PaperlayerView exact revision on arXiv

Source-linked AI summary

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

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

arXiv:2609.28895v1stat.APcs.LG

TL;DR

GeoDose-CP addresses intervention-oriented EO inference when treatment shift and spatial dependence jointly shape candidate reassignment. It constructs a support-aware graph-local target-orbit law and applies conformal inference; MineDoseBench results report strong coverage across configurations and close exact–sparse agreement, while NSW evidence exposes practical support and deployment limits.

  • Problem

    Intervention-induced treatment shift and spatially dependent calibration jointly change candidate reassignment likelihoods, so separate treatment and spatial weights do not generally recover the needed reference law.

    Source: §I · p. 2

  • Method

    GeoDose-CP constructs a graph-local target-orbit law that jointly represents treatment shift, inverse outcome-scale Jacobian, and graph-dependent residual likelihood for supported localized stochastic potential outcomes.

    Source: §I · p. 2

  • Results

    MineDoseBench showed strong selective and lower-tail local coverage across all 27 registered configurations, with exact and sparse inference agreeing closely at aggregate and decision levels.

    Source: §VI · p. 17

  • Takeaways & Limitations

    Unsupported treatment values and endpoint atoms are not extrapolated, and treatment-dependent queries are not constructed when the scientifically required treatment variable is unavailable.

    Source: E. Support-Aware Refusal · p. 5

    NSW coverage varied by mine and model, and fitted spatial diagnostics and associated N3 quantities are not finite-sample certified coverage bounds.

    Source: D. Earth-Observation Applicability,… · p. 17

Abstract

from arXiv · show

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.

I. INTRODUCTION

The introduction identifies a gap in intervention-oriented EO inference: treatment shift and spatially dependent calibration require a joint reference law. GeoDose-CP combines that law with support-aware conformal inference, while restricting its target to supported interventions and separating causal identification from conformal validity.

I. INTRODUCTION

  • Intervention-induced treatment shift and spatially dependent calibration jointly alter reassignment likelihoods, so independent treatment and spatial weights do not generally define the required reference law.Existing spatial prediction, continuous-treatment causal inference, and conformal methods address parts of the problem but do not compose automatically.Source: §I · pp. 1–2
  • GeoDose-CP introduces a graph-local target-orbit law that combines treatment shift, the inverse outcome-scale Jacobian, and graph-dependent residual likelihood.It connects this law to exact candidate inversion, a sparse approximation with discrepancy accounting, and refusal when treatment or spatial support is inadequate.Source: §I · p. 2

II. GEODOSE-CP: PROBLEM FORMULATION AND METHOD

  • The evaluation pairs known-truth experiments and MineDoseBench with an NSW EO study that leaves treatment-dependent inference nonoperational without auditable longitudinal rehabilitation treatment.The method hierarchy distinguishes the finite-orbit law (G1), graph-local target-orbit law (G2), exact inversion (G3), sparse graph approximation (N2), and practical coverage-transfer layer (N3).Source: §I · p. 2, §II · p. 2

A. Supported Continuous-Dose Target and Identification

  • The supported target is a localized stochastic intervention around a specified dose, not an unrestricted deterministic potential outcome.Identification requires consistency, supported conditional ignorability, positivity, no material interference for the primary estimand, and stability of the relevant conditional outcome law; identification alone does not establish conformal coverage.Source: A. Supported Continuous-Dose Target… · pp. 2–3

B. Residual Representation and Failure of Naive Factorization

GeoDose-CP standardizes reassigned outcomes before evaluating spatial residual dependence; this coupling makes naive multiplication of separate treatment and spatial weights invalid in general.

