mlsanityData to 7 Oct 2026

TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression

arXiv 2310.18953 ↗First posted 29 Oct 2023cs.LG cs.CV eess.IVcited by 4

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Abstract (arXiv)

Deep heteroscedastic regression involves jointly optimizing the mean and covariance of the predicted distribution using the negative log-likelihood. However, recent works show that this may result in sub-optimal convergence due to the challenges associated with covariance estimation. While the literature addresses this by proposing alternate formulations to mitigate the impact of the predicted covariance, we focus on improving the predicted covariance itself. We study two questions: (1) Does the predicted covariance truly capture the randomness of the predicted mean? (2) In the absence of supervision, how can we quantify the accuracy of covariance estimation? We address (1) with a Taylor Induced Covariance (TIC), which captures the randomness of the predicted mean by incorporating its gradient and curvature through the second order Taylor polynomial. Furthermore, we tackle (2) by introducing a Task Agnostic Correlations (TAC) metric, which combines the notion of correlations and absolute error to evaluate the covariance. We evaluate TIC-TAC across multiple experiments spanning synthetic and real-world datasets. Our results show that not only does TIC accurately learn the covariance, it additionally facilitates an improved convergence of the negative log-likelihood. Our code is available at https://github.com/vita-epfl/TIC-TAC

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 27 of its 45 references that are in the map. First posted on arXiv 29 Oct 2023.

Builds on

27 of 45 references.

References · 27

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15 more
  1. 2019PifPaf: Composite Fields for Human Pose Estimationcited by 120
  2. 2022On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networkscited by 119
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Cited by year

Citing papers per year: 2024: 1; 2025: 3.

4 papers.

  1. 2024MotionMap: Representing Multimodality in Human Pose Forecastingcited by 7
  2. 2025Towards Self-Supervised Covariance Estimation in Deep Heteroscedastic Regressioncited by 2
  3. 2025Cooperative Variance Estimation and Bayesian Neural Networks for Disentangling Aleatoric and Epistemic Uncertaintiescited by 1
  4. 2025On the Effect of Regularization on Nonparametric Mean-Variance Regressioncited by 0