SlowGuess/NeurIPS_2023_OCR huggingface dataset:
$$
\begin{array}{l} \sum_ {s} p (s) \mathbb {E} _ {\hat {\theta} \sim p (\hat {\theta} | s)} [ \log \mathcal {D} _ {s} ^ {*} (\hat {\theta}) ] + H (S) \\ = \sum_ {s} p (s) \mathbb {E} _ {\hat {\theta} \sim p (\hat {\theta} | s)} [ \log p (s | \hat {\theta}) ] - \sum_ {s} p (s) \log p (s) \\ = \int \sum_ {s} p (s) p (\hat {\theta} | s) \log \frac {p (\hat {\theta} | s)}{p (\hat {\theta})} d \hat {\theta} \tag {14} \\ = \sum_ {s} p (s) K L (p (\hat {\theta} | s) | | p (\hat {\theta})) \\ = J S _ {p (s)} \left(p (\hat {\theta} | s)\right) = I (\hat {\theta}, S) \\ \end{array}
$$
Here, the second last equality is due to the definition of the Jensen-Shannon divergence, and the last equality is due to its equivalence to the mutual information [24]. This completes the proof.
We have established a connection between  $U_{L}$  and  $I(\hat{\theta}, S)$  through Lemma A.1. Consequently, fairness can be achieved by minimizing Eq. (11) with a fixed optimal discriminator  $\mathcal{D}^*$ .
In this proof, we explain how FairLISA builds the relationship between fairness goal  $I(\hat{\theta}, S) = 0$  with user data with known sensitive attributes  $U_N$  through Lemma A.1.
Lemma A.2. Given the optimal discriminator  $\mathcal{D}_s^* (\hat{\theta})$  and let  $p(\hat{\theta})$  be the distribution of users' filtered representation, we have,
$$
\begin{array}{l} I (\hat {\theta}, S) = \mathbb {E} _ {\hat {\theta} \sim p (\hat {\theta})} \sum_ {s} \mathcal {D} _ {s} ^ {*} (\hat {\theta}) \log \mathcal {D} _ {s} ^ {*} (\hat {\theta}) + H (S) \tag {15} \\ = - H \left(\mathcal {D} _ {s} ^ {*} (\hat {\theta})\right) + H (S). \\ \end{array}
$$
$$
I (\hat {\theta}, S) = J S _ {p (s)} \left(p (\hat {\theta} | s)\right) = \sum_ {s} p (s) K L \left(p (\hat {\theta} | s) \mid \mid p (\hat {\theta})\right). \tag {16}
$$
$$
\sum_ {s} p (s) K L \left(p (\hat {\theta} | s) \right| | p (\hat {\theta}) = \int \sum_ {s} p (s) p (\hat {\theta} | s) \log \frac {p (\hat {\theta} | s)}{p (\hat {\theta})} d \hat {\theta}. \tag {17}
$$
$$
\begin{array}{l} \int \sum_ {s} p (s) p (\hat {\theta} | s) \log \frac {p (\hat {\theta} | s)}{p (\hat {\theta})} d \hat {\theta} \\ = \int \sum_ {s} p (s) p (\hat {\theta} | s) \log \frac {p (s) p (\hat {\theta} | s)}{p (\hat {\theta})} d \hat {\theta} + H (S) \tag {18} \\ = \int p (\hat {\theta}) \sum_ {s} \frac {p (s) p (\hat {\theta} | s)}{p (\hat {\theta})} \log \frac {p (s) p (\hat {\theta} | s)}{p (\hat {\theta})} d \hat {\theta} + H (S) \\ = \int p (\hat {\theta}) \sum_ {s} p (s | \hat {\theta}) \log p (s | \hat {\theta}) d \hat {\theta} + H (S). \\ \end{array}
$$
$$
\begin{array}{l} \int p (\hat {\theta}) \sum_ {s} p (s | \hat {\theta}) \log p (s | \hat {\theta}) d \hat {\theta} + H (S) \\ = \int p (\hat {\theta}) \sum_ {s} \mathcal {D} _ {s} ^ {*} (\hat {\theta}) \log \mathcal {D} _ {s} ^ {*} (\hat {\theta}) d \hat {\theta} + H (S) \tag {19} \\ = \mathbb {E} _ {\hat {\theta} \sim p (\hat {\theta})} \sum_ {s} \mathcal {D} _ {s} ^ {*} (\hat {\theta}) \log \mathcal {D} _ {s} ^ {*} (\hat {\theta}) + H (S) \\ = - H \left(\mathcal {D} ^ {*} (\hat {\theta})\right) + H (S). \\ \end{array}
$$
We have successfully established the relationship between  $I(\hat{\theta}, S)$  and  $U_N$  through Lemma A.2. Consequently, we can minimize our fairness criterion  $I(\theta, S)$  directly by minimizing Eq. (15) using  $U_N$  without the need to predict unknown sensitive attribute labels.
