# Calibrated Reliable Regression using Maximum Mean Discrepancy

arXiv: https://arxiv.org/abs/2006.10255 · HTML: https://mlsanity.com/paper/2006.10255/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2020.

## Built on by (most cited first, 30 of 36)

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- [Evaluating Aleatoric Uncertainty via Conditional Generative Models](https://mlsanity.com/paper/2206.04287/) (2022)
- [Calibration and generalizability of probabilistic models on low-data chemical datasets with DIONYSUS](https://mlsanity.com/paper/2212.01574/) (2022)
- [Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection](https://mlsanity.com/paper/2207.01242/) (2022)
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- [FlowECG: Using Flow Matching to Create a More Efficient ECG Signal Generator](https://mlsanity.com/paper/2509.10491/) (2025)
- [f-Cal: Calibrated aleatoric uncertainty estimation from neural networks for robot perception](https://mlsanity.com/paper/2109.13913/) (2021)
- [Likelihood Annealing: Fast Calibrated Uncertainty for Regression](https://mlsanity.com/paper/2302.11012/) (2023)
- [Distribution-Free Model-Agnostic Regression Calibration via Nonparametric Methods](https://mlsanity.com/paper/2305.12283/) (2023)
- [Uncertainty Calibration for Counterfactual Propensity Estimation in Recommendation](https://mlsanity.com/paper/2303.12973/) (2023)
- [Parity Calibration](https://mlsanity.com/paper/2305.18655/) (2023)
- [Conformal Depression Prediction](https://mlsanity.com/paper/2405.18723/) (2024)
- [Accurate and Reliable Forecasting using Stochastic Differential Equations](https://mlsanity.com/paper/2103.15041/) (2021)
- [Ensemble Multi-Quantiles: Adaptively Flexible Distribution Prediction for Uncertainty Quantification](https://mlsanity.com/paper/2211.14545/) (2022)
- [Improving Uncertainty Quantification of Variance Networks by Tree-Structured Learning](https://mlsanity.com/paper/2212.12658/) (2022)
- [Measuring and Modeling Uncertainty Degree for Monocular Depth Estimation](https://mlsanity.com/paper/2307.09929/) (2023)
- [Deep sub-ensembles meets quantile regression: uncertainty-aware imputation for time series](https://mlsanity.com/paper/2312.01294/) (2023)
- [Causally-Aware Unsupervised Feature Selection Learning](https://mlsanity.com/paper/2410.12224/) (2024)
- [Localization Meets Uncertainty: Uncertainty-Aware Multi-Modal Localization](https://mlsanity.com/paper/2504.07677/) (2025)
- [Cooperative Variance Estimation and Bayesian Neural Networks for Disentangling Aleatoric and Epistemic Uncertainties](https://mlsanity.com/paper/2505.02743/) (2025)
- [Deep Hidden Cognition Facilitates Reliable Chain-of-Thought Reasoning](https://mlsanity.com/paper/2507.10007/) (2025)
- [Evaluating the Quality of the Quantified Uncertainty for (Re)Calibration of Data-Driven Regression Models](https://mlsanity.com/paper/2508.17761/) (2025)
- [Microstructure-based Variational Neural Networks for Robust Uncertainty Quantification in Materials Digital Twins](https://mlsanity.com/paper/2512.18104/) (2025)
- [Transfer Learning Through Conditional Quantile Matching](https://mlsanity.com/paper/2602.02358/) (2026)
- [Pointwise Metrics Mislead: An Evaluation Protocol for Multimodal Inverse Problems](https://mlsanity.com/paper/2605.22891/) (2026)
- [Decision-Aligned Evaluation of Uncertainty Quantification](https://mlsanity.com/paper/2606.26990/) (2026)

## Abstract (arXiv)

Accurate quantification of uncertainty is crucial for real-world applications of machine learning. However, modern deep neural networks still produce unreliable predictive uncertainty, often yielding over-confident predictions. In this paper, we are concerned with getting well-calibrated predictions in regression tasks. We propose the calibrated regression method using the maximum mean discrepancy by minimizing the kernel embedding measure. Theoretically, the calibration error of our method asymptotically converges to zero when the sample size is large enough. Experiments on non-trivial real datasets show that our method can produce well-calibrated and sharp prediction intervals, which outperforms the related state-of-the-art methods.