Minimax Estimation

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10 papers in the last four weeks, up 233% on the four weeks before. 0.1% of all new papers.

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Sample Complexities of Estimating Gumbel--Max Watermark Proportions with and without Reduction to Pivotal Statistics
Jun 30, 2026Shuwen Chai, Qiaosen WangMinimax Estimation LLM Watermarking
Northwestern University · University of Chicago
The Fundamental Limits of Valid Transport Map Estimation
Jun 29, 2026Sivaraman BalakrishnanMinimax Estimation Generative Modeling
Department of Statistics and Data Science† · Machine Learning Department‡
Adversarial Contamination Meets Hard Thresholding: An Iterative Algorithm with Signal Adaptivity and Minimax Optimality
Jun 26, 2026Shixiang Liu, Hanming YangRobust Regression Sparse Recovery
School of Statistics, Renmin University of China · Institute of Statistics and Big Data, Renmin University of China
Fast algorithms for learning a Gaussian under halfspace truncation with optimal sample complexity
Jun 25, 2026Haitong Liu, Deepak Narayanan Sridharan, David Steurer +1Minimax Estimation Statistical Learning Theory
ETH Zurich
Black-Box Assisted Regression: Phase Transitions and Minimax Optimality
Jun 24, 2026Yan ZhouResidual Learning Nonparametric Regression
School of Mathematics and Statistics, Changsha University of Science and Technology.
On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA
Jun 20, 2026Syamantak Kumar, Shourya Pandey, Purnamrita Sarkar +1Principal Component Analysis Minimax