B. Residual Representation and Failure of Naive Factorization

  • The primary two-sided nonconformity score uses residuals standardized by fitted outcome location and scale functions held fixed during calibration.The fitted spatial dependence of residuals is statistical and distinct from the causal-interference condition.Source: B. Residual Representation and Failure… · p. 3
  • Reassigning a treatment–outcome payload changes the treatment likelihood, standardized residual, and graph-dependent residual likelihood together, invalidating separate treatment and spatial weights in general.Product factorization is recovered only under additional structure that compatibly separates those contributions.Source: B. Residual Representation and Failure… · p. 3

C. Exact Graph-Local Target-Orbit Law

The exact graph-local target-orbit law conditions inference on a finite set of distinct local payload assignments, then weights those states under their joint reference law.

1) Finite Local Orbit:

  • For each candidate response, the target outcome is replaced and duplicate physical states are quotiented, yielding a finite set of distinct local orbit states.Slot and design information remain fixed while treatment–outcome payloads are reassigned within the block.Source: 1) Finite Local Orbit · p. 4
  • Conditional on the finite-orbit information, each distinct state receives probability proportional to its joint reference-law density under the stated permutation-invariant density assumption.Duplicate states appear once; their stabilizer multiplicities cancel after normalization.Source: 1) Finite Local Orbit · p. 4

2) Graph-Local Target Law:

  • The G2 target weight jointly couples the intervention-to-observational treatment likelihood, inverse outcome-scale Jacobian, and graph-local residual likelihood.The Jacobian is required when outcome scale varies across orbit states; residual factors wholly outside the moved block cancel, leaving the moved block and incident graph boundary in the spatial term.Source: 2) Graph-Local Target Law · p. 4
  • The target-design factor cancels within normalized orbit probabilities, but remains relevant to target-population transport and scalable coverage accounting.Exact treatment weighting requires the observational treatment likelihood or a theorem-equivalent joint assignment likelihood; a target-versus-observational classifier is not a substitute.Source: 2) Graph-Local Target Law · p. 4

3) Gaussian Markov Specialization:

The Gaussian Markov specialization reduces spatial computation to the moved block and its boundary, while exact candidate inversion uses weighted upper-tail p-values.

3) Gaussian Markov Specialization:

  • For a Gaussian Markov residual model, only sparse operations on the moved block and its external boundary are needed, avoiding inversion of the full spatial covariance matrix.This is a computational specialization; G2 itself is non-Gaussian and requires the stated positive graph-factorized residual law.Source: 3) Gaussian Markov Specialization · p. 4

1) Exact Weighted Candidate Inversion:

  • Exact inversion computes a weighted upper-tail p-value under the target-orbit law and retains candidate responses meeting the inversion rule.Structural ties are included in the upper tail, and the resulting raw prediction set may be disconnected; a displayed convex hull is presentation-only.Source: 1) Exact Weighted Candidate Inversion · pp. 4–5

D. Exact Candidate Inversion and Scalable Coverage

  • Once the correct target-orbit reference law is established, candidate inversion follows generalized conformal validity machinery; GeoDose-CP’s structural contribution is G2.The raw set’s disconnected components are retained rather than replaced by a visualization hull.Source: 1) Exact Weighted Candidate Inversion · p. 5

2) Sparse Graph Approximation:

GeoDose-CP uses a target-weighted sparse approximation for larger domains and tracks the resulting law discrepancy when transferring marginal coverage. N3 is treated as a certificate only when its required finite-sample controls are established; otherwise its quantities are diagnostics.

2) Sparse Graph Approximation:

  • For larger domains, N2 uses a Vecchia-type sparse conditional approximation and target-weighted information loss to support coverage transfer.The approximation is assessed under a finite target-weighted information assumption; exact orbit evaluation remains feasible for small local blocks.Source: 2) Sparse Graph Approximation · p. 5

3) Practical Marginal Coverage:

  • Structural misspecification, nuisance estimation, and numerical approximation contribute separate total-variation discrepancies in the practical reference-law ladder.The sparse approximation is controlled through KL divergence and Pinsker’s inequality, while subsequent law discrepancies are combined on the total-variation scale.Source: 3) Practical Marginal Coverage · p. 5
  • N3 is a marginal coverage-transfer statement, and the term “N3 certificate” is reserved for cases with formally established discrepancy bounds and good-event probability.Otherwise, N3 quantities are reported as empirical diagnostics; conditional coverage requires corresponding conditional total-variation control.Source: 3) Practical Marginal Coverage · p. 5

E. Support-Aware Refusal

GeoDose-CP returns a supported prediction set or refuses when its target law cannot be justified, rather than extrapolating unsupported treatment values or substituting proxy exposure. Its inference procedure combines support checks and candidate inversion, and the evaluation substrate separates controlled, benchmark, and real-data evidence.

