FairDRL-ST: Fair Urban Demand Forecasting

• The paper introduces FairDRL-ST, a framework leveraging a spatio-temporal VAE with disentangled latent components to forecast urban mobility while addressing fairness.
• It employs adversarial training to concentrate sensitive features in one latent space and prevent leakage in the predictive component, improving fairness metrics like RFG and IFG.
• Experiments on NYC taxi and bike data show that FairDRL-ST maintains high accuracy while significantly reducing disparities across demographic and regional groups.

Searching arXiv for the primary paper and closely related work to ground citations. FairDRL-ST is a fairness-aware spatio-temporal mobility prediction framework for city-scale demand forecasting over urban grids. It is introduced for taxi and bike flow prediction in New York City and is designed to reduce disparities across demographic and regional groups while retaining high predictive accuracy, without using fairness labels such as region-based or individual-based fairness targets during training. Architecturally, it is a spatio-temporal variational autoencoder with disentangled latent variables, adversarial training, and heterogeneous urban inputs, and its central premise is that sensitive information should be concentrated in one latent component and removed from the task-relevant component used for forecasting (Zhao et al., 11 Aug 2025).

1. Problem formulation and fairness criteria

The task is mobility demand prediction over a partitioned urban area. The study area is divided into grid cells $\mathcal{C}=\{c_1,\dots,c_n\}$, with $x_{i,t}$ denoting the available mobility resource in cell $c_i$ at time interval $t$, $X_t \in \mathbb{R}^n$ the citywide tensor at time $t$, and $\hat{y}_{i,t}$ the predicted demand for future time(s). In the reported experiments, both TaxiNYC and BikeNYC are aggregated into 30-minute, grid-based spatio-temporal tensors over New York City, and each cell is assigned a population weight $p_i$ with $\sum_i p_i=1$ (Zhao et al., 11 Aug 2025).

Fairness is defined with respect to demographic or socio-economic attributes $S$, such as race, income, or proxies such as region type. For evaluation, cells are grouped into advantaged and disadvantaged regions, denoted $x_{i,t}$0 and $x_{i,t}$1, and each cell can also be decomposed into within-cell proportions $x_{i,t}$2 and $x_{i,t}$3 for advantaged and disadvantaged individuals. The paper’s motivation is explicitly structural: urban mobility data reflect unequal resource availability and historical under-service, so naïvely trained deep spatio-temporal predictors may under-predict demand in disadvantaged areas and over-predict it in advantaged areas, thereby reinforcing existing inequalities (Zhao et al., 11 Aug 2025).

Three fairness metrics are used. The Region-based Fairness Gap (RFG) compares per-capita predicted demand across advantaged and disadvantaged regions: $x_{i,t}$4 The Individual-based Fairness Gap (IFG) refines this by using within-cell group proportions: $x_{i,t}$5 Lower absolute values indicate more similar per-capita predicted demand. The third metric is Spearman’s rank correlation (SR) between predicted demand rankings and disadvantaged-group fraction across regions; values near $x_{i,t}$6 indicate weaker dependence. Predictive accuracy is measured by MAE between $x_{i,t}$7 and $x_{i,t}$8 (Zhao et al., 11 Aug 2025).

A common misconception is suggested by the acronym. In some urban AI literature, “DRL” denotes deep reinforcement learning, including fairness-aware traffic signal control formulations (Raeis et al., 2021). In FairDRL-ST, however, the operative mechanism is disentangled representation learning, not reinforcement learning (Zhao et al., 11 Aug 2025).

2. Architectural design and latent-variable decomposition

FairDRL-ST is organised as a four-part system: an encoder with a disentangled representation learning module, a sensitive module, a non-sensitive module, and a decoder. Its backbone is a 3D convolutional encoder-decoder based on a Convolutional Denoising Autoencoder extended into a sequential VAE with temporal prior networks. Spatial structure is handled implicitly through the grid representation; the method does not use explicit GCNs or graph transformers (Zhao et al., 11 Aug 2025).

