Heteroscedastic Regression

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Heteroscedastic regression studies settings where observations have different noise levels depending on their inputs, rather than one shared error variance. Common approaches predict the mean and variance together using likelihood losses, or estimate variance afterward; these ideas also appear in Gaussian processes, boosted mixed models, and robust regression with heavy-tailed errors. Modeling input-dependent uncertainty can improve forecasts, scientific inference, and robot policies by distinguishing reliable from noisy predictions. Open challenges include stabilizing training, ensuring uncertainty is both calibrated and meaningful across different regimes, and evaluating methods reliably when results vary across runs.

Latest papers

16 papers3 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Revisiting Tabular Deep Regression: Objectives and the Limits of Global Early Stopping
Oct 9, 2026Danil Rudenko, Georgii Bulgakov, Nikolay Kartashev +3Tabular Regression Quantile Regression
Yandex Research · BRAInLab · HSE University
Residual Modeling Closes the Regression and Generative Policy Gap in Robot Learning
Oct 8, 2026Yuchen Zhou, Jiacheng You, Weikang Wan +3Robot Policy Learning Robot Imitation Learning
University of Pennsylvania · Tsinghua University · UC San Diego
Fast Non-Parametric Heteroscedastic Imitation Learning With Geometric Priors
Oct 6, 2026Maximilian Mühlbauer, Arne Sachtler, Markus Knauer +4Robotic Manipulation Data-Efficient Robot Learning
Department of Computer Engineering, Technical University of Munich, Friedrich-Ludwig-Bauer-Str. 3, Garching, Germany. · German Aerospace Center (DLR), Robotics and Mechatronics Center (RMC), Münchener Str. 20, 82234 Weßling, Germany. · School of Computer Science, University of Leeds, Leeds, UK.
Halo: Improving forecast accuracy through heteroscedastic estimation
Sep 6, 2026Adam CataldoTime Series Forecasting Heteroscedastic Regression
AI Quant Researcher
Beyond Homoscedasticity: Decoupled Uncertainty Optimization for Deep Imbalanced Regression
Sep 4, 2026Juncheng Zhou, Jiaxi Lu, Weijing Zeng +3Heteroscedastic Regression Class-Imbalanced Learning
School of Cyber Science and Engineering, Wuhan University Wuhan, China · School of Mathematics and Statistics, Wuhan University Wuhan, China · School of Synthetic Biology and Biomanufacturing, Tianjin University Tianjin, China
Heteroscedastic Neural Surrogate Modeling for Robust and Rapid Bayesian Inference in Fusion Plasma Diagnostics
Aug 19, 2026Liyun Zhang, Naoya Mamada, Kentaro Sakai +2Neural Surrogate Modeling Bayesian Inference
GSFS, The University of Tokyo Japan
Algorithms for adaptive and heteroskedastic linear regression at the computational threshold
Aug 19, 2026Spencer Compton, Tselil SchrammMinimax Estimation Heteroscedastic Regression
Stanford University
Fisher8: Stabilizing Neural Heteroscedastic Regression via Output-Layer Fisher Geometry
Aug 11, 2026Sumedh Vemuganti, Nickvash KaniNatural Gradient Methods Heteroscedastic Regression
Electrical and Computer Engineering Department, University of Illinois at Urbana-Champaign
CUPA-T2*: Covariance-Aware Uncertainty Propagation and Alignment for T2* Mapping in Accelerated MRI
Aug 9, 2026Gideon N. L. Rouwendaal, Natascha Niessen, Hannah Eichhorn +3Uncertainty Quantification Heteroscedastic Regression
Institute of Machine Learning in Biomedical Imaging, Helmholtz Munich, Germany · School of Computation, Information & Technology, Technical University of Munich, Germany · GE HealthCare, Munich, Germany +6
Multi-Fidelity SINDy: Sparse Discovery of Nonlinear Dynamical Systems with Fidelity-Weighted Measurements
Jun 14, 2026Filippo Zacchei, Ana Larrañaga, Attilio Frangi +2Sparse Identification of Nonlinear Dynamics Nonlinear System Identification
MOX – Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy · Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195, United States · Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
Physically Constrained Ensemble Gaussian Process Modelling for Expensive Quantum Systems with Heteroskedastic Noise
May 29, 2026Arpan Biswas, Sutirtha Paul, Joseph Agada +2Surrogate Modeling Uncertainty Quantification
University of Tennessee-Oak Ridge Innovation Institute, University of Tennessee, Knoxville, TN 37996, USA · Institute for Advanced Materials and Manufacturing, University of Tennessee, Knoxville, Tennessee 37996, USA · Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA. +2
A Tale of Two Variances: When Single-Seed Benchmarks Fail in Bayesian Deep Learning
Apr 25, 2026Qishi Zhan, Minxuan Hu, Liang He +2Bayesian Neural Networks Deep Ensembles
Department of Mathematical and Statistical Sciences Marquette University, USA · Cornell Ann S. Bowers College of Computing and Information Science Cornell University, USA · Physics Science and Engineering Tongji University, China +2
Conformalized Super Learner
Apr 24, 2026Zhanli Wu, Fabrizio Leisen, Miguel-Angel Luque-Fernandez +1Ensemble Learning Conformal Prediction
Department of Mathematics King’s College London London, UK · Department of Statistics and Operations Research University of Granada Granada, Spain · Department of Statistical Science University College London London, UK
Practical Deep Heteroskedastic Regression
Mar 2, 2026Mikkel Jordahn, Jonas Vestergaard Jensen, James Harrison +2Uncertainty Quantification Heteroscedastic Regression
Technical University of Denmark · Google DeepMind
Learning Complex Physical Regimes via Coverage-oriented Uncertainty Quantification: An application to the Critical Heat Flux
Feb 25, 2026Michele Cazzola, Alberto Ghione, Lucia Sargentini +2Uncertainty Quantification Heteroscedastic Regression
Université Paris Saclay, Cea, Service Thermo-hydraulique et Mécanique des Fluides (Stmf), Gif-sur-Yvette, F-91191, France · Université Paris Saclay, Cea, Service de Génie Logiciel pour la Simulation (Sgls), Gif-sur-Yvette, F-91191, France
Gradient Boosted Mixed Models: Flexible Estimation of Mean and Variance Components for Clustered Data
Oct 31, 2025Mitchell L. Prevett, Francis K. C. Hui, Zhi Yang Tho +2Gradient-Boosted Decision Trees Heteroscedastic Regression
Research School of Finance, Actuarial Studies and Statistics The Australian National University Canberra, ACT 2601, Australia