Algorithm 1: The FairLISA framework
Input: Training user set  $U$  item set  $V$  ; interaction records  $R$  ; Filter  $\mathcal{F}$  Discriminator  $\mathcal{D}$  Training epochs  $M$  Discriminator training steps  $T$  hyperparameters  $\lambda_1,\lambda_2,\lambda_3$  Initialize: User modeling results  $\theta ,\forall \theta \in U$    
for epoch  $\longleftarrow$  1 to M do for  $u\in U$  do  $\hat{\theta}\gets \mathcal{F}(\theta)$  Optimize  $\mathcal{F}$  through  $\mathcal{L}_{\mathcal{F}}$  in Eq.(9) with  $\mathcal{D}$  fixed; for  $t\longleftarrow 1$  to T do Optimize  $\mathcal{D}$  through  $\mathcal{L}_{\mathcal{D}}$  in Eq.(10) with  $\theta ,\mathcal{F}$  fixed; end end
B Training Algorithm for FairLISA
C.1 User Modeling Tasks
To verify the effectiveness of our model, we choose two representative issues in real-world user modeling scenarios. The first is user capability modeling in areas such as education which is called cognitive diagnosis [40]. We choose several representative models:
- IRT [30] is a cognitive diagnosis method that models the cognitive processes from students' exercise records with a logistic-like function.
- MIRT [4] is a variant of the basic IRT model, which extends the unidimensional latent traits of students and exercises in IRT to multidimensional vectors.
- NCD [41] is a deep neural cognitive diagnosis framework that models the complex interaction from students' exercising records with a multilayer perceptron (MLP).
The second is user preference modeling in recommender system [39]. We choose several representative models:
- PMF [34] is the Probabilistic Matrix Factorization algorithm by adding Gaussian prior distribution of user and item latent factors into the classical matrix factorization algorithm.
- NCF [15] is a state-of-the-art collaborative filtering model based on deep neural networks.
- LightGCN [16] is a state-of-the-art GCN-based recommender system model which learns user embeddings by linearly propagating them on the user-item interaction graph.
C.2 Dataset Description
PISA2015<sup>4</sup> is released by Program for International Student Assessment (PISA), which collects students' information from over one hundred regions or countries. It contains 403,609 students, 183 exercises, and the records between students and exercises are 11,488,234. We select region, gender, family education, and family economic as sensitive attributes. For region, users are divided into two groups according to whether users' region belongs to Organisation for Economic Co-operation and Development (OECD) countries. According to whether the highest education degree of parents is above primary level, we divide users into two groups. Similarly we do so according to whether there are houses belonging to users. More details of the PISA dataset can be found in [52].
MovieLens-1M<sup>5</sup> is a benchmark dataset for recommender systems. It contains 1 million rating records for about 4,000 movies from 6,040 users. We select gender, age, and occupation as user
<sup>4</sup>https://www.oecd.org/pisa/data/2015database/
<sup>5</sup>https://grouplens.org/datasets/movielens/1m/
Table 2: The fairness performance of baselines on cognitive diagnosis task (AUC scores of all attackers). R, A, E, C represent region, age, family education, family economic. The smaller values of AUC denote better fairness performance with less sensitive information leakage (the fairer). The best results are highlighted in bold.
