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Generalized Fast Exact Conformalization
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Proposes a generalized fast exact conformalization method that traces the piecewise-smooth homotopy solution path over candidate labels via an ODE system, yielding exact full conformal prediction sets much faster than grid search.
Problem
Full conformal prediction requires refitting the model for every candidate label across the latent label space, which is computationally prohibitive; existing exact accelerations rely on strong assumptions or are model-specific, or give only approximate sets.
Approach
Treats the conformal solution path over candidate labels as a piecewise-smooth trajectory of a generalized penalized estimator, derives an autonomous ODE for its gradient flow (with Clarke subdifferentials for nonsmooth points and constraints handled by sweep operators), and integrates it with a numerical ODE solver (lsoda) to obtain all solutions in one run.
Key results
- Exact conformalization achieves coverage around 0.80 matching grid and split baselines on fried, cadata, delta and elevator datasets (Table 2).
- Exact method is substantially faster than grid-search baselines as training set size grows (Figure 2), and remains faster even with sparse grids (Figure 3).
- Number of kinks along the path is small (e.g., 2 to 13 across datasets), with 97.1% of runs in Figure 4 showing a small number of kinks.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Exact conformalization instead of grid-search conformalization | NLS, GFM, and IGR · Real-world benchmark datasets in Table 2 | running time | Helped |
| Use Exact conformalization instead of grid-search conformalization | NLS, GFM, and IGR · Real-world benchmark datasets in Table 2 | coverage | No clear effect |
| Use Exact conformalization instead of grid-search conformalization | NLS, GFM, and IGR · Real-world benchmark datasets in Table 2 | length | No clear effect |
| Use Exact conformalization instead of split conformal prediction | NLS, GFM, and IGR · Real-world benchmark datasets in Table 2 | length | Helped |
Limitations
- Higher memory requirement since all training samples must be stored for gradient queries.
- Analysis restricted to affine constraints and scalar labels; multidimensional labels not covered.
- Choice of label parameterization affects efficiency.
Experimental setup
Datasets: fried cadata delta elevator
Benchmarks: fried cadata delta elevator
Metrics: empirical coverage average prediction interval length running time number of kinks
Baselines: Grid1 grid-point conformal Grid2 warm-restart grid-point conformal split conformal prediction
Builds on: conformal prediction LASSO path algorithms elastic net path Clarke subdifferential
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