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A Hybrid State-Space Approach for Census-Tract Population Estimation

Jackson R. Ye, Alexandre V. Morozov

arXiv:2608.30094v1cs.CVcs.LG

TL;DR

Population estimation from satellite imagery remains dominated by grid-based predictions, although census data is collected for administrative units and grid disaggregation may introduce spatial bias. MambaPop models each tract’s polygon-masked image as a sequence and pairs it directly with the tract’s population label. Across 2020 contiguous-US tracts, it matches YOLOv11 on standard tracts and is reported as more robust on oversized tracts withheld from training.

  • Problem

    Population-estimation systems commonly predict or disaggregate population on grid cells rather than directly at the administrative-unit level, and disaggregation may introduce spatial bias.

    Source: §1 · p. 2

  • Method

    MambaPop models each administrative unit’s polygon-masked satellite image as a sequence of patches and pairs it directly with its population label.

    Source: §1 · p. 2, §7 · p. 9

  • Results

    Across approximately 84,000 2020 contiguous-US tracts, MambaPop equals YOLOv11 on standard tracts and is the most robust of the three backbones on oversized tracts withheld from training.

    Source: §7 · p. 10

  • Takeaways & Limitations

    The results support MambaPop as a low-cost complement to in-person enumeration for population predictions at time points without authoritative SF1 data.

    Source: §7 · p. 10

    Training excludes approximately 14,000 largest tracts (19% of contiguous-US tracts) because their images exceed the 512 × 512 crop limit.

    Source: §6 · p. 9

Abstract

from arXiv · show

Sequence models---the architecture family behind large language models and, increasingly, state-of-the-art image recognition---have redefined how machines learn from high-dimensional data. Yet population estimation from satellite imagery, a task that underpins infrastructure planning, public health, and disaster response, has scarcely benefited: leading systems still bind population to a uniform raster, disaggregating census counts onto grid cells through weighting surfaces built from ancillary data (e.g., in WorldPop and LandScan), which can introduce systematic spatial bias, and predicting population per grid cell with convolutional neural networks. In this approach, the administrative-unit structure in which the census was actually collected is discarded. We close this gap with MambaPop, which renders each administrative unit as a single polygon-masked satellite image and treats tract-level population estimation as a sequence-modeling problem over its image patches, pairing each tract image directly with its population label and eliminating the disaggregation step entirely. Built on the hybrid state-space--attention MambaVision backbone, MambaPop is, to our knowledge, the first method to learn population directly from an administrative unit's own image as well as the first to apply a state-space based (Mamba) hybrid architecture to the population estimation task. Across all $\sim$84{,}000 contiguous-US census tracts of the 2020 census, MambaPop attains a mean absolute error (MAE) of $1{,}141$ persons per tract, matching the strongest convolutional baseline (YOLOv11, MAE $1{,}122$).

1 Introduction

Population estimation from satellite imagery matters for planning and response, but existing grid-based approaches can introduce spatial bias and discard census administrative units. MambaPop pairs each tract image directly with its population label and uses sequence modeling, with the introduction highlighting generalization across time and space.

1 Introduction

  • Census counts are costly to collect and typically arrive only once per decade or less, while satellite imagery is continuously acquired and globally available.The passage frames imagery-based estimation as a complement to in-person enumeration.Source: §1 · p. 1
  • Grid-based pipelines disaggregate census counts using ancillary-data weighting surfaces, a step that may introduce spatial bias and discards administrative-unit structure.Such pipelines can also depend on the availability and quality of ancillary inputs.Source: §1 · p. 2
  • The approach pairs each tract’s variable-size, polygon-masked satellite image with its authoritative SF1 population label, eliminating disaggregation.MambaPop applies sequence modeling directly at the administrative-unit level using a hybrid state-space model.Source: §1 · p. 2
  • MambaPop predicts population for oversized tracts withheld from training, demonstrating extrapolation in both time and space.The contributions describe training on a single decennial census and testing on a later census.Source: §1 · p. 2

2 Related Work

Prior population-mapping work largely assigns counts to grid cells, whether through ancillary-data weighting or image-based prediction. Recent sequence and transformer approaches retain grid-based units, while adjacent work also uses satellite imagery for socioeconomic prediction and related tasks.

2 Related Work

  • Operational systems such as WorldPop and LandScan disaggregate census counts onto fine grids using ancillary data, with weighting heuristics that may introduce bias and depend on input availability and quality.The passage also identifies building-footprint constraints in newer WorldPop releases.Source: §2 · p. 2
  • Earlier image-based population studies used CNNs or combined imagery with geodata and other predictors, often producing fine-grid estimates or aggregating predictions to counties.Examples include Robinson et al., POMELO, and urban or regional mapping studies.Source: §2 · p. 2
  • More recent sequence and transformer approaches still predict grid-cell populations, and the cited work identifies no prior direct administrative-unit prediction or population-estimation use of state-space models.Yan et al. disaggregates county counts onto a 500 m grid before regression.Source: §2 · p. 2
  • Related satellite-imagery research also predicts consumption and asset wealth and maps population through building-footprint detection.The passages additionally note a local climate-zone classification dataset used in satellite-imagery research.Source: §2 · pp. 2–3

3 Dataset

The dataset pairs contiguous-US census tracts with Landsat imagery and tract-level population counts. It constructs polygon-masked tract images from RGB data and prepares them as model inputs alongside population-class labels.

3 Dataset

  • The dataset covers the contiguous United States and integrates satellite imagery with census-tract-level population data.Each tract image is paired directly with its population label.Source: §3 · p. 3, §3.2 · p. 3

3.1 Landsat 7 Surface Reflectance Data

  • The study uses Landsat 7 Surface Reflectance imagery and extracts only RGB bands at 30-meter resolution, with imagery from 2010 for training and 2020 for cross-decade evaluation.Clouds, shadows, and water are removed using the QA band, and pixel values are normalized from the 2nd to 98th percentile.Source: §3.1 · p. 3

3.2 Census Tract Population Labels (P001001 / SF1)

  • The P001001 field in the 2010 Census Summary File 1 supplies each tract’s authoritative total-population label.The study assumes tract imagery contains visual demographic-related cues such as building density and land use.Source: §3.2 · p. 3

3.3 Tract-Level Image Construction

  • The construction pipeline aligns Landsat imagery to tract polygons, crops to tract bounds, and masks pixels outside each polygon.Contrast stretching and scaling make structural and land-use patterns more visible in the resulting images.Source: §3.3 · p. 3
  • Tract images are resized to 512×512 and tokenized into fixed-length patch sequences, while training excludes native images larger than that limit.The population counts are grouped into 18 k-means classes, with original population ranges retained for conversion back to estimates.Source: §3.3 · p. 3

4 Methodology

The methodology trains a state-space image model to predict population directly from tract-level RGB imagery, without pixel-level or gridded labels. Its backbone combines state-space recurrence with windowed self-attention for token mixing.

4 Methodology

  • The method predicts tract population directly from Landsat-derived RGB imagery without requiring pixel-level or gridded population labels.The model is trained using the dataset described in the paper.Source: §4 · p. 4

4.1 Mamba block

  • Mamba’s state-space block models sequential data with a continuous-time formulation implemented as a discretized recurrence inside MambaVision Mixer blocks.The passage describes the recurrence as h_t = Āh_(t−1) + B̄x_t and y_t = Ch_t.Source: §4.1 · pp. 4–5

4.2 Self-attention

  • Self-attention mixes information across token positions through weighted pairwise interactions, and its combination with state-space recurrence in a backbone for administrative-unit prediction had remained unexplored.The described hybrid architectures pair recurrence with windowed self-attention.Source: §4.2 · p. 5

4.3 Model Architecture

MambaPop uses MambaVision’s hybrid state-space and attention backbone, then converts population-bin classifications into continuous tract estimates. The experiments use a filtered contiguous-US tract dataset and compare the model with three architectural baselines under a shared pipeline.

4.3 Model Architecture

  • MambaVision combines convolutional early stages with MambaVision Mixer and windowed self-attention blocks in later stages, followed by pooling and a classification head.The MambaVision Mixer models long-range dependencies, while the head predicts one of 18 population bins; inference converts the predicted bin to its mean tract population.Source: §4.3 · p. 5, §4.4.2 · p. 5, Figure 3 · p. 6

4.4.1 Dataset Statistics.

  • The final dataset contains 58,437 tracts after excluding images larger than 512 × 512 pixels from 72,539 contiguous-US tracts.An 80%/20% stratified split balances representation across population-density ranges and geographic regions.Source: §4.4.1 · p. 5

4.5 Training Details

  • MambaPop and the baselines are initialized from ImageNet1k checkpoints except VGG11, which is trained from random initialization.Models are trained on 2010 SF1 labels, with 2020 tract boundaries held out for temporal-generalization experiments.Source: §4.5 · p. 5

4.6 Baseline Comparisons

  • VGG11, YOLOv11, and ViT-B/16 are compared with MambaPop using identical tract images, population-bin labels, and classify-then-convert inference.This shared pipeline is intended to make performance differences reflect the backbone rather than the training setup.Source: §4.6 · p. 6

4.7 Evaluation Metrics

The evaluation reports absolute-error, variance-explanation, squared-error, and percentage-error metrics. MAPE is interpreted alongside absolute-error metrics because it can be highly sensitive to sparsely populated tracts.

4.7 Evaluation Metrics

  • MAE and MedAE summarize typical absolute deviations between predicted and observed tract populations.The metrics use observed and predicted populations for each tract, with the evaluation-set tract count denoted by n.Source: §4.7 · p. 6
  • R^2 measures the proportion of target variance explained by the model relative to the variance of actual values around their mean.The evaluation describes RSS as residual sum of squares and TSS as total sum of squares.Source: §4.7 · p. 6
  • RMSE and MAPE are also reported, with MAPE expressing mean absolute relative error as a percentage.MAPE can exceed 100% because its per-tract denominator is small for sparsely populated tracts, so it is listed alongside absolute-error metrics rather than alone.Source: §4.7 · p. 6

5 Results

MambaPop and YOLOv11 retain positive predictive power on 2020 census boundaries, while MambaPop degrades less on large out-of-distribution tracts. The results also cover training cost, geographic errors, and county-level change.

