Posts by Collection

Fair Data Representation for Machine Learning at the Pareto Frontier

Published in Journal of Machine Learning Research (JMLR), 24 (2023), 1–63, 2023

We develop a principled framework for constructing fair data representations that achieve explicit, controllable trade-offs between utility and fairness—characterizing and computing solutions along a Pareto frontier.

Recommended citation: Shizhou Xu, Thomas Strohmer. (2023). “Fair Data Representation for Machine Learning at the Pareto Frontier.” Journal of Machine Learning Research, 24, 1–63.
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On the (In)Compatibility between Individual and Group Fairness

Published in Under review (SIAM Journal on Mathematics of Data Science — SIMODS), 2024

We analyze fundamental tensions between individual and group fairness notions, clarifying when they can or cannot be simultaneously satisfied and what trade-offs are unavoidable.

Recommended citation: Shizhou Xu, Thomas Strohmer. (2024). “On the (In)Compatibility between Individual and Group Fairness.” Under review at SIAM Journal on Mathematics of Data Science.
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WHOMP: Improving Upon Randomized Controlled Trials via Wasserstein Homogeneity

Published in Under review (Journal of the American Statistical Association), 2024

We introduce WHOMP, a Wasserstein-homogeneity optimality principle for subgroup splitting in comparative experiments (clinical trials, social experiments, and A/B tests). The method yields interpretable criteria, efficient estimators, and strong empirical gains over random partitioning, covariate-adaptive randomization, rerandomization, and anti-clustering baselines.

Recommended citation: Shizhou Xu, Thomas Strohmer. (2024). “WHOMP: Improving Upon Randomized Controlled Trials via Wasserstein Homogeneity.” Under review at Journal of the American Statistical Association.
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Forgetting-MarI: LLM Unlearning via Marginal Information Regularization

Published in Under review (ICLR 2026), 2025

We propose marginal-information regularization for LLM unlearning, targeting targeted forgetting with strong utility retention and practical, evaluation-driven design.

Recommended citation: Shizhou Xu, Yuan Ni, Stefan Broecker, Thomas Strohmer. (2025). “Forgetting-MarI: LLM Unlearning via Marginal Information Regularization.” Under review at ICLR 2026.
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Machine Unlearning via Information-Theoretic Regularization

Published in Manuscript (available on request), 2025

We develop information-theoretic regularization principles for machine unlearning, aiming to remove targeted information while maintaining general utility and enabling principled evaluation.

Recommended citation: Shizhou Xu, Thomas Strohmer. (2025). “Machine Unlearning via Information-Theoretic Regularization.” Manuscript.
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Multi-resolution Enhancement for Full Spectrum Neural Representations

Published in Under review (Nature Machine Intelligence), 2025

We develop multi-resolution enhancement strategies for full-spectrum neural representations, improving fidelity across scales with an emphasis on robust learning and generalization.

Recommended citation: Yuan Ni, Z. Chen, Shizhou Xu, C. Peng, R. Plumley, C. H. Yoon, J. Thayer, J. Turner. (2025). “Multi-resolution Enhancement for Full Spectrum Neural Representations.” Under review at Nature Machine Intelligence.
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Utility–Separation Pareto Frontier: An Information-Theoretic Characterization

Published in Under review (Journal of Machine Learning Research — JMLR), 2025

We provide an information-theoretic characterization of the utility–separation trade-off, yielding a principled Pareto frontier perspective for designing and evaluating separation-based objectives.

Recommended citation: Shizhou Xu. (2025). “Utility–Separation Pareto Frontier: An Information-Theoretic Characterization.” Under review at Journal of Machine Learning Research.
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Fair Data Representation for Machine Learning

Published: January 01, 2022

Talk on fairness objectives and data pre-processing approaches for controlling fairness–accuracy trade-offs.

Fairness in Machine Learning

Published: January 01, 2022

Invited talk introducing core fairness notions, practical pitfalls, and research directions in trustworthy ML.

Fair Data Representation for Machine Learning at the Pareto Frontier

Published: January 01, 2023

Workshop talk on provable fairness–utility trade-offs and algorithmic construction along the Pareto frontier.

Fair Data Representation for Machine Learning at the Pareto Frontier

Published: July 01, 2024

Conference presentation of the JMLR work on fair data representation via Pareto-frontier trade-offs.

Fair Data Representation for Machine Learning at the Pareto Frontier

Published: September 01, 2024

Invited talk on Pareto-frontier methods for fair data representation with provable trade-offs.

Machine Unlearning for Scientific Discovery

Published: January 01, 2025

Invited talk on why unlearning matters for scientific workflows (data governance, model updates, and reliability), and how to evaluate it.

Machine Unlearning via Information-Theoretic Regularization

Published: January 01, 2025

Seminar talk on information-theoretic unlearning: objectives, algorithms, and empirical evaluation considerations.

WHOMP: Improving Upon Randomized Controlled Trials via Wasserstein Homogeneity

Published: February 01, 2025

Seminar talk introducing WHOMP, theory/algorithms, and empirical comparisons for experimental design.

WHOMP: Improving Upon Randomized Controlled Trials via Wasserstein Homogeneity

Published: March 01, 2025

Spotlight talk presenting WHOMP and its advantages over classical randomization and rerandomization baselines.

WHOMP: Improving Upon Randomized Controlled Trials via Wasserstein Homogeneity

Published: April 01, 2025

Workshop talk on WHOMP: optimality criteria and algorithms for subgroup splitting in comparative experiments.

Machine Unlearning via Information-Theoretic Regularization

Published: October 01, 2025

Conference talk connecting unlearning goals to principled regularization and measurable evaluation pipelines.

Machine Unlearning via Information-Theoretic Regularization

Published: January 01, 2026

Talk (to appear). Overview of information-theoretic regularization for machine unlearning, with emphasis on auditability and evaluation.

Machine Unlearning via Information-Theoretic Regularization

Published: January 01, 2026

Talk (to appear). Mathematical framing of unlearning objectives and practical verification-oriented evaluation.

MATH 127C — Real Analysis (Summer 2025)

, , 2025

This page mirrors announcements, policies, and a living schedule for the Summer 2025 offering. Lecture notes and problem sets reflect the topics we covered this term: metric spaces, compactness/connectedness, multivariable differentiability (Jacobian, chain/implicit/inverse theorems), $k$–volume and Gram determinants, change of variables, Fubini/Tonelli, and Green/Stokes/Divergence.