Fairness in
Machine Learning

by Novi Quadrianto

with thanks to Oliver Thomas and Thomas Kehrenberg

Algorithmic fairness definitions

## Mutual exclusivity by Bayes' rule

<small>
$$
\underbrace{\text{Pr}(Y=1|\hat{Y}=1)}_{\text{Positive Predicted Value (PPV)}} = \frac{\text{Pr}(\hat{Y}=1|Y=1)\overbrace{\text{Pr}(Y=1)}^{\text{Base Rate (BR)}}}{\underbrace{\text{Pr}(\hat{Y}=1|Y=1)}_{\text{True Positive Rate (TPR)}}\text{Pr}(Y=1) + \underbrace{\text{Pr}(\hat{Y}=1|Y=-1)}_{\text{False Positive Rate (FPR)}}(1-\text{Pr}(Y=1))}
$$
</small>

- Suppose we have FPR<sub>S=1</sub> = FPR<sub>S=0</sub> and TPR<sub>S=1</sub> = TPR<sub>S=0</sub> (<span class="highlight">equalised odds</span>), can we have PPV<sub>S=1</sub> = PPV<sub>S=0</sub> (<span class="highlight">predictive parity</span>)?
- YES! But only if we have a <span class="highlight">perfect dataset</span> (i.e. BR<sub>S=1</sub> = BR<sub>S=0</sub>) or a <span class="highlight">perfect predictor</span> (i.e. FPR=0 and TPR=1 for S=1 and S=0)

<span class="citeme">Kehrenberg, Chen, NQ: Tuning fairness by marginalizing latent target labels, Oct 2018</span>
<div style="height:20px;font-size:1px;"> </div>
<span class="citeme">Roth, Impossibility results in fairness as Bayesian inference, Feb 2019</span>

Confusion Tables

blue Applicants

	Accepted	Not
Actually Graduate
Don't Graduate

green Applicants

	Accepted	Not
Actually Graduate
Don't Graduate

Solving this problem with statistical parity fairness metric?

???

Select 50% of applicants of both blue and green applicants

blue Applicants

	Accepted	Not
Actually Graduate	4000 (80%)	1200
Don't Graduate	1000 (20%)	3800
	5000

green Applicants

	Accepted	Not
Actually Graduate	3300	500 (10%)
Don't Graduate	1700	4500 (90%)
	5000

10% of qualified blue applicants are being rejected whilst an additional 10% of unqualified green are being accepted

Solving this problem with equality of opportunity fairness metric?

???

Select 55.5% of blue applicants and 44.5% of green applicants, giving a TPR of 85.4% for both groups.

blue Applicants

	Accepted	Not
Actually Graduate	4440	760
Don't Graduate	1110	3690
	5550

green Applicants

	Accepted	Not
Actually Graduate	3245	555
Don't Graduate	1205	4995
	4450

4.5% of qualified blue applicants are being rejected whilst an additional 4.5% of unqualified green are being accepted

Solving this problem with predictive parity fairness metric?

???

Select only the applicants who pass the test

blue Applicants

	Accepted	Not
Actually Graduate	4800	400
Don't Graduate	1200	3600
	6000

green Applicants

	Accepted	Not
Actually Graduate	3200	600
Don't Graduate	800	5400
	4000

Could lead to systemic reinforcement of bias

Algorithmic fairness methods

Problems with doing this?

Any Ideas?

Interpretability in fairness

Fair and interpretable representations

- Analysis on the relationship feature on Adult Income dataset

- Feature values of the minority group are transformed to match the majority group

- Here, the wife value is translated to husband

Fair and interpretable representations

Interpretable can be fair!

	original $X$		fair & interpretable $X$		latent embedding $Z$
	Accuracy $\uparrow$	Eq. Opp $\downarrow$	Accuracy $\uparrow$	Eq. Opp $\downarrow$	Accuracy $\uparrow$	Eq. Opp $\downarrow$
LR	$85.1\pm0.2$	$\mathbf{9.2\pm2.3}$	$84.2\pm0.3$	$\mathbf{5.6\pm2.5}$	$81.8\pm2.1$	$\mathbf{5.9\pm4.6}$
SVM	$85.1\pm0.2$	$\mathbf{8.2\pm2.3}$	$84.2\pm0.3$	$\mathbf{4.9\pm2.8}$	$81.9\pm2.0$	$\mathbf{6.7\pm4.7}$
Fair Reduction LR	$85.1\pm0.2$	$\mathbf{14.9\pm1.3}$	$84.1\pm0.3$	$\mathbf{6.5\pm3.2}$	$81.8\pm2.1$	$\mathbf{5.6\pm4.8}$
Fair Reduction SVM	$85.1\pm0.2$	$\mathbf{8.2\pm2.3}$	$84.2\pm0.3$	$\mathbf{4.9\pm2.8}$	$81.9\pm2.0$	$\mathbf{6.7\pm4.7}$
Kamiran & Calders LR	$84.4\pm0.2$	$\mathbf{14.9\pm1.3}$	$84.1\pm0.3$	$\mathbf{1.7\pm1.3}$	$81.8\pm2.1$	$\mathbf{4.9\pm3.3}$
Kamiran & Calders SVM	$85.1\pm0.2$	$\mathbf{8.2\pm2.3}$	$84.2\pm0.3$	$\mathbf{4.9\pm2.8}$	$81.9\pm2.0$	$\mathbf{6.7\pm4.7}$
Zafar et al.	$85.0\pm0.3$	$\mathbf{1.8\pm0.9}$	---	---	---	---