E. Support-Aware Refusal

  • Refusal is an inferential outcome: unsupported treatment values and endpoint atoms are not extrapolated or created, and treatment-dependent queries are not constructed without the required treatment variable.Support diagnostics include effective sample size, weight concentration, graph support, and endpoint checks, but do not generally guarantee coverage.Source: E. Support-Aware Refusal · p. 5

F. GeoDose-CP Inference Algorithm

A. Evidence Architecture and Data Substrate

  • The evidence architecture combines controlled known-truth experiments, MineDoseBench with generated counterfactual truth, and an NSW applicability study without counterfactual truth.Together these address controlled validity, realistic known-truth performance, and real-data applicability.Source: A. Evidence Architecture and Data… · pp. 5–6
  • The NSW mine substrate uses a 90 m lattice and queen contiguity, retaining 27,042 cells and 102,893 within-mine graph edges across five mines.The analysis footprint comes from rehabilitation and disturbance polygons, which are not treated as the longitudinal rehabilitation exposure required by the estimand.Source: A. Evidence Architecture and Data… · p. 6
  • The EO archive contains 81,126 block–year records, with 23,610 cells meeting the complete three-year EO-quality criteria for the selected real-data study.The quality screen required at least three accepted observations annually and specified validity, water-fraction, and unmixing-error criteria.Source: A. Evidence Architecture and Data… · p. 6
  • MineDoseBench nuisance predictors exclude outcome-year, outcome-derived, oracle, sample-role, and mapped rehabilitation variables, while training, support construction, calibration, and testing are spatially separated.Scenario definitions, targets, and operating rules were specified before performance evaluation.Source: A. Evidence Architecture and Data… · p. 6

B. Controlled Validation and MineDoseBench

Validation combines controlled experiments with MineDoseBench, a realistic known-truth benchmark built around mine geometry and generated counterfactual outcomes. The comparison separates treatment shift, spatial recalibration, their naive factorization, and the joint procedure, while reporting coverage, return, and efficiency as distinct dimensions.

B. Controlled Validation and MineDoseBench

  • Controlled validation comprises 4,190 replications and 52,740 queries, varying treatment and target shifts, spatial dependence, overlap, residual structure, measurement error, endpoint support, and calibration information.The increasing-domain experiment varies spatial extent on 17×17, 25×25, and 35×35 lattices at fixed 90-m resolution.Source: B. Controlled Validation and… · p. 6
  • MineDoseBench is the primary realistic known-truth evaluation, retaining NSW mine geometry, graph structure, pretreatment EO history, and environmental context while generating treatment, potential outcomes, residual dependence, and target-population shift.Its benchmark response is fractional-cover change, with truth generated directly within the physical response range.Source: B. Controlled Validation and… · p. 6
  • The benchmark has 27 configurations with 20 replications each and five ranked targets in each of five mines, yielding 13,500 primary target identities.Additional configurations test dependence, measurement error, reduced information, endpoint support, combined perturbations, and cross-mine transfer.Source: B. Controlled Validation and… · p. 7

