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Localized conformal model selection

Yuhao Wang, Tengyao Wang

TL;DR

A localized conformal model selection framework that integrates local adaptivity with post-selection validity for distribution-free prediction is proposed and a data-dependent safe index set is constructed that contains the oracle model and preserves exchangeability.

Abstract

We propose a localized conformal model selection framework that integrates local adaptivity with post-selection validity for distribution-free prediction. By performing model selection symmetrically across calibration points using upper and lower surrogate intervals, we construct a data-dependent safe index set that contains the oracle model and preserves exchangeability. The resulting ensemble procedure retains exact finite-sample marginal coverage while adapting to spatial heterogeneity and model complexity. Simulations demonstrate substantial reductions in interval length compared to the best fixed model, especially in heterogeneous and low-noise settings.

Localized conformal model selection

TL;DR

A localized conformal model selection framework that integrates local adaptivity with post-selection validity for distribution-free prediction is proposed and a data-dependent safe index set is constructed that contains the oracle model and preserves exchangeability.

Abstract

We propose a localized conformal model selection framework that integrates local adaptivity with post-selection validity for distribution-free prediction. By performing model selection symmetrically across calibration points using upper and lower surrogate intervals, we construct a data-dependent safe index set that contains the oracle model and preserves exchangeability. The resulting ensemble procedure retains exact finite-sample marginal coverage while adapting to spatial heterogeneity and model complexity. Simulations demonstrate substantial reductions in interval length compared to the best fixed model, especially in heterogeneous and low-noise settings.
Paper Structure (4 sections, 1 theorem, 16 equations, 1 figure, 2 tables)

This paper contains 4 sections, 1 theorem, 16 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. A new localized conformal model selection
  3. Numerical simulations
  4. Discussion

Key Result

Theorem 1

Consider a dataset $\{(Y_i, X_i)\}_{i = 1}^{n + 1}$ that are i.i.d. realizations from a distribution $\mathbb{P}$, where $Y_{n + 1}$ is unobserved. Given a sequence of fixed functions $f_1, \ldots, f_K$, we have that the $C_{\mathrm{LCP-MS}}(\cdot)$ constructed in eq:finalcp satisfies for any $\alpha \in [0, 1]$.

Figures (1)

  • Figure 1: Localized ensemble conformal prediction intervals evaluated at each test point. The black curve denotes the true mean regression function, while the light blue curves indicate the true 90% confidence bands. Vertical bars represent ensemble conformal prediction intervals, with colours corresponding to different models selected within the ensemble. In highly oscillatory regions, models with smaller bandwidths are predominantly selected (blue), whereas in smoother regions the ensemble favours models with larger bandwidths (red and purple).

Theorems & Definitions (2)

  • Theorem 1
  • proof