Urbanization, while offering increased access to resources and opportunities, also presents growing inequalities in accessing urban facilities and exploiting urban opportunities. These inequalities manifest across various demographic groups, including gender, socioeconomic status, and ethnicity. Existing research often relies on limited datasets or flawed correlation analysis, hindering a comprehensive understanding of the causal relationships. This study aims to address these limitations by leveraging large-scale mobility data from SafeGraph, covering millions of residents' interactions with urban venues across six major U.S. metropolitan areas. The study goes beyond simple correlation, employing propensity score matching (PSM) to quantify the causal effects of resident demographics on mobility patterns. Furthermore, a novel Counterfactual RANdom-walks-based Embedding (CRANE) method is designed to efficiently reveal micro-neighborhood level accessibility gaps, learning continuous embedding vectors that disentangle confounding effects. The study aims to provide a more nuanced and robust understanding of urban accessibility gaps and inform urban design policies to promote equitable access to urban resources and opportunities.

Existing literature demonstrates a growing interest in understanding mobility inequalities in urban spaces. Studies have examined the relationship between gender and daily mobility, finding women tend to visit fewer locations and distribute their time less equally than men. Research has also linked socioeconomic status and age to mobility range, with higher socioeconomic status and younger age correlating with greater mobility. Studies in South America highlight how diverse mobility patterns exist across socioeconomic classes. Research on the COVID-19 pandemic revealed that poorer populations showed lower reductions in mobility levels. Additionally, the impact of planned spatial factors, such as public transportation infrastructure and neighborhood walkability, on urban mobility has been investigated. However, existing studies suffer from limitations, often relying on small-scale survey data or biased large-scale estimation using hypothetical models based on spatial proximity. The availability of large-scale, precise mobility data offers the opportunity to overcome these limitations.

This study utilizes demographic data from the 2019 U.S. Census Bureau's American Community Survey and SafeGraph's Patterns and Core Places datasets. The demographic data provides information on neighborhood characteristics (e.g., gender ratio, race, income, education, disability) at the census block group (CBG) level. SafeGraph data provides fine-grained records of residents' visits to Points of Interest (POIs). The study employs two key methods: Propensity Score Matching (PSM) and Counterfactual RANdom-walks-based Embedding (CRANE). **Propensity Score Matching (PSM):** PSM is used to estimate the causal effects of demographic features on mobility patterns. This method addresses confounding effects by matching neighborhoods with similar characteristics but differing in a specific demographic feature. An ordinal regression model is used to estimate propensity scores, and matching is performed based on the disparity in propensity scores. The average treatment effect is then calculated to assess the causal impact of each demographic feature. **Counterfactual RANdom-walks-based Embedding (CRANE):** CRANE is a novel representation learning algorithm designed to capture micro-level disparities in facility accessibility. It involves conducting counterfactual random walks on an urban mobility network, comparing observed associations between demographic features and POI accessibility with alternative outcomes in counterfactual scenarios where the demographic feature has no causal impact. The difference between observed and alternative outcomes is used to update node embeddings, preserving real-world accessibility gaps. The algorithm uses a loss function to maximize the similarity between co-occurrences of observed outcomes and minimize the similarity between co-occurrences of alternative outcomes, incorporating regularization terms for spatial and demographic feature continuity. The Adam optimizer is used to learn 64-dimensional embedding vectors for POI categories, POIs, neighborhoods, and treatment levels of demographic features.

The study reveals several key findings regarding mobility inequality in the six major U.S. metropolitan areas analyzed. **Mobility Frequency:** Neighborhoods with higher average income consistently exhibit higher mobility frequency, reflecting the cost of urban mobility. Conversely, neighborhoods with a higher proportion of bachelor's degree holders show significantly lower mobility frequencies, suggesting that highly educated individuals may access urban facilities less frequently, even when controlling for income and other factors. Neighborhoods with a higher white population ratio also demonstrate higher mobility frequencies, indicating racial disparities in access to urban facilities. **Mobility Reduction during COVID-19:** The analysis shows that neighborhoods with a higher bachelor's degree holder ratio experienced greater mobility reduction during the COVID-19 pandemic, likely due to the ability to transition to remote work. Similarly, neighborhoods with higher white population ratios showed less mobility reduction, indicating disparities in resilience to pandemic shocks. **Urban Facility Accessibility:** The study finds disparities in access to different types of POIs. Sports and education venues were more frequently visited by higher-income and white populations. Accessibility to health services was higher in neighborhoods with higher disability and female ratios. Interestingly, lower-income neighborhoods also showed higher visitation rates to health services in some cities, possibly due to differences in healthcare access and utilization. **CRANE Performance:** The CRANE method effectively captures both macro (MSA-level) and micro (neighborhood-level) accessibility gaps. In predictive analyses, CRANE outperforms baseline methods in most cases, showing improved prediction performance in out-of-sample scenarios and demonstrating cross-city knowledge transfer capabilities. A case study in Houston illustrates how CRANE disentangles confounding effects between demographic features, offering a more nuanced understanding of POI-level accessibility gaps.

The findings demonstrate significant and persistent inequalities in urban mobility across various demographic groups in U.S. cities. The use of propensity score matching successfully controls for confounding factors, offering stronger causal inferences compared to traditional correlational approaches. The CRANE method enhances the understanding of these inequalities by providing a micro-level perspective, identifying specific neighborhoods and POIs where disparities are most pronounced. The ability of CRANE to transfer knowledge across cities suggests that the identified patterns are not unique to specific locations but reflect broader systemic issues. These findings highlight the need for urban planning and policy interventions that address these inequalities and promote equitable access to urban resources and opportunities for all residents.

This study provides a comprehensive analysis of urban mobility inequalities in U.S. cities using large-scale mobility data and novel analytical methods. The findings reveal significant income and racial disparities in mobility frequency and access to various types of urban venues. The CRANE method proves effective in capturing these disparities at both macro and micro levels, enabling robust predictions and cross-city knowledge transfer. These findings underscore the urgent need for urban design policies aimed at reducing these inequalities and fostering more equitable and inclusive urban environments. Future research could investigate the impact of other factors, such as spatial characteristics (road networks, public transport availability), and explore the long-term implications of the observed inequalities.

While this study provides valuable insights into urban mobility inequalities, some limitations should be acknowledged. The study's reliance on SafeGraph data introduces potential biases related to data collection and representativeness. The study focuses on six major U.S. metropolitan areas; findings might not be generalizable to smaller or differently structured cities. The analysis focuses primarily on demographic factors; other factors, such as individual preferences, transportation options, and physical limitations, could also significantly impact mobility patterns. Future research should consider incorporating these additional factors to obtain a more comprehensive understanding of urban accessibility.