C. Methods, Operating Rules, and Evaluation Metrics

  • The primary M2–M6 comparison distinguishes dose-only weighting, spatial-only residual calibration, naive treatment–spatial factorization, graph-safe weighted calibration, and full GeoDose-CP.M4 multiplies the M2 treatment marginal by the M3 spatial marginal, while M6 uses the joint treatment–spatial target law.Source: C. Methods, Operating Rules, and… · p. 7
  • M6 combines applicable weight and graph-support gates with a finite, positive N3 operating requirement, while ESS and weight concentration diagnose support and stability rather than establish coverage or treatment-model correctness.Operating thresholds were selected in a separate pilot and frozen before production evaluations.Source: C. Methods, Operating Rules, and… · p. 7
  • Selective coverage, return or refusal, target-local coverage, coverage-matched width, exact–sparse discrepancy, and endpoint behavior are evaluated separately; q0.05 summarizes the lower tail across mine and spatial-rank cells.q0.05 is a lower-tail diagnostic, not exact conditional coverage; refusals are not recoded as noncoverage.Source: C. Methods, Operating Rules, and… · p. 8

D. Treatment-Density Sensitivity and External Comparator Evaluation

Treatment-density sensitivity and external conformal comparisons are designed to isolate treatment-law specification and compare method families under their native support conditions. The NSW analysis instead assesses real-data applicability: without an auditable longitudinal rehabilitation treatment, treatment-dependent procedures are nonoperational and are not replaced by a proxy.

D. Treatment-Density Sensitivity and External Comparator Evaluation

  • Treatment-density sensitivity compares oracle, fitted, and deliberately misspecified treatment laws while holding the remaining RF-primary M6 pipeline fixed across seven configurations.The comparison retains all 20 replications and common target identities, isolating treatment-law specification.Source: D. Treatment-Density Sensitivity and… · p. 8
  • The external comparison adapts continuous-treatment, weighted distribution-shift, and spatial/local conformal families, none of which implements Theorem 1’s candidate-specific joint treatment–spatial target law.The adaptations are not byte-for-byte reproductions, and E1 is natively nonapplicable at exact treatment atoms under its continuous-treatment formulation.Source: D. Treatment-Density Sensitivity and… · p. 8

E. Real NSW Earth-Observation Demonstration

  • The NSW study evaluates real-world EO applicability rather than causal performance of the full treatment-dependent pipeline, using three mines and 41,244 method–query records.Its response is annual change in the observed satellite photosynthetic-vegetation product, not an error-free latent measure of ecological recovery.Source: E. Real NSW Earth-Observation… · pp. 8–9
  • The NSW archive lacks an auditable longitudinal continuous rehabilitation treatment consistent with the estimand, so M2, M4, and M6 are nonoperational and no proxy exposure is introduced.The analysis uses M1, M3, and a treatment-free graph-safe fallback instead.Source: E. Real NSW Earth-Observation… · p. 9
  • Geographically buffered partitioning is the primary NSW validation design, with random splitting, leave-one-mine-out analysis, and 90-to-180-m comparison used only for specified diagnostics or sensitivity analyses.M3 widths come from a targeted 144-inversion subset, not the full test frame or population-level efficiency; its fitted spatial nuisance is not finite-sample theorem-certified.Source: E. Real NSW Earth-Observation… · p. 9

IV. RESULTS

GeoDose-CP achieved high selective coverage across MineDoseBench configurations and maintained strong lower-tail local coverage. As spatial dependence increased, coverage remained above nominal, while matched-coverage efficiency relative to M5 varied by regime.

A. Controlled Validation and Overall MineDoseBench Performance

B. Spatial Dependence and Coverage-Matched Efficiency

  • M6’s selective coverage declined from 0.9844 at ρ = 0 to 0.9733 at ρ = 0.8 as spatial dependence strengthened.Source: B. Spatial Dependence and… · p. 9
  • Under coverage matching, M6 was 3.8%, 4.9%, and 11.4% narrower than M5 at ρ = 0, 0.2, and 0.4, but 31.2% wider at ρ = 0.6.No comparison was made at ρ = 0.8 because the 0.03 coverage-matching tolerance was not met; widths provide targeted structural-efficiency evidence, not population-level sharpness estimates.Source: B. Spatial Dependence and… · pp. 9–10

C. Approximation, Stress, and Support Boundaries

GeoDose-CP’s sparse route closely matches exact inference in aggregate and decision-level comparisons, while retaining pointwise discrepancies. Stress tests show that results depend on support conditions, treatment-law specification, and the comparison regime.

