# Calibrated Multivariate Regression with Localized PIT Mappings

arXiv: https://arxiv.org/abs/2409.10855 · HTML: https://mlsanity.com/paper/2409.10855/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 49 references that are in the map.
- First posted on arXiv 17 Sep 2024.

## Builds on (most cited first, 24 of 24)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Distribution Calibration for Regression](https://mlsanity.com/paper/1905.06023/) (2019)
- [Individual Calibration with Randomized Forecasting](https://mlsanity.com/paper/2006.10288/) (2020)
- [Robust Neural Posterior Estimation and Statistical Model Criticism](https://mlsanity.com/paper/2210.06564/) (2022)
- [Deep Learning with Long Short-Term Memory for Time Series Prediction](https://mlsanity.com/paper/1810.10161/) (2018)
- [Local Implicit Normalizing Flow for Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2303.05156/) (2023)
- [Regression Diagnostics meets Forecast Evaluation: Conditional Calibration, Reliability Diagrams, and Coefficient of Determination](https://mlsanity.com/paper/2108.03210/) (2021)
- [Isotonic Distributional Regression](https://mlsanity.com/paper/1909.03725/) (2019)
- [A Large-Scale Study of Probabilistic Calibration in Neural Network Regression](https://mlsanity.com/paper/2306.02738/) (2023)
- [Addressing Misspecification in Simulation-based Inference through Data-driven Calibration](https://mlsanity.com/paper/2405.08719/) (2024)
- [High-Dimensional Probability Estimation with Deep Density Models](https://mlsanity.com/paper/1302.5125/) (2013)
- [Estimating Uncertainty Intervals from Collaborating Networks](https://mlsanity.com/paper/2002.05212/) (2020)
- [Towards Instance-Wise Calibration: Local Amortized Diagnostics and Reshaping of Conditional Densities (LADaR)](https://mlsanity.com/paper/2205.14568/) (2022)
- [Marginally-calibrated deep distributional regression](https://mlsanity.com/paper/1908.09482/) (2019)
- [Score-based calibration testing for multivariate forecast distributions](https://mlsanity.com/paper/2211.16362/) (2022)
- [Recalibration: A post-processing method for approximate Bayesian computation](https://mlsanity.com/paper/1704.06374/) (2017)
- [Multivariate postprocessing methods for high-dimensional seasonal weather forecasts](https://mlsanity.com/paper/1907.09716/) (2019)
- [Boosting Distributional Copula Regression for Bivariate Binary, Discrete and Mixed Responses](https://mlsanity.com/paper/2403.02194/) (2024)
- [Model-Free Local Recalibration of Neural Networks](https://mlsanity.com/paper/2403.05756/) (2024)

## 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.