairness trade-offs?

The What

Short Answer: Data and Label Space Trade-Offs

What are the Trade-Offs in Fair Machine Learning?

Data Space Trade-Off

$$ \begin{equation} \inf_{f\in \mathcal H_X} \left\{(1-\lambda)\underbrace{\inf_{g_Y\in \mathcal H_Y }\mathbb E_{X,Y} \left[\mathcal L_Y\left (g_Y(f(X), Y \right)\right]}_{Loss} + \lambda \underbrace{Dep(f(X),S|Y=y)}_{Unfairness} \right\}\nonumber \end{equation} $$

Label Space Trade-Off

$$ \begin{equation} \inf_{Z\in \mathcal{L}^2} \left\{(1-\lambda)\underbrace{\inf_{g_Y\in \mathcal H_Y }\mathbb E_{Y} \left[\mathcal L_Y\left (g_Y\left(Z\right), Y \right)\right]}_{Loss} + \lambda \underbrace{Dep(Z,S|Y=y)}_{Unfairness} \right\}\nonumber \end{equation} $$

"On Characterizing the Trade-off in Invariant Representation Learning," TMLR 2022
"Utility-Fairness Trade-offs and How to Find Them," CVPR 2024

Fairness: The Multi-Headed Hydra

Verma and Rubin, "Fairness Definitions Explained," International Workshop on Software Fairness, 2018

Fairness Definitions: Statistical Parity

$P(\hat{Y}=1|S=1) = P(\hat{Y}=1|S=0)$

Probability of correct prediction is the same across demographic groups.

$\hat{Y} \perp \!\!\! \perp S$

Fairness Definitions: Equalized Odds

$P(\hat{Y}=y|Y=y, S=1) = P(\hat{Y}=y|Y=y, S=0)$

True positive rate of predictions is the same across demographic groups.

$\hat{Y} \perp \!\!\! \perp S | Y$

Fairness Definitions: Equality of Opportunity

$P(\hat{Y}=1|Y=1, S=1) = P(\hat{Y}=1|Y=1, S=0)$

Among eligible candidates, probability of correct prediction is the same across demographic groups.

$\hat{Y} \perp \!\!\! \perp S | Y=1$

The When

Short Answer: Target and demographic attributes are related.

A Causal Perspective

$Y$ is related to $S \Rightarrow$ trade-off exists.

$Y$ is independent of $S \Rightarrow$ no trade-off should exist.

A Subspace Geometry Perspective

Case 1: when $\mathcal{S} \perp \!\!\! \perp \mathcal{T}$ (Gender, Age)

Case 3: when $\mathcal{S} \sim \mathcal{T}$ ($\mathcal{T}\subseteq\mathcal{S}$)

Case 2: when $\mathcal{S} \not\perp \!\!\! \perp \mathcal{T}$ (High Cheekbones, Gender)

"Adversarial Representation Learning with Closed-Form Solutions," CVPRW 2020

The How

Short Answer: It depends

From Fair Learning to Fair Representation Learning

$Z \perp \!\!\! \perp S \Rightarrow \hat{Y} \perp \!\!\! \perp S$

Learning Fair Representations

Target Attribute: Smile & Demographic Attribute: Gender

Problem Definition:

Learn a representation $\mathbf{z} \in \mathbb{R}^d$ from data $\mathbf{x}$
Retain information necessary to predict target attribute $\mathbf{t}\in\mathcal{T}$
Remove information related to a desired demographic attribute $\mathbf{s}\in\mathcal{S}$

A Fork in the Road

Design metric to measure sensitive demographic attribute information

non-parameteric statistical dependence measures, this talk

Learn metric to measure semantic attribute information

probably feasible, many attempts

Adversarial Representation Learning

Game Theoretic Formulation

Three player game between:

Encoder extracts features $\mathbf{z}$
Target Predictor for desired task from features $\mathbf{z}$
Adversary extracts sensitive information from features $\mathbf{z}$

$$ \begin{equation} \begin{aligned} \min_{\mathbf{\Theta}_E,\mathbf{\Theta}_T} & \underbrace{\color{cyan}{J_t(\mathbf{\Theta}_E,\mathbf{\Theta}_T)}}_{\color{cyan}{\text{error of target}}} \quad s.t. \text{ } \min_{\mathbf{\Theta}_A} \underbrace{\color{orange}{J_s(\mathbf{\Theta}_E,\mathbf{\Theta}_A)}}_{\color{orange}{\text{error of adversary}}} \geq \alpha \nonumber \end{aligned} \end{equation} $$

Adversary: learned measure of semantic attribute information

How do we learn model parameters?

Simultaneous/Alternating Stochastic Gradient Descent

Update target while keeping encoder and adversary frozen.
Update adversary while keeping encoder and target frozen.
Update encoder while keeping target and adversary frozen.

ARL is Suboptimal

Unstable Optimization

Lack of Invariance Guarantees

Overview of FRL Solutions

Standard Adversarial Representation Learning
Linear Adversarial Measure: linear dependency between $Z$ and $S$ [ICCV 2019, CVPRW 2020]
Non-Linear Adversarial Measure: Beyond linear dependency between $Z$ and $S$, but not all types [ECML 2021]
Universal Dependence Measure: All types of dependency between $Z$ and $S$ [TMLR 2022]
End-to-End Universal Dependence Measure: All types of dependency between $Z$ and $S$ [CVPR 2024].

Covariance Operator and Dependence Measure

Linear Dependence: $ C_{SZ}\approx \frac{1}{n}\tilde{\mathbf S} \tilde{\mathbf Z}^T$

Universal Dependence: $\Sigma_{SZ}\approx\frac{1}{n}\tilde{\mathbf K}_S\tilde{\mathbf K}_Z$

$\mathcal H_Z\times\mathcal H_S\rightarrow \mathbb R:\ Cov\left(\alpha(Z),\ \beta(S)\right)$ $=\big\langle \beta, \Sigma_{SZ}\, \alpha \big\rangle_{\mathcal H_S}, \Sigma_{SZ}:\mathcal H_Z\rightarrow \mathcal H_S$ $Z \perp \!\!\! \perp S \Leftrightarrow \Sigma_{SZ} =0 \Leftrightarrow \left\|\Sigma_{SZ}\right\| =0$, where $\|\cdot\|$ can be any operator norm HSIC$(Z,S)=\left\|\Sigma_{SZ}\right\|^2_{\text{HS}}=\displaystyle\sum_{\alpha\in\mathcal U_Z}\sum_{\beta\in \mathcal H_S}Cov^2(\alpha(Z),\beta(S))$

Universal Dependence Measure

$\mathcal A_r:=\Big\{(f_1,\cdots,f_r)\,|\,Cov(f_i(X), f_j(X))+\gamma \langle f_i, f_j\rangle_{\mathcal H_X}=\delta_{i,j} \Big\}$

$\displaystyle\sup_{\mathbf f\in\mathcal A_r} {\Big\{J(\mathbf f):=(1-\lambda)\,\text{Dep}(Z, Y)}-\lambda\,\text{Dep}(Z, S)\Big\}$

Solution: eigenfunctions corresponding to the $r$ largest eigenvalues of $\big((1-\lambda)\, \Sigma_{YX}^*\,\Sigma_{YX}-\lambda\,\Sigma_{SX}^*\Sigma_{SX}\big)\mathbf f = \tau (\Sigma_{XX}+\gamma I)\mathbf f$