The latent variable $x_{i,t}$9 is explicitly partitioned into a sensitive component $c_i$0 and time-dependent non-sensitive components $c_i$1. The paper’s key design principle is that sensitive information should be concentrated in $c_i$2, while $c_i$3 should retain the spatio-temporal factors needed for forecasting but exclude sensitive content. In this sense, prediction and reconstruction are intended to depend primarily on $c_i$4, with only a controlled role for $c_i$5 (Zhao et al., 11 Aug 2025).

The framework ingests heterogeneous multimodal inputs. The 3D stream comprises mobility flows; the 2D stream comprises static contextual maps such as POI categories; and the 1D stream comprises citywide temporal variables such as temperature, humidity, and pressure. Each input type is passed through three convolutional layers with kernel counts $c_i$6, $c_i$7, and $c_i$8, yielding aligned representations that are broadcast across time or space as needed and then stacked before entering the disentanglement module. Two additional 3D convolutional layers with filters $c_i$9 and $t$0 produce the compact latent representation that is split into $t$1 and $t$2 (Zhao et al., 11 Aug 2025).

This design places FairDRL-ST in the lineage of fair representation learning rather than fairness-by-constraint approaches. The practical difference is important: instead of directly penalising RFG or IFG in the predictive objective, the method attempts to make the forecasting representation itself less sensitive to protected attributes (Zhao et al., 11 Aug 2025).

3. Variational objective and adversarial fairness mechanism

The latent structure combines a time-invariant sensitive prior and a sequential prior for non-sensitive dynamics. The paper specifies

$t$3

and

$t$4

where $t$5 are generated by a spatio-temporal prior network. The decoder models

$t$6

with a transposed 3D-convolutional network reconstructing the grid tensor at each time step (Zhao et al., 11 Aug 2025).

The base learning signal is an ELBO-style VAE objective containing a reconstruction term and KL regularisation for both $t$7 and $t$8. To encourage disentanglement, the model additionally uses FactorVAE-style total-correlation regularisation, estimated adversarially, to penalise dependence among latent dimensions. This pushes the representation toward factor separation and supports the intended isolation of sensitive variation (Zhao et al., 11 Aug 2025).

The VAE alone does not guarantee that sensitive content will be localised in $t$9. FairDRL-ST therefore adds two adversarially opposed modules. The sensitive module contains a generator $X_t \in \mathbb{R}^n$0 that maps $X_t \in \mathbb{R}^n$1 to a generated sensitive attribute $X_t \in \mathbb{R}^n$2, together with a discriminator $X_t \in \mathbb{R}^n$3 that distinguishes real $X_t \in \mathbb{R}^n$4 from generated $X_t \in \mathbb{R}^n$5. Its loss is expressed as

$X_t \in \mathbb{R}^n$6

so minimising $X_t \in \mathbb{R}^n$7 with respect to the encoder and generator encourages $X_t \in \mathbb{R}^n$8 to be informative about $X_t \in \mathbb{R}^n$9 (Zhao et al., 11 Aug 2025).

The non-sensitive module contains a predictor $t$0 that attempts to infer $t$1 from $t$2, with loss

$t$3

In the full objective this term is subtracted, so the encoder is trained to make $t$4 fail. The result is a two-sided disentanglement mechanism: one branch encourages sensitive information to be recoverable from $t$5, while the other discourages any sensitive leakage into $t$6 (Zhao et al., 11 Aug 2025).

4. Optimisation, training protocol, and the meaning of “unsupervised”

The complete objective is

$t$7

where $t$8 controls the strength of the fairness and disentanglement pressure. When $t$9, the model reduces to a standard spatio-temporal VAE. As $\hat{y}_{i,t}$0 increases, the encoder is pushed more strongly to concentrate sensitive information in $\hat{y}_{i,t}$1 and exclude it from $\hat{y}_{i,t}$2 (Zhao et al., 11 Aug 2025).

Optimisation is a min-max game. The encoder, decoder, priors, and sensitive generator minimise the combined objective; the discriminator in the sensitive module maximises its ability to distinguish real from generated sensitive attributes; and the predictor in the non-sensitive module minimises its own prediction loss while the encoder tries to increase that loss through the negated term. The paper characterises this as a three-player game analogous to standard adversarial fairness schemes, but implemented over a disentangled spatio-temporal latent space rather than over direct predictors (Zhao et al., 11 Aug 2025).

