Uncertainty Quantification for Topological Treatment Effects
Abstract
We present a unified framework for uncertainty quantification over filtration scale, extending the topological average treatment effect (TATE) analysis of \citet{kim-lee} to conditional mean confidence and individual effect prediction. For the conditional topological average treatment effect (CTATE), we derive multiplier confidence bands at a fixed covariate value, simultaneous over filtration scale, and prove validity in a correctly specified finite-dimensional regression regime, with explicit control of smoothing bias and nuisance-estimation error. For the individual topological treatment effect (ITTE), we integrate existing weighted and functional split-conformal methods to obtain finite-sample marginal prediction coverage under known target-to-calibration likelihood ratios, with a total-variation bound for estimated ratios. We also extend the current TATE silhouette stability analysis to the diagram-independent bound |Φr(D)−Φr(D')|∞ ≤ (1+2r)W1(D,D') for r≥1, recovering the known r=1 constant, and propagate diagram approximation error to prediction bands. The installable Python library \texttt{tcda\_uq} integrates mean confidence, individual prediction, and topological preprocessing, with tutorials and reproduction materials. Simulations and a PACCE lesion-measurement application illustrate the distinct coverage targets and the importance of declaring the target population.
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BibTeX
@misc{souto2026uncertainty,
title = {{Uncertainty Quantification for Topological Treatment Effects}},
author = {Hugo G. Souto and Ioannis Diamantis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41593},
eprint = {2610.41593},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41593},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Uncertainty Quantification for Topological Treatment Effects
AU - Hugo G. Souto
AU - Ioannis Diamantis
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41593
UR - https://arxiv.org/abs/2610.41593
AB - We present a unified framework for uncertainty quantification over filtration scale, extending the topological average treatment effect (TATE) analysis of \citet{kim-lee} to conditional mean confidence and individual effect prediction. For the conditional topological average treatment effect (CTATE), we derive multiplier confidence bands at a fixed covariate value, simultaneous over filtration scale, and prove validity in a correctly specified finite-dimensional regression regime, with explicit control of smoothing bias and nuisance-estimation error. For the individual topological treatment effect (ITTE), we integrate existing weighted and functional split-conformal methods to obtain finite-sample marginal prediction coverage under known target-to-calibration likelihood ratios, with a total-variation bound for estimated ratios. We also extend the current TATE silhouette stability analysis to the diagram-independent bound |Φ_r(D)−Φ_r(D')|_∞ ≤ (1+2r)W_1(D,D') for r≥1, recovering the known r=1 constant, and propagate diagram approximation error to prediction bands. The installable Python library \texttt{tcda\_uq} integrates mean confidence, individual prediction, and topological preprocessing, with tutorials and reproduction materials. Simulations and a PACCE lesion-measurement application illustrate the distinct coverage targets and the importance of declaring the target population.
ER -