C. Approximation, Stress, and Support Boundaries

  • Mean |∆p| for the sparse route rose from approximately zero at ρ = 0 to 0.00690 at ρ = 0.8, with two decision disagreements at ρ = 0.8.Unambiguous target-level linkage between discrepancy and ESS/maximum-weight diagnostics was available for only 51/2,700 identities, so no general diagnostic association was inferred.Source: C. Approximation, Stress, and Support… · pp. 10–11
  • Only 9 of 2,700 targets (0.33%) changed inclusion status at α = 0.10 between exact and sparse M6, despite a maximum |∆p| of 0.42945.The median discrepancy was numerically zero; aggregate and decision-level agreement does not imply pointwise numerical equivalence.Source: C. Approximation, Stress, and Support… · p. 10, Figure 4 · p. 11
  • The product construction agreed with the joint graph-local construction under the reduction condition, but its candidate-specific relationship became nonconstant in the nonfactorizing treatment–spatial regime.The audit therefore confirms that the product construction does not generally reproduce the G2 target-orbit law.Source: C. Approximation, Stress, and Support… · p. 11
  • Genuine endpoint atoms yielded selective coverage of 0.980 and 0.990 with 100% return, while an interior-only law refused every endpoint query; leave-one-mine-out transfer refused all 375 M6 queries.Under severe-tail stress, M6 returned 60% of queries with selective coverage 1.000; false support remained 0.05. Predictive coverage of 0.966 under hidden spatial confounding does not restore conditional ignorability for causal interpretation.Source: C. Approximation, Stress, and Support… · pp. 11–12
  • M6 selective coverage remained above nominal under target-design shift (0.9644), non-Gaussian dependence (0.9667), measurement-error perturbations (0.966–0.972), and 90-m/180-m change of support (0.9640/0.9578).Return rates for the two spatial supports were 100% and 90%, respectively.Source: C. Approximation, Stress, and Support… · p. 11, Table II · p. 12

1) Treatment-Density Sensitivity:

  • Support diagnostics appeared most favorable for GMISSPECIFIED (mean ESS 415.47; mean maximum normalized weight 0.0714), despite its weakest lower-tail local coverage.Large ESS and diffuse normalized weights indicate favorable support concentration but do not establish correctness of the treatment model.Source: 1) Treatment-Density Sensitivity · p. 12
  • Mean selective coverage was 0.9830 for GORACLE and 0.9825 for GESTIMATED, while GMISSPECIFIED retained 0.9786 but had lower mean and minimum local q0.05 of 0.9545 and 0.8882.Under strong dependence combined with target-design shift, local q0.05 was 0.9347, 0.9267, and 0.8882 for oracle, estimated, and misspecified treatment laws, respectively.Source: 1) Treatment-Density Sensitivity · p. 12, Table III · p. 13

2) External Comparator Evaluation:

E. Real NSW Observed-Product Results

NSW observed-product coverage varied by spatial support, predictor, and mine, while validation geometry materially changed apparent performance. These analyses do not establish universal nominal coverage or treatment-dependent inference, which was nonoperational without an authentic longitudinal treatment.