The training pipeline consists of preprocessing and alignment of 1D, 2D, and 3D inputs; encoding them into $\hat{y}_{i,t}$3 and $\hat{y}_{i,t}$4; decoding to reconstruct the sequence; generating and discriminating $\hat{y}_{i,t}$5; and predicting $\hat{y}_{i,t}$6 from $\hat{y}_{i,t}$7. Parameters are updated with alternating steps. The experiments vary $\hat{y}_{i,t}$8 across $\hat{y}_{i,t}$9, $p_i$0, and $p_i$1 to study fairness-utility trade-offs. The paper notes standard GAN-style and FactorVAE-style stabilisation assumptions but does not introduce a separate novel stabilisation method (Zhao et al., 11 Aug 2025).

The paper’s use of the term unsupervised is specific. It does not mean the model has no access to sensitive attributes; rather, it means fairness metrics such as RFG and IFG are not used as training targets, and group-level fairness labels are not used for regularisation. Sensitive attributes $p_i$2 are used only in the adversarial latent-shaping modules and in evaluation (Zhao et al., 11 Aug 2025).

5. Data sources, preprocessing, and benchmark configuration

The empirical study uses two New York City datasets. TaxiNYC consists of taxi in/out flows from January to March 2015. BikeNYC consists of Citi Bike flows from April to September 2014. Both are aggregated into 30-minute spatio-temporal tensors over a regular grid. Additional context includes weather variables from NCEI and POI maps from NYC Open Data, with categories including business, food, government, hospitals, schools, and transportation (Zhao et al., 11 Aug 2025).

All inputs are rasterised into non-overlapping grid cells. Missing values are filled by local averages, and features are scaled to $p_i$3. The 1D data are aggregated into 30-minute slots, 2D contextual features are rasterised by counts or area-weighted aggregation, and 3D mobility data are aggregated per cell per 30-minute interval. This preprocessing follows the paper’s grid-centric view of urban prediction and is consistent with the absence of explicit graph operators in the model (Zhao et al., 11 Aug 2025).

The benchmark includes simple, non-fair, and fairness-aware baselines: HA, CNN, ConvLSTM, FairST with region-based or individual-based fairness regularisers, and two Equitensor variants with different numbers of context features. All models are evaluated using MAE, RFG, IFG, and SR. This matters methodologically because the paper compares FairDRL-ST not only to accuracy-oriented forecasting baselines but also to models that explicitly encode fairness terms in the training loss (Zhao et al., 11 Aug 2025).

6. Empirical behaviour, trade-offs, and ablations

On TaxiNYC, the best MAE among all models is reported for ConvLSTM at $p_i$4, while FairDRL-ST achieves $p_i$5, outperforming the FairST variants and Equitensor-3 and coming close to Equitensor-9 at $p_i$6. On BikeNYC, ConvLSTM attains $p_i$7 and FairDRL-ST is reported at $p_i$8, effectively tying it. These results support the paper’s claim that fairness can be improved with minimal predictive degradation (Zhao et al., 11 Aug 2025).

The fairness metrics show larger differences. On TaxiNYC, the ground-truth RFG is $p_i$9, ConvLSTM yields $\sum_i p_i=1$0, Equitensor-9 yields $\sum_i p_i=1$1, and FairDRL-ST yields $\sum_i p_i=1$2, which is the best among unsupervised methods; the supervised FairST+IF reaches $\sum_i p_i=1$3 but with higher MAE. For IFG on TaxiNYC, the ground truth is $\sum_i p_i=1$4, ConvLSTM yields $\sum_i p_i=1$5, Equitensor-9 yields $\sum_i p_i=1$6, and FairDRL-ST yields $\sum_i p_i=1$7, close to FairST+IF at $\sum_i p_i=1$8. SR on TaxiNYC moves from $\sum_i p_i=1$9 for ConvLSTM and $S$0 for Equitensor-9 to $S$1 for FairDRL-ST, the closest to zero among the unsupervised models (Zhao et al., 11 Aug 2025).

