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  "Title": "Functional Propensity Score for Causal Inference",
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  "Description": "Implements functional propensity score (FPS) weighting for\ncausal inference with functional treatments. The method\nestimates weights that balance observed confounders by removing\ntheir dependence on the functional treatment and uses a dual\nformulation of the weighting problem for efficient\nunconstrained optimization. The framework supports scalar,\nbinary, and functional outcomes, as well as functional\ncovariates, and can be used to estimate marginal causal effects\nin settings with time-varying exposures. The methodology\nfollows Ciardulli, S., Fontana, N., Vantini, S., and Ieva, F.\n(2026) \"Generalized propensity score weighting for functional\ncausal inference framework\" <doi:10.48550/arXiv.2608.03200>.",
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      "title": "Estimate causal effect of a functional treatment",
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