Likelihood over Estimation: Robust Quadratic Discriminant Analysis for Heavy-Tailed Distributions with Theory and Evidence

Niranjana Ambadi, Eugene Pinsky
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:2267-2306, 2026.

Abstract

Quadratic Discriminant Analysis (QDA) assumes Gaussian class-conditional distributions, causing systematic misclassification when data exhibit heavy tails. We propose Stable-QDA, which replaces the Gaussian likelihood with a symmetric $\alpha$-stable likelihood that decays polynomially rather than exponentially in Mahalanobis distance. Crucially, we find that correcting likelihood misspecification yields larger gains than robustifying parameter estimation: standard estimators (sample mean, Ledoit–Wolf covariance) often outperform robust alternatives when class heteroscedasticity is discriminative. We provide consistency guarantees under infinite-variance regimes, data-driven diagnostics for estimator selection, and demonstrate 15–53% error reduction on real-world heavy-tailed benchmarks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-ambadi26a, title = {Likelihood over Estimation: Robust Quadratic Discriminant Analysis for Heavy-Tailed Distributions with Theory and Evidence}, author = {Ambadi, Niranjana and Pinsky, Eugene}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {2267--2306}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/ambadi26a/ambadi26a.pdf}, url = {https://proceedings.mlr.press/v306/ambadi26a.html}, abstract = {Quadratic Discriminant Analysis (QDA) assumes Gaussian class-conditional distributions, causing systematic misclassification when data exhibit heavy tails. We propose Stable-QDA, which replaces the Gaussian likelihood with a symmetric $\alpha$-stable likelihood that decays polynomially rather than exponentially in Mahalanobis distance. Crucially, we find that correcting likelihood misspecification yields larger gains than robustifying parameter estimation: standard estimators (sample mean, Ledoit–Wolf covariance) often outperform robust alternatives when class heteroscedasticity is discriminative. We provide consistency guarantees under infinite-variance regimes, data-driven diagnostics for estimator selection, and demonstrate 15–53% error reduction on real-world heavy-tailed benchmarks.} }
Endnote
%0 Conference Paper %T Likelihood over Estimation: Robust Quadratic Discriminant Analysis for Heavy-Tailed Distributions with Theory and Evidence %A Niranjana Ambadi %A Eugene Pinsky %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-ambadi26a %I PMLR %P 2267--2306 %U https://proceedings.mlr.press/v306/ambadi26a.html %V 306 %X Quadratic Discriminant Analysis (QDA) assumes Gaussian class-conditional distributions, causing systematic misclassification when data exhibit heavy tails. We propose Stable-QDA, which replaces the Gaussian likelihood with a symmetric $\alpha$-stable likelihood that decays polynomially rather than exponentially in Mahalanobis distance. Crucially, we find that correcting likelihood misspecification yields larger gains than robustifying parameter estimation: standard estimators (sample mean, Ledoit–Wolf covariance) often outperform robust alternatives when class heteroscedasticity is discriminative. We provide consistency guarantees under infinite-variance regimes, data-driven diagnostics for estimator selection, and demonstrate 15–53% error reduction on real-world heavy-tailed benchmarks.
APA
Ambadi, N. & Pinsky, E.. (2026). Likelihood over Estimation: Robust Quadratic Discriminant Analysis for Heavy-Tailed Distributions with Theory and Evidence. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:2267-2306 Available from https://proceedings.mlr.press/v306/ambadi26a.html.

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