On BikeNYC, the ground-truth RFG is $S$2, ConvLSTM gives $S$3, Equitensor-9 gives $S$4, and FairDRL-ST gives $S$5, which is the best RFG reported. For IFG, the ground truth is $S$6, ConvLSTM gives $S$7, Equitensor-9 gives $S$8, and FairDRL-ST gives $S$9, slightly worse than Equitensor-9 but with better RFG and MAE. SR is $x_{i,t}$00 for FairDRL-ST, compared with $x_{i,t}$01 for Equitensor-9 and $x_{i,t}$02 for ConvLSTM, again indicating the weakest ranking dependence on disadvantaged-group proportions (Zhao et al., 11 Aug 2025).

The paper’s $x_{i,t}$03-sweep on BikeNYC shows a non-monotonic fairness-utility frontier. As $x_{i,t}$04 increases from small values, RFG and IFG initially decrease while MAE remains stable or increases only slightly. Beyond a threshold, both fairness gaps deteriorate and MAE worsens, indicating that excessive fairness pressure can remove task-relevant information. The paper notes that IFG degrades earlier than RFG as $x_{i,t}$05 grows, which suggests that within-cell composition is more sensitive to over-aggressive feature suppression (Zhao et al., 11 Aug 2025).

Ablation results isolate the roles of the two fairness modules. Removing either the sensitive module or the non-sensitive module increases fairness gaps substantially. The non-sensitive module, which suppresses sensitive leakage in $x_{i,t}$06, produces the larger fairness gains when used alone, indicating that preventing sensitive information from contaminating the predictive latent space is especially important. By contrast, the best MAE is sometimes obtained with only the sensitive module at moderate $x_{i,t}$07, while adding the non-sensitive module slightly worsens MAE but substantially improves RFG and IFG. The full model with both modules and $x_{i,t}$08 is presented as the paper’s preferred balance (Zhao et al., 11 Aug 2025).

7. Interpretation, limitations, and position within fair urban AI

Interpretability in FairDRL-ST is primarily structural rather than visual. The model is interpretable to the extent that $x_{i,t}$09 is explicitly trained to regenerate sensitive attributes and $x_{i,t}$10 is explicitly trained to fail at predicting them. The paper does not present latent visualisations, but it treats the success of the sensitive generator and the failure of the non-sensitive predictor as empirical evidence that sensitive and non-sensitive factors have been separated. FactorVAE total-correlation regularisation further supports this interpretation by encouraging independence among latent dimensions (Zhao et al., 11 Aug 2025).

The method also makes several assumptions. Sensitive attributes or good proxies must be available for the adversarial modules, even though fairness labels are not used in the main predictive objective. The fairness notion is restricted to group-based resource parity and rank independence; it does not address equalized odds, causal fairness, or trajectory-level individual fairness. Spatial structure is represented as a grid rather than an explicit mobility network. The paper also notes that large $x_{i,t}$11 can damage both accuracy and fairness, and that adversarial disentanglement may not perfectly isolate sensitive factors, leaving residual bias (Zhao et al., 11 Aug 2025).

Relative to prior baselines in the same experimental setting, FairDRL-ST is positioned as distinct from FairST, which adds RFG or IFG directly as supervised regularisers in the prediction loss, and from Equitensor, which learns debiased urban representations without explicit sensitive/non-sensitive factor separation. The paper’s stated novelty lies in combining a spatio-temporal VAE, a latent split between $x_{i,t}$12 and $x_{i,t}$13, and the two-sided adversarial mechanism that simultaneously concentrates sensitive information and suppresses sensitive leakage, while keeping fairness metrics out of the training objective itself (Zhao et al., 11 Aug 2025).

A plausible implication is that FairDRL-ST is best understood as a fair representation-learning framework for rasterised urban forecasting rather than as a special-purpose mobility model. The paper explicitly suggests transfer to other spatio-temporal prediction tasks such as traffic flow prediction, air quality forecasting, and resource allocation settings where sensitive attributes can be defined at the region level and inputs can be expressed on a grid (Zhao et al., 11 Aug 2025).