E. Real NSW Observed-Product Results

  • Without an authentic longitudinal rehabilitation treatment, M2, M4, and M6 were nonoperational, and no proxy treatment was introduced.The held-out mine also lacked a connected local calibration orbit for the graph-dependent route, so successful cross-mine local-orbit transfer was not established.Source: E. Real NSW Observed-Product Results · pp. 13–14
  • Under RF, pooled M1/M3/GS coverage was 0.8381/0.8154/0.8447 at 90 m and 0.9401/0.8231/0.9201 at 180 m; XGBoost yielded 0.9028/0.9050/0.8644 and 0.9472/0.8545/0.9344.The changes indicate support- and model-sensitivity rather than superiority of the coarser resolution.Source: E. Real NSW Observed-Product Results · p. 13
  • At 90 m under RF, M1/M3/GS coverage was 0.9595/0.9285/0.9619 at Mt Arthur, 0.8028/0.7306/0.7780 at HVO, and 0.6193/0.6995/0.6885 at Bulga.Under 90-m XGBoost, Bulga M1/M3 coverage increased to 0.9927/0.9873, whereas HVO remained at 0.7963/0.7909; the study does not support universal 0.90 observed-product coverage.Source: E. Real NSW Observed-Product Results · p. 13
  • Ten of 12 mine×scale×predictor fits selected ρ = 0.8, the upper limit of the specified grid; the exceptions were Bulga at 180 m.The exceptions were ρ = 0.4 for RF and ρ = 0.6 for XGBoost; these fitted quantities are empirical, not finite-sample theorem-certified.Source: E. Real NSW Observed-Product Results · p. 13
  • The stricter UE≤20 threshold retained 94.6–98.3% of eligible 90-m cells and 88.7–96.5% at 180 m, with only small qualitative changes to coverage patterns.The primary site, support, and model sensitivities were not attributable solely to the primary UE eligibility threshold.Source: E. Real NSW Observed-Product Results · p. 13
  • On the common frozen 60-target subset, mean widths were 0.3097 for M1, 0.3575 for M3, and 0.3247 for GS.These widths characterize a targeted subset, not full-test-frame or population-level efficiency.Source: E. Real NSW Observed-Product Results · pp. 13–14
  • Random splitting gave coverage 0.8957, mean width 0.1279, and RMSE 0.0540, versus 0.8381, 0.3097, and 0.1016 under geographically buffered validation.The narrower intervals and lower error under random splitting are consistent with optimistic assessment when training and test observations remain spatially proximate,,.Source: E. Real NSW Observed-Product Results · p. 14

V. DISCUSSION

GeoDose-CP’s discussion emphasizes the joint graph-local target law and reports strong supported-regime coverage and lower-tail robustness, while distinguishing those results from universal efficiency or causal guarantees. It also qualifies sparse approximation, fitted treatment models, and real-data certification.

A. What GeoDose-CP Establishes

  • G2 jointly represents the intervention/observational treatment likelihood, inverse outcome-scale Jacobian, and graph-dependent residual likelihood rather than relying on independently constructed treatment and spatial weights.Compatible additional conditions can recover a product form, so GeoDose-CP does not claim product weighting is always invalid.Source: A. What GeoDose-CP Establishes · pp. 14–15
  • M6 maintained nominal-or-higher configuration-level selective coverage across all 27 MineDoseBench configurations and had the strongest minimum local q0.05 among M2–M6.On the selected external-comparator subset, M6 had the strongest minimum selective coverage and lower-tail local robustness, while E3 was the strongest external comparator; M3 and M4 had higher average local coverage, and M4 performed well empirically without general G2 justification.Source: A. What GeoDose-CP Establishes · p. 16

B. Validity, Refusal, and Efficiency

  • Under severe-tail stress, M6 returned finite sets for 60% of queries and attained selective coverage of 1.000 among those returned.E1 and E2 produced infinite sets for more than 93% of their applicable severe-tail queries; refusal and vacuous inference can preserve coverage in different ways.Source: B. Validity, Refusal, and Efficiency · p. 16
  • A false-support rate of 0.05 remained under severe-tail stress, and observable support diagnostics cannot certify causal assumptions such as conditional ignorability.ESS, weight concentration, graph support, and endpoint checks identify observable failure modes but cannot replace assumptions about the treatment and outcome-generating process.Source: B. Validity, Refusal, and Efficiency · p. 16
  • At ρ = 0, 0.2, and 0.4, M6 was 3.8%, 4.9%, and 11.4% narrower than M5 under the matched-coverage rule; at ρ = 0.6, it was 31.2% wider.At ρ = 0.8 the methods were not coverage-matched, and the finite-domain audit does not establish population-level sharpness; E3 can also be substantially sharper than M6 on coverage-matched restricted inversions.Source: B. Validity, Refusal, and Efficiency · p. 16