IRT	MIRT	NCD
AUC-R	AUC-A	AUC-E	AUC-C	AUC-R	AUC-A	AUC-E	AUC-C	AUC-R	AUC-A	AUC-E	AUC-C
Origin	0.5864	0.5191	0.5930	0.5565	0.6271	0.5351	0.6329	0.5831	0.6307	0.5344	0.6327	0.5808
ComFair	0.5661	0.5178	0.5858	0.5515	0.5727	0.5226	0.5806	0.5618	0.5786	0.5300	0.5795	0.5609
FairGo	0.5699	0.5179	0.5828	0.5489	0.5700	0.5201	0.5965	0.5624	0.5724	0.5220	0.5950	0.5597
FairGNN	0.5468	0.5165	0.5452	0.5284	0.5680	0.5181	0.5952	0.5562	0.5761	0.5209	0.5944	0.5591
FairLISA	0.5412	0.5163	0.5490	0.5279	0.5540	0.5154	0.5727	0.5429	0.5540	0.5154	0.5727	0.5429
FairGo+FairLISA	0.5355	0.5152	0.5419	0.5279	0.5510	0.5154	0.5720	0.5422	0.5622	0.5190	0.5704	0.5513
Table 3: The accuracy performance of baselines on cognitive diagnosis task. Bold represents the best results, and underline represents runner-up results.
IRT	MIRT	NCD
ACC	AUC	MAE	MSE	ACC	AUC	MAE	MSE	ACC	AUC	MAE	MSE
Origin	0.6932	0.7475	0.3932	0.2042	0.7152	0.7868	0.3529	0.1903	0.7486	0.8111	0.3555	0.1704
ComFair	0.6834	0.7380	0.3953	0.2095	0.7141	0.7864	0.3607	0.1887	0.7253	0.8000	0.3605	0.1816
FairGo	0.6853	0.7422	0.3996	0.2072	0.7147	0.7804	0.3618	0.1897	0.7299	0.8019	0.3597	0.1799
FairGNN	0.6853	0.7423	0.3972	0.2084	0.7110	0.7857	0.3616	0.1893	0.7301	0.8025	0.3584	0.1800
FairLISA	0.6923	0.7469	0.3942	0.2044	0.7148	0.7867	0.3565	0.1896	0.7300	0.8039	0.3572	0.1796
FairGo+FairLISA	0.6905	0.7411	0.3927	0.2045	0.7140	0.7864	0.3590	0.1897	0.7313	0.8041	0.3573	0.1793
sensitive features, where gender is a binary feature, occupation is a 21-class feature, and users are assigned to 7 groups based on age.
C.3 Fairness-aware Baselines
we compare FairLISA with the following baselines:
- Origin: basic user models without fairness consideration.
ComFair [3] is a classical fairness-aware adversarial method in fully sensitive attributes situations.
- FairGo [45] is the state-of-the-art method to improve fairness in fully sensitive attribute situations from a graph perspective.
- FairGNN [5] is the state-of-the-art fairness-aware method in limited sensitive situations relying on a sensitive attribute predictor.
C.4 Result of Cognitive Diagnosis
The fairness and accuracy results of cognitive diagnosis task are shown in Table 2, Table 3. We have several observations from the out outcomes.
- From the perspective of model fairness (i.e., Table 2), the AUC of attackers on origin user modeling models are significantly higher than 0.5, which means that the sensitive information is exposed by user modeling results even such information is not explicitly used. Further, all fairness-aware methods can improve fairness. Among these methods, models which can simultaneously deal with the known and unknown sensitive attributes information (i.e., FairGNN, FairLISA, FairGo+FairLISA) get better fairness performance. It shows that data with unknown sensitive attributes also benefit fair user modeling. More importantly, we find our methods (i.e., FairLISA, FairGo+FairLISA) outperform others, suggesting the effectiveness of our work.
- From the perspective of model accuracy (i.e., Table 3), all fairness-improving methods lose some accuracy compared with origin user models. This is the inevitable result of the trade-off between accuracy and fairness [3, 33, 45]. The reason is that the fairness-aware methods are aiming at filtering out the information of certain sensitive features from user modeling results, which will to some extent reduce the information contained, thus decreasing accuracy. Among these fairness-aware methods, we could find FairLISA, FairGo+FairLISA have the best accuracy performance, and they could even maintain comparable accuracy with origin models in some cases.
