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When Correlations Mislead: Confounder-Aware Multi-View Urban Region Representation Learning

Sean Bin Yang, Ying Sun, Zongyi Xu, Tung Kieu, Jilin Hu, Bin Yang, Kristian Torp, Hua Lu, Torben Bach Pedersen

arXiv:2609.15305v1cs.LGcs.AI

TL;DR

Existing multi-view urban region methods may overlook view-specific structures and propagate correlations induced by shared latent factors. CURE preserves per-view graph structure, separates a shared component before cross-view interaction, and fuses residual representations using local and global contexts. Experiments across three cities and tasks report improved predictive performance, robustness to incomplete and noisy observations, and reliable integration.

  • Problem

    Multi-view methods may overlook view-specific regional structures and propagate correlations induced by shared latent factors, creating a reliability challenge.

    Source: §I · p. 2

  • Method

    CURE graph-encodes each view, estimates a shared latent component for residual-space interaction, and fuses residual views under local and global graph contexts.

    Source: §I · pp. 2–3

  • Results

    Across three real-world cities and analytics tasks, CURE improves predictive performance, remains robust to incomplete and noisy views, and supports reliable cross-view integration.

    Source: §I · p. 3

  • Takeaways & Limitations

    Shared component separation and adaptive view weighting support reliable integration of stable, task-relevant residual representations.

    Source: §VI · p. 14

Abstract

from arXiv · show

Urban region representation learning commonly combines heterogeneous data sources, such as mobility flows, points of interest, and land-use information, to support tasks including mobility analysis, public safety forecasting, and service demand estimation. Existing multi-view methods typically improve region embeddings by strengthening interactions across views. However, such methods often overlook view-specific regional structures and may propagate correlations induced by shared latent factors, which can reduce the stability of downstream predictions. To overcome this major limitation, we propose CURE, a confounder-aware framework for multi-view urban region representation learning. CURE first encodes each view with its regional graph structure, estimates a shared latent component, and then reduces its projected influence before cross-view interaction. A hierarchical graph-aware fusion module subsequently aggregates the residual view representations using local and global regional contexts Experiments on three real-world cities show that CURE improves predictive performance, remains robust under missing and noisy input views, and provides reliable cross-view integration through shared component separation and context-dependent view weighting.

I. INTRODUCTION

CURE addresses the risk that multi-view methods overlook view-specific regional structure and propagate correlations induced by shared latent factors. It preserves per-view structure, separates shared components before cross-view interaction, and fuses residual views using regional contexts.

I. INTRODUCTION

  • Single-view methods capture only part of urban semantics, while conventional multi-view interaction may propagate shared-factor correlations that do not reflect stable, task-relevant information.Potential shared factors include population density, commercial intensity, transportation accessibility, and socioeconomic activity.Source: §I · p. 1
  • The challenges include preserving each view’s regional structure, avoiding misleading correlation-driven interaction, and adapting view contributions to local and global contexts.Mobility, POI, and land-use views encode different dependencies, and their relevance can vary across regions and tasks.Source: §I · p. 2
  • Across three real-world cities and urban analytics tasks, CURE improves predictive performance and shows robustness to incomplete and noisy views, with reliable cross-view integration.Ablations and further analyses examine its components, shared component separation, and adaptive view weighting.Source: §I · p. 3
  • A graph-guided intra-view encoder preserves mobility, POI, and land-use structures, providing structured view-specific signals under incomplete or noisy views.The framework constructs and exploits a regional graph for each urban view before cross-view interaction.Source: §I · pp. 2–3
  • CURE estimates a shared latent component and interacts in residual representation space to reduce direct propagation of shared latent correlations.The design aims to focus cross-view learning on complementary view-specific information.Source: §I · pp. 2–3
  • Hierarchical graph-aware residual fusion aggregates view representations under local and global contexts, with adaptive weights emphasizing stable, task-relevant information.The framework combines these components to improve prediction, integration reliability, and robustness to incomplete or noisy observations.Source: §I · p. 3

II. RELATED WORK

Urban region representation learning moves from single-source encodings toward multi-view integration, while this paper targets shared-factor confounding. The preliminaries define regions and the urban views used for representation learning.

A. Urban Region Representation Learning

  • Single-view methods capture only part of the urban environment, while multi-view methods combine heterogeneous signals but often treat cross-view dependencies as reliable.CURE instead reduces the influence of shared latent factors before cross-view interaction and fusion.Source: A. Urban Region Representation Learning · p. 3

B. Reliable Multi-View Urban Data Integration

C. Confounder-Aware Representation Learning

  • Confounding describes observed dependencies that may arise from latent factors rather than meaningful causal or semantic relationships.The paper connects this challenge to heterogeneous urban views and cross-view fusion.Source: C. Confounder-Aware Representation… · pp. 3–4

III. PRELIMINARIES

A. Definitions

  • Urban regions are bounded analytical units, and the three views characterize movement connectivity, functional composition, and planning-oriented spatial structure.The paper uses mobility, POIs, and land-use, while noting that its method extends naturally to more views.Source: A. Definitions · p. 4

B. Problem Definition

The problem is to learn unified region embeddings from heterogeneous urban views while preserving view-specific semantics and mitigating spurious shared dependencies. CURE’s overview begins with graph-guided encoding of each view’s regional structure.