C. Scalable Inference and Practical Certification

  • Exact and sparse M6 selective coverage were 0.9885 and 0.9874, and 9/2,700 targets (0.33%) changed inclusion status at α = 0.10.Individual discrepancies could be larger, with max |∆p| = 0.42945; approximation sensitivity increased with spatial dependence across S4, but a universal mechanism for the largest errors was not established.Source: C. Scalable Inference and Practical… · p. 16
  • Deliberate treatment-density misspecification reduced minimum local q0.05 to 0.8882 despite producing more favorable ESS and maximum-weight diagnostics.GESTIMATED closely tracked GORACLE in aggregate, but support-concentration metrics cannot validate the correctness of g(A | U).Source: C. Scalable Inference and Practical… · p. 16
  • Empirical agreement between exact and sparse inference, or between oracle and estimated treatment models, does not make approximation error or fitted nuisances theorem-certified.N2 and N3 keep the distinctions among the exact law, sparse approximation, fitted nuisance models, and finite-sample certification explicit.Source: C. Scalable Inference and Practical… · p. 16

D. Earth-Observation Applicability, Limitations, and Outlook

The NSW analysis tests real-data applicability but cannot validate treatment-dependent inference without an authentic longitudinal rehabilitation treatment. The paper concludes that support and uncertainty boundaries should remain explicit rather than be replaced with unsupported extrapolation.

D. Earth-Observation Applicability, Limitations, and Outlook

  • The NSW archive lacks an auditable longitudinal continuous rehabilitation treatment consistent with the estimand, so treatment-dependent procedures remain nonoperational and the analysis uses M1, M3, and treatment-free GS.A snapshot-derived proxy would change the scientific question rather than validate the intended intervention.Source: D. Earth-Observation Applicability,… · p. 17
  • M1, M3, and GS concern observed DEA photosynthetic-vegetation change, not an error-free latent measure of ecological recovery or causal GeoDose-CP validity.Their coverage and width characterize observed-product predictive uncertainty, not uncertainty in latent ecological state.Source: D. Earth-Observation Applicability,… · p. 17
  • NSW coverage depended on mine, predictor, and spatial support; 10 of 12 spatial fits selected ρ = 0.8, the fitted-grid upper boundary.The fitted spatial nuisances and associated N3 quantities are empirical diagnostics, not finite-sample certified coverage bounds.Source: D. Earth-Observation Applicability,… · p. 17
  • Stricter UE≤20 screening retained most eligible cells without materially changing principal patterns, whereas random partitioning produced substantially narrower intervals and lower prediction error than geographically buffered validation.This is consistent with optimistic assessment when training and test observations remain spatially proximate –.Source: D. Earth-Observation Applicability,… · p. 17
  • Leave-one-mine-out evaluation did not demonstrate successful cross-mine local-orbit transfer because the held-out mine lacked a connected local calibration orbit.Dense EO observations do not guarantee intervention support when treatment provenance or spatial calibration structure is absent.Source: D. Earth-Observation Applicability,… · p. 17

VI. CONCLUSION

  • GeoDose-CP links supported intervention targeting, graph-local conformal inference, scalable approximation, and principled refusal while keeping treatment authenticity and inferential support explicit.MineDoseBench showed strong selective and lower-tail local coverage, with close aggregate and decision-level exact–sparse agreement but not pointwise equivalence.Source: §VI · p. 17

CODE AND DATA AVAILABILITY

  • The frozen reproducibility release is available in the project repository, while original third-party data are not redistributed and reconstruction provenance is provided.Redistributable derived materials are included.Source: CODE AND DATA AVAILABILITY · pp. 17–18
Loading 2609.28895v1…