Figure 5: Effects of different hyperparameters on NCD.
Figure 6: Effects of different hyperparameters on LightGCN.
- From the perspective of balancing the model accuracy and fairness. Our methods can achieve both better accuracy performance and fairness promotion in all cases. Hences, we argue that our framework achieves better performance in balancing the model accuracy and fairness, which also suggests that making full use of data with unknown sensitive attributes can alleviate the problem of fairness-accuracy trade-off to some extent.
C.5 Influence of  $U_{L}, U_{N}$  (RQ3)
FairLISA unifies the treatment of data with known sensitive attributes  $U_{L}$  and data with unknown sensitive attributes  $U_{N}$  from a mutual information perspective, thus  $U_{L}, U_{N}$  can be directly leveraged to improve fairness. In this part, we investigate their influence on fair user modeling results by adjusting the hyperparameter  $\lambda_{2}(U_{L}), \lambda_{3}(U_{N})$ . As for the user models, we choose the representative models which achieve the best performance results in RQ1 (i.e., NCD, LightGCN). More specifically, we vary the values of  $\lambda_{2}, \lambda_{3}$  on NCD as  $\{0, 0.5, 1, 1.5\}$  and the values of  $\lambda_{2}, \lambda_{3}$  on LightGCN as  $\{0, 5, 10, 15\}$ . The results are shown in Figure 5 (the lower, the fairer). On the one hand, we find  $\lambda_{2}$  always has a huge impact than  $\lambda_{3}$ , which means  $U_{L}$  makes a greater contribution to fairness than  $U_{N}$ . This is reasonable because of the sensitive attribute labels in  $U_{L}$  being as the guidance to filter the effect of sensitive attributes. On the other hand, as the values get larger, both of the results get fairer, which indicates that both  $U_{L}$  and  $U_{N}$  can contribute to fairness. This observation also demonstrates that making use of  $U_{N}$  can improve the fairness of the user modeling result.
C.6 Relation to classical group fairness metrics (RQ4)
Previous experiments have shown the effectiveness of our framework in terms of avoiding leaking sensitive information from user modeling results. In this part, we show the results of our proposed
Figure 7: Performance of group fairness metrics on NCD and LightGCN (the lower, the better).
Figure 8: Performance of group fairness metrics on MIRT, NCF (the lower, the better).
Figure 9: Performance of group fairness metrics on IRT, PMF (the lower, the better).
model on classical fairness metrics. We choose two group fairness metrics (i.e., Demographic Parity [7], Equal Opportunity [13]) to evaluate the results. Demographic Parity [7] is widely used to measure the predicted rating discrepancy for binary valued sensitive attributes [45]. Take binary attribute (i.e., gender) for example, the detailed formula is as  $DP = \frac{1}{N}\sum_{v=1}^{N}||E_{u\in male}[\hat{r}_{uv}] - E_{u\in female}[\hat{r}_{uv}|||$ . For attributes with multiple values, we borrow the idea of demographic parity and divide users into different groups based on their sensitive values. Then we take the standard deviation of predicted ratings of each user group to measure demographic parity. Equal Opportunity [13] is another classical fairness definition, it advances demographic parity fairness by considering the parity of prediction accuracy of each group. For binary attribute, take gender for example, the detailed formulas are as  $EO = \frac{1}{N}\sum_{v=1}^{N}||E_{u\in male}[\hat{r}_{uv} - r_{uv}] - E_{u\in female}[\hat{r}_{uv} - r_{uv}|||$ . For attributes with multiple values, it has the same way as demographic parity. The results of these two group fairness metrics on the user models are shown in Figure 7, Figure 8, Figure 9. We can find both user modeling tasks are unfair on these two classical metrics, which also indicates the necessity to explore fairness in user modeling. Then, all fairness-aware methods aiming to remove the effect of sensitive attributes can improve the fairness of the two metrics. It shows that the goal of removing the effect of sensitive attributes also benefits the classical group fairness metrics. Among all these methods, we could find that the methods (FairGNN, FairGo+FairLISA, FairLISA) can always achieve better results, which shows that it is necessary to explore fairness in limited situations. Meanwhile, we find FairLISA can achieve the best performances, suggesting the effectiveness of our methods.