## Fair and interpretable representations</h2>
- <span class="highlight">Left</span>: Examples of the spurious residual and non-spurious translation on<span class="highlight"> CelebFaces Attributes dataset</span>
- <span class="highlight">Right</span>: In the semantic attribute domain ... same conclusion (<span class="highlight">changes in the eyes and lips regions</span>)
<center>
  <table style="border-collapse: collapse; border: none;">
        <tbody ><tr style="border: none;"><td width="30%" colspan="3" style="border: none;"></td><td width="30%" style="border: none;"></td><td width="40%" style="border: none;"></td></tr>
        <tr style="border: none;">
            <td width="10%" style="border: none;">Translated</td>
            <td width="20%" style="border: none;"><img src="images/celeba_res/006126.jpg" width=70% title="Im1"/></td>
            <td width="30%" rowspan="2" style="border: none;"><hr width="2" size="250"></td>
            <td width="40%" rowspan="2" style="border: none;"><img src="images/features.png" width=100% title="features"/></td>
        </tr>
        <tr style="border: none;">
            <td width="10%" style="border: none;">Residual</td>
            <td width="20%" style="border: none;"><img src="images/celeba_res/006126res.jpg" width=60% title="RIm1"/></td>
        </tr></tbody>
    </table></center>

## Contrastive on Adult Income dataset
- Connections to <span class="highlight">counterfactuals</span> based on the Nabi \& Shpitser's (2018) causal graph
 - To remove bias towards females, the direct effect of gender on income, as well as, the <span class="highlight">effect of gender on income through marital status have to be suppressed</span>
- Experimental results
<small>
  <table>
        <tbody><tr>
            <td></td>
            <td width="10%">Accuracy $\uparrow$</td>
            <td width="10%">TPR Diff. $\downarrow$</td>
            <td width="10%">FPR Diff. $\downarrow$</td>
        </tr>
        <tr>
            <td width="10%">LR (Real)</td>
            <td width="10%">$85.16\pm0.14$ </td>
            <td width="10%">$7.98\pm1.52$ </td>
            <td width="10%">$7.23\pm0.41$</td>
        </tr>
        <tr>
            <td width="10%">Kamiran & Calders LR (Real)</td>
            <td width="10%">$84.37\pm0.28$ </td>
            <td width="10%">$14.3\pm1.16$ </td>
            <td width="10%">$1.17\pm0.29$ </td>
        </tr>
        <tr>
            <td width="20%">LR (Real and NN contrastive)</td>
            <td width="10%">$85.01\pm0.25$ </td>
            <td width="10%">$14.80\pm1.90$ </td>
            <td width="10%">$8.20\pm0.51$ </td>
        </tr>
        <tr>
            <td width="20%">LR (Real and GAN contrastive)</td>
            <td width="10%">$82.48\pm0.44$ </td>
            <td width="10%">$4.95\pm3.67$ </td>
            <td width="10%">$3.94\pm1.33$ </td>
        </tr>
			</tbody>
    </table>
    </small>

Fairness in
Machine Learning

Algorithmic fairness definitions

Confusion Tables

blue Applicants

green Applicants

blue Applicants

green Applicants

blue Applicants

green Applicants

blue Applicants

green Applicants

Algorithmic fairness methods

Problems with doing this?

Any Ideas?

Interpretability in fairness

Fair and interpretable representations

Fair and interpretable representations

Homework

Practical Session

Further Resources

Google Crash Course: Fairness in ML

Fast.ai lecture with Fairness discussion

Fairness in Machine Learning

Algorithmic fairness definitions

Confusion Tables

blue Applicants

green Applicants

blue Applicants

green Applicants

blue Applicants

green Applicants

blue Applicants

green Applicants

Algorithmic fairness methods

Problems with doing this?

Any Ideas?

Interpretability in fairness

Fair and interpretable representations

Fair and interpretable representations

Homework

Practical Session

Further Resources

Google Crash Course: Fairness in ML

Fast.ai lecture with Fairness discussion

Fairness in
Machine Learning