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Calibrated Multivariate Regression with Localized PIT Mappings

arXiv 2409.10855 ↗First posted 17 Sep 2024stat.ME stat.MLcited by 0

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Abstract (arXiv)

Calibration ensures that predicted uncertainties align with observed uncertainties. While there is an extensive literature on recalibration methods for univariate probabilistic forecasts, work on calibration for multivariate forecasts is much more limited. This paper introduces a novel post-hoc recalibration approach that addresses multivariate calibration for potentially misspecified models. Our method involves constructing local mappings between vectors of marginal probability integral transform values and the space of observations, providing a flexible and model free solution applicable to continuous, discrete, and mixed responses. We present two versions of our approach: one uses K-nearest neighbors, and the other uses normalizing flows. Each method has its own strengths in different situations. We demonstrate the effectiveness of our approach on two real data applications: recalibrating a deep neural network's currency exchange rate forecast and improving a regression model for childhood malnutrition in India for which the multivariate response has both discrete and continuous components.

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References · 24

  1. 2017On Calibration of Modern Neural Networkscited by 4,860
  2. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  3. 2016Density estimation using Real NVPcited by 2,029
  4. 2021A Survey of Uncertainty in Deep Neural Networkscited by 675
  5. 2018Accurate Uncertainties for Deep Learning Using Calibrated Regressioncited by 417
  6. 2019Distributional conformal predictioncited by 104
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  8. 2020Individual Calibration with Randomized Forecastingcited by 50
  9. 2022Robust Neural Posterior Estimation and Statistical Model Criticismcited by 45
  10. 2018Deep Learning with Long Short-Term Memory for Time Series Predictioncited by 39
  11. 2023Local Implicit Normalizing Flow for Arbitrary-Scale Image Super-Resolutioncited by 34
  12. 2021Regression Diagnostics meets Forecast Evaluation: Conditional Calibration, Reliability Diagrams, and Coefficient of Determinationcited by 31
12 more
  1. 2019Isotonic Distributional Regressioncited by 28
  2. 2023A Large-Scale Study of Probabilistic Calibration in Neural Network Regressioncited by 26
  3. 2024Addressing Misspecification in Simulation-based Inference through Data-driven Calibrationcited by 26
  4. 2013High-Dimensional Probability Estimation with Deep Density Modelscited by 17
  5. 2020Estimating Uncertainty Intervals from Collaborating Networkscited by 10
  6. 2022Towards Instance-Wise Calibration: Local Amortized Diagnostics and Reshaping of Conditional Densities (LADaR)cited by 9
  7. 2019Marginally-calibrated deep distributional regressioncited by 6
  8. 2022Score-based calibration testing for multivariate forecast distributionscited by 6
  9. 2017Recalibration: A post-processing method for approximate Bayesian computationcited by 4
  10. 2019Multivariate postprocessing methods for high-dimensional seasonal weather forecastscited by 1
  11. 2024Boosting Distributional Copula Regression for Bivariate Binary, Discrete and Mixed Responsescited by 1
  12. 2024Model-Free Local Recalibration of Neural Networkscited by 1

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