B. Problem Definition

  • The objective is a unified region embedding that preserves regional structure, reduces dependence between residual views and the estimated shared component, and supports downstream analytics.The objective combines a structure-preserving similarity reconstruction with a decorrelation regularizer.Source: B. Problem Definition · p. 4

IV. METHODOLOGY

  • CURE learns unified region embeddings from mobility, POI, and land-use views while mitigating spurious dependencies caused by shared latent factors.Source: §IV · pp. 4–5

A. Framework Overview

  • The framework encodes view-specific structures, interacts in residual space, fuses representations under local and global graph contexts, and refines region embeddings.The resulting embedding is H.Source: A. Framework Overview · p. 5, Figure 2 · p. 5

B. Graph-Guided Intra-View Encoding

C. Confounder-Aware Inter-View Interaction

CURE estimates a shared latent component as a proxy for commonality across views, then reduces its projected influence before interacting residual representations. A learnable mixing coefficient combines interacted and original residuals.

C. Confounder-Aware Inter-View Interaction

  • CURE estimates a shared latent component, reduces its projected influence through soft residualization, and performs cross-view interaction on the resulting residual representations.This is intended to suppress correlations explained by the shared component while retaining view-specific information.Source: C. Confounder-Aware Inter-View… · p. 6
  • A learnable coefficient β mixes the interacted residual representations with the original residuals to encourage focus on complementary view-specific information.Source: C. Confounder-Aware Inter-View… · p. 6

D. Hierarchical Graph-Aware Residual Fusion

CURE fuses residual views using local and global graph contexts, with region-wise weights that adapt to structural context and task relevance.

D. Hierarchical Graph-Aware Residual Fusion

  • The fusion module combines each residual view with local and global graph contexts, then uses region-wise weights to emphasize stable, task-relevant signals.The global graph represents functional similarity, while the local graph captures regional structure.Source: D. Hierarchical Graph-Aware Residual… · p. 6

E. Region-Level Refinement

Region-level refinement captures higher-order dependencies among regions by applying a Transformer-style module to the graph-enhanced representation.

E. Region-Level Refinement

  • The fused graph-enhanced representation is refined to capture higher-order dependencies among regions.The section identifies this refinement as the next step after fusion.Source: E. Region-Level Refinement · p. 7
  • The refinement module operates on the graph-enhanced representation to produce the region-level representation.This pipeline role follows from the stated refinement step and the named RegionFusion module.Source: E. Region-Level Refinement · p. 7
  • RegionFusion applies a Transformer-style module composed of multi-head self-attention, residual connections, layer normalization, and a feed-forward network.Source: E. Region-Level Refinement · p. 7

F. Training of CURE

CURE trains its representations with objectives that preserve mobility, POI, and land-use similarity structures while reducing dependence between residual views and the estimated shared component.

F. Training of CURE

  • The multi-objective training loss preserves region-level similarity structures encoded by mobility, POI, and land-use features.Source: F. Training of CURE · p. 7
  • Feature-oriented representations decode the unified region embedding for outgoing and incoming mobility, POI, and land-use structures.The feature-specific objectives use pairwise similarities computed from the corresponding original feature types.Source: F. Training of CURE · p. 7
  • The mobility objective jointly preserves outgoing and incoming flow structures, while separate objectives preserve POI and land-use structures.Source: F. Training of CURE · p. 7
  • A decorrelation regularizer reduces dependence between the shared latent component and residual view representations.The regularizer uses a dimension-wise Pearson correlation matrix computed across urban regions; its strength is controlled by λ and it is introduced gradually during training.Source: F. Training of CURE · p. 7
  • The final objective jointly optimizes the training losses and the decorrelation regularizer.CURE gradually introduces the decorrelation loss to stabilize optimization.Source: F. Training of CURE · p. 7

A. Experimental Settings

The experiments evaluate embeddings on region-level regression tasks across New York, Chicago, and San Francisco, using a shared protocol and a set of representative urban-region baselines.