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Revisiting Tabular Deep Regression: Objectives and the Limits of Global Early Stopping

Danil Rudenko, Georgii Bulgakov, Nikolay Kartashev, Ivan Rubachev+2

Yandex Research · BRAInLab · HSE University

Tabular Regression Quantile Regression Heteroscedastic Regression Robust Loss Functions Early Stopping

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While deep learning models for tabular data have recently received significant research attention, the choice of objective functions for regression tasks remains an understudied degree of freedom. Several lines of research offer alternatives to the standard Mean Squared Error (MSE), but differences in datasets, backbones, and evaluation protocols make their practical benefits difficult to compare. In this work, we address this gap by performing a systematic re-evaluation of regression objectives across a broad collection of established tabular datasets and multiple neural backbones. Our comparison reveals that many proposed objectives provide limited or inconsistent gains over a properly tuned MSE baseline, while quantile loss yields consistent aggregate improvements over MSE across the tested backbones. We then identify a limitation that remains even with this strong objective: regions with different levels of target noise can reach their best predictive performance at different training epochs. Consequently, a single global early-stopping checkpoint can impose a compromise between uncertainty regions, even when the objective can represent heteroskedastic target distributions. Motivated by this limitation, we introduce a heteroskedasticity-aware extension of quantile loss that uses input-dependent label smoothing as a potential remedy and improves over quantile loss on several backbones. Overall, our results provide a modern empirical picture of regression objectives for tabular deep learning and highlight how differences in optimal stopping times across uncertainty regions can limit the effectiveness of global early stopping. The code is available at https://github.com/yandex-research/tabular-regression.