GeoDose-CP: Graph-Local Conformal Inference for Continuous-Treatment Earth Observation

Md Khalid Hasan Sakib; Dristi Datta; Manoranjan Paul; Davina White

stat.APSep 24, 2026

GeoDose-CP: Graph-Local Conformal Inference for Continuous-Treatment Earth Observation

Authors: Md Khalid Hasan Sakib, Dristi Datta, Manoranjan Paul, Davina White

Organizations: Department of Computer Science and Engineering, Uttara University, Dhaka, Bangladesh · School of Computing, Mathematics and Engineering, Charles Sturt University, Bathurst, NSW 2795, Australia · Australian Integrated Carbon (AiCarbon), Level 4, 191 Pulteney Street, Adelaide, SA 5000, Australia

Abstract

Reliable intervention-oriented uncertainty quantification from Earth observation (EO) remains challenging when continuous treatment shifts, spatial dependence, limited support, and satellite-outcome uncertainty must be addressed simultaneously. Existing causal, conformal, and spatial approaches address parts of this problem, but their direct combination does not generally recover the appropriate interventional reference law because candidate reassignment jointly alters treatment likelihood, standardized residuals, and graph-dependent residual likelihood. This study presents GeoDose-CP, a support-aware conformal framework for localized stochastic potential outcomes under continuous or mixed continuous-atomic treatment. Its central methodological contribution is a graph-local target-orbit law that jointly represents intervention-induced treatment shift, the inverse outcome-scale Jacobian, and spatial residual dependence. The framework further provides exact weighted candidate inversion, a scalable sparse approximation with explicit discrepancy accounting, and refusal under inadequate support. Evaluation used controlled known-truth experiments, MineDoseBench, treatment-density sensitivity analysis, external conformal comparators, and a multi-mine New South Wales (NSW) study. In MineDoseBench, GeoDose-CP achieved mean selective coverage of 0.9692 across 27 configurations and a minimum local q0.05 of 0.8951; exact-sparse auditing produced nine inclusion disagreements over 2,700 targets. In the NSW study, the absence of an auditable longitudinal rehabilitation treatment rendered treatment-dependent inference nonoperational rather than forcing inference through a proxy exposure.

Figures & tables

Fig. 1: Operational workflow of GeoDose-CP. Spatial graph and EO data, together with frozen nuisance models and the supported-intervention conditions C1–C5, define the inputs to candidate evaluation. For each candidate response, G1 constructs the local candidate orbit and G2 evaluates the joint target-orbit law through the treatment likelihood, inverse-scale Jacobian, and graph-residual likelihood. Inference then proceeds through exact weighted inference (G3) or the sparse approximation (N2), followed by weighted $p$ -value calculation and candidate inversion. Support and numerical checks, together with the applicable N3 assessment for the sparse route, determine whether the query returns a prediction set with diagnostics or an explicit refusal.

Method	Mean Sel. Cov.	Min. Sel. Cov.	Cases $\boldsymbol{\geq 0.90}$	Mean Local $\boldsymbol{q_{0.05}}$	Min. Local $\boldsymbol{q_{0.05}}$	Return Rate
M2	0.8855	0.8022	8/27	0.8265	0.7079	0.9500
M3	0.9856	0.8360	26/27	0.9725	0.7464	1.0000
M4	0.9805	0.9422	27/27	0.9574	0.8804	0.9500
M5	0.8989	0.8360	12/27	0.8385	0.7694	0.8945
M6	0.9692	0.9140	27/27	0.9488	0.8951	0.9500

TABLE I: Overall MineDoseBench Performance Across 27 Configurations

Fig. 2: MineDoseBench selective coverage, local robustness, and support-aware refusal across 27 configurations. (a) Configuration-wise selective coverage of full GeoDose-CP (M6). (b) Fifth-percentile target-local selective coverage for M2–M6. (c) Operational refusal rates for M2–M6. Dashed horizontal lines denote nominal 0.90 coverage. Results correspond to the RF-primary evaluation on the observed benchmark-response scale.

Fig. 3: Effect of increasing spatial dependence in S4. (a) RF-primary selective coverage of M2–M6 for $\rho\in\{0,0.2,0.4,0.6,0.8\}$ ; error bars denote 95% replication-by-mine cluster-bootstrap confidence intervals. (b) Mean finite-domain interval/hull width on $\mathcal{Y}_{\mathrm{MDB}}=[-1,1]$ for the same prespecified S4 target identities. For M3, M4, and M6, widths are obtained from full finite-domain candidate inversion; for M2 and M5, closed-form returned intervals are intersected with $\mathcal{Y}_{\mathrm{MDB}}$ for this efficiency-only representation. Error bars denote 95% replication-by-mine cluster-bootstrap confidence intervals for mean width. Width is interpreted as efficiency only when the selective-coverage difference satisfies the prespecified 0.03 coverage-matching criterion; the $\rho=0.8$ M6–M5 comparison is therefore not interpreted as an efficiency comparison.