A. Experimental Settings

  • The evaluation covers New York, Chicago, and San Francisco, with spatial regions serving as units for feature construction and downstream analytics.The cities have diverse spatial layouts, population distributions, and activity patterns.Source: A. Experimental Settings · p. 7
  • The three tasks are check-in prediction, crime forecasting, and service call prediction, each formulated as region-level regression.Learned embeddings are fed to a Lasso regression predictor.Source: A. Experimental Settings · p. 7
  • Performance is assessed with MAE, RMSE, and R2, where lower MAE and RMSE and higher R2 indicate better results.Source: A. Experimental Settings · p. 8
  • The comparison includes mobility-based, semantic-based, heterogeneous-graph, contrastive, and attention-based representation methods.The five named baselines are MVURE, MGFN, RegionDCL, HREP, and HAFusion.Source: A. Experimental Settings · p. 8
  • All methods use the same data split and downstream regression protocol, with training capped at 2000 epochs and validation-based early stopping.CURE uses a 256-dimensional hidden representation and multi-head attention in its encoding, interaction, and refinement modules.Source: A. Experimental Settings · p. 8

B. Main Results

CURE improves prediction across the reported urban analytics settings, remains competitive on Chengdu socioeconomic tasks, and outperforms shared–private and adversarial multi-view alternatives overall.

B. Main Results

  • CURE achieves the best reported results across cities and metrics for check-in, crime, and service-call prediction, including improvements over HAF.Examples include NY check-in R2 rising from 0.844 to 0.875, Chi crime R2 from 0.631 to 0.732, and Chi service-call R2 from 0.613 to 0.736.Source: B. Main Results · p. 9

C. Evaluation on the Chengdu Dataset

  • On Chengdu, CURE achieves competitive performance on carbon-emissions, GDP, and population prediction.The evaluation applies its view-specific graphs, shared-component estimation, residualization, and multi-view fusion to mobility outflow, mobility inflow, and POI views.Source: C. Evaluation on the Chengdu Dataset · p. 9

D. Comparison with Shared–Private and Adversarial Multi-View Methods

  • CURE achieves the best overall performance across New York, Chicago, and San Francisco compared with MISA, DSN, and MEGAN.The authors report that shared–private separation or adversarial multi-view learning alone is insufficient to address potentially confounding cross-view dependencies.Source: D. Comparison with Shared–Private and… · p. 10

E. Ablation Study

CURE’s component ablations, parameter sensitivity tests, and scalability analysis examine how its design choices and regional coverage relate to prediction performance and computational cost.

E. Ablation Study

  • Across tasks, cities, and metrics, full CURE outperforms variants without GIVE, CIVI, or HGRF.Removing GIVE raises Chi check-in MAE from 762 to 1000 and lowers R2 from 0.916 to 0.876; removing CIVI or HGRF also degrades performance.Source: E. Ablation Study · p. 10
  • CURE also outperforms direct concatenation and standard cross-attention across NY, Chi, and SF.The comparison suggests gains are not attributable solely to increased fusion or interaction capacity.Source: E. Ablation Study · p. 10, Table VII · p. 11

F. Parameter Sensitivity Analysis

G. Model Scalability

  • Prediction performance generally improves as the number of regions grows, especially for NY check-in prediction and crime forecasting from 36 to 180 regions.SF benefits across all three tasks; in Chi, crime and service call prediction improve as more regions are included.Source: G. Model Scalability · pp. 11–12, Figure 5 · p. 12
  • As the scale ratio increases from 0.2 to 1.0, epoch time and peak GPU memory rise, while training-time growth remains moderate.In NY, AET rises from 0.1269s to 0.1590s and PA from 168.14MB to 328.91MB; full-scale Chi uses 0.0839s per epoch and 117.40MB peak memory.Source: G. Model Scalability · p. 12

H. Robustness and Reliability Analysis

CURE is evaluated for robustness to missing or noisy views and for reliability in separating shared components and adapting view contributions. The reported analyses find performance degradation under input corruption alongside evidence of residual separation and context-dependent weighting.

H. Robustness and Reliability Analysis

  • Removing any single view generally degrades performance, with missing mobility often causing the largest drops in check-in and service call prediction.CURE retains reasonable performance when one view is removed; missing POI or land-use usually causes smaller degradation.Source: Figure 6 · p. 12, H. Robustness and Reliability Analysis · p. 12
  • Performance generally declines as Gaussian feature noise increases, but CURE shows gradual rather than abrupt degradation.Mobility perturbations often cause sharper declines, while POI and land-use perturbations are more moderate in several cases.Source: Figure 7 · p. 13, H. Robustness and Reliability Analysis · p. 13
  • All views contain non-negligible shared components, while residual dependence is consistently close to zero across cities and views.The analysis uses shared component ratio (SR) to measure removed information and residual dependence (RD) to measure residual alignment with the shared component.Source: Table IX · p. 13, H. Robustness and Reliability Analysis · p. 13
  • Learned fusion weights vary across cities and tasks, with NY check-in emphasizing mobility, crime emphasizing POI, and service calls emphasizing land-use.Similar task- and city-dependent patterns are reported for Chi and SF.Source: H. Robustness and Reliability Analysis · pp. 13–14, Figure 8 · p. 14

VI. CONCLUSION

  • Across three cities and three tasks, CURE improves prediction, remains robust to incomplete and noisy observations, and supports reliable integration through shared component separation and adaptive view weighting.Source: §VI · p. 14

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