5.1 Population Estimation Performance

  • On 2020 boundaries, MambaPop (MAE 1,141, R2 = 0.21) and YOLOv11 (MAE 1,122, R2 = 0.21) retain positive predictive power, while ViT-B/16 falls to R2 = −0.05.On the 2010 validation split, MambaPop has MAE 1,177 and YOLOv11 has MAE 1,127; ViT-B/16 falls from R2 = 0.38 to −0.05 across years.Source: §5.1 · pp. 6–7, Table 1 · p. 7

5.2 Generalization to Large, Out-of-Distribution Tracts

  • Beyond 10^6 px2, MambaPop’s median relative error rises less rapidly, staying near 50–70% on the largest tracts, versus above 100% for YOLOv11 and 95–100% for ViT-B/16.Training was capped at 512 × 512 pixels; larger test tracts extend to an order of magnitude beyond the training area.Source: §5.2 · p. 7, §5.1 · p. 7, Figure 5 · p. 8

5.3 Training Efficiency Analysis

  • MambaPop converges in 1.6 days, compared with 0.95 days for YOLOv11 and 9.2 days for ViT-B/16.All models were trained on one NVIDIA GeForce RTX 3090 GPU; the hybrid backbone combines linear-time state-space recurrence with windowed attention.Source: §5.3 · p. 8, Table 2 · p. 9

5.4 Geographic Distribution Analysis

  • High-error tracts concentrate in sparsely populated areas, while MambaPop’s median relative error falls from 16% at county level to 5.2% at state level.Aggregation reduces relative error as over- and under-predictions cancel; no state exceeds 20% median error.Source: §5.4 · pp. 8–9

5.5 County-Level Change Validation (2010 → 2020)

  • Across 1,352 counties, the models recover the direction of 2010–2020 population change for roughly 70% of counties, but underestimate its magnitude.The predicted-versus-observed change correlations are 0.56 for MambaPop, 0.62 for YOLOv11, and 0.52 for ViT-B/16; the models track relative change even when ViT-B/16 is biased in absolute estimates.Source: §5.5 · p. 9

6 Limitations and Future Work

The study is limited to capped-resolution training, RGB Landsat 7 inputs, and the contiguous United States; the authors identify larger-tract training, additional bands, international validation, and continuous temporal monitoring as future directions.

Training scale

  • Training excludes about 14,000 of the largest tracts, or 19% of CONUS tracts, because their images exceed the 512 × 512 crop.The authors identify training at full resolution on these tracts as a next step.Source: §6 · p. 9

Imagery bands

  • The study uses only Landsat 7 RGB bands, leaving near-infrared and shortwave-infrared bands unused.The authors note that those bands underlie NDVI and built-up-area indices known to correlate with population.Source: §6 · p. 9

Geographic scope

  • Evaluation focuses on the contiguous United States, so international validation remains a follow-up direction.The authors single out regions with sparse census infrastructure for that validation.Source: §6 · p. 9

Temporal scope

  • The current framework is not yet extended to continuous population monitoring from multi-year satellite imagery.The authors propose tracking changes over user-specified periods rather than only decennial census cycles.Source: §6 · p. 9

7 Conclusion

MambaPop estimates population from each administrative unit’s polygon-masked image, paired directly with its true SF1 label. Across contiguous-US 2020 census tracts, it matched YOLOv11 on standard tracts and showed robustness on oversized tracts withheld from training.

7 Conclusion

  • MambaPop represents each administrative unit as a polygon-masked image sequence paired with its true SF1 label, eliminating grid-based disaggregation and aggregation.Source: §7 · p. 9
  • 770 persons MAE for MambaPop, versus 752 for YOLOv11 and 862 for ViT-B/16, in county-level temporal-change validation.Pearson correlation and OLS slope were 0.56 and 0.47 for MambaPop, 0.62 and 0.56 for YOLOv11, and 0.52 and 0.53 for ViT-B/16.Source: Figure 7 · p. 10
  • Across ∼84,000 contiguous-US 2020 census tracts, MambaPop equaled YOLOv11 on standard tracts, preserved inter-decennial predictive capability, and was most robust on oversized tracts withheld from training.The comparison was achieved at a fraction of the Vision Transformer’s training cost.Source: §7 · p. 10

A Population Binning Details

The appendix describes population binning into classes using one-dimensional k-means clustering of 2010 SF1 tract counts.

A Population Binning Details

B Representative Per-Tract Error Maps

The maps show MambaPop’s per-tract absolute percentage error in four representative states and regions.

B Representative Per-Tract Error Maps

  • Colors encode per-tract absolute percentage error from 0% to 100%; gray marks tracts with no prediction or zero ground-truth population.The mapped examples are New Jersey, Massachusetts, Southern California, and Central Washington.Source: Figure 8 · p. 13

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