Fig. 4: Exact–sparse M6 discrepancy across 2,700 paired registered target identities. The empirical cumulative distribution function shows the absolute difference $|\Delta p|$ between full-graph exact inference and the sparse $m=64$ route. Vertical reference lines mark the 0.90, 0.95, and 0.99 quantiles ( $0.01607$ , $0.03467$ , and $0.09739$ , respectively). The median discrepancy is numerically zero and the maximum is $0.42945$ . Only 9 of 2,700 targets (0.33%) changed inclusion status at $\alpha=0.10$ , so close aggregate and decision-level agreement does not imply pointwise numerical equivalence.

Audit	Selective coverage	Return/support	Principal finding
Target-design shift	0.9644	90% return	Coverage remains above the nominal 0.90 level under nonidentity target-design shift.
Non-Gaussian spatial law	0.9667	90% return	Coverage remains above nominal under the non-Gaussian residual-dependence setting.
Measurement-error perturbations	0.966–0.972	100% return	Coverage remains above nominal across all five measurement-error perturbations.
Change of spatial support	90 m: 0.9640; 180 m: 0.9578	90 m: 100% return; 180 m: 90% return	Coverage remains above nominal at both independently anchored spatial supports, with lower return at 180 m.
Supported endpoint atoms	$A=0$ : 0.980; $A=1$ : 0.990	100% return at both atoms	Both genuine endpoint atoms remain supported under the mixed treatment measure.
Unsupported endpoints	—	100% refusal at $A=0,1$	The interior-only treatment law refuses unsupported endpoint queries rather than assigning artificial endpoint mass.

TABLE II: Stress, Support, and Applicability Audits for GeoDose-CP

Treatment law	Mean sel. cov.	Min. sel. cov.	Mean local $q_{0.05}$	Min. local $q_{0.05}$	Return rate
$G_{\mathrm{ORACLE}}$	0.9830	0.9680	0.9661	0.9347	0.9571
$G_{\mathrm{ESTIMATED}}$	0.9825	0.9644	0.9655	0.9267	0.9071
$G_{\mathrm{MISSPECIFIED}}$	0.9786	0.9537	0.9545	0.8882	0.9857

TABLE III: Treatment-Density Sensitivity for M6

Method	Mean	Min.	Cases	Mean local	Min. local	Native	Return	Infinite-set
	sel. cov.	sel. cov.	$\boldsymbol{\geq 0.90}$	$\boldsymbol{q_{0.05}}$	$\boldsymbol{q_{0.05}}$	applicability	$\boldsymbol{\mid}$ applicable	$\boldsymbol{\mid}$ returned
E1 continuous-treatment	0.8970	0.8120	3/6	0.8310	0.7193	0.8571	1.0000	0.3097
E2 weighted shift	0.9191	0.8580	5/7	0.8701	0.7940	1.0000	1.0000	0.2714
E3 spatial/local	0.9463	0.9180	7/7	0.9134	0.8817	1.0000	1.0000	0.0000
M6 GeoDose-CP	0.9825	0.9644	7/7	0.9655	0.9267	1.0000	0.9071	0.0000

TABLE IV: External-Comparator Performance on the Selected MineDoseBench Evaluation Subset

Fig. 5: External-comparator performance on the selected MineDoseBench evaluation subset. The three panels show configuration-level selective coverage, lower-tail local $q_{0.05}$ , and return rate conditional on native applicability, respectively. E1, E2, and E3 denote the adapted continuous-treatment, weighted distribution-shift, and spatial/local conformal families; M6 denotes GeoDose-CP using the primary estimated treatment density. Dashed horizontal lines in the upper two panels denote nominal 0.90 coverage. E1 is natively inapplicable in the poor-overlap atomic-target configuration, so no conditional return-rate value is defined there; this is nonapplicability rather than refusal.

Fig. 6: Spatial design and empirical uncertainty diagnostics for the NSW demonstration at 90-m support. (a) Buffered partition for Mt Arthur Coal, HVO, and Bulga Complex, including nuisance-training, support, calibration, held-out test, buffer, secondary, and ineligible regions. (b) M3 conformity p-values for held-out RF-primary targets; lower values indicate weaker conformity with the fitted spatial reference. The p-values are empirical diagnostics, not causal evidence or theorem-certified coverage guarantees.

Fig. 7: Held-out NSW observed-product uncertainty at 90-m support under the primary RF track. (a) Pooled observed-product coverage for M1, M3, and the treatment-free graph-safe fallback GS over the held-out test frame; the dashed horizontal line denotes nominal 0.90 coverage. (b) Mean interval width for M1, M3, and GS evaluated on the same frozen 60-target outcome-blind subset used for finite-domain M3 inversion. The width comparison is therefore restricted to this common target subset and is not interpreted as population-level efficiency. M2, M4, and M6 are nonoperational because an authentic longitudinal rehabilitation treatment is unavailable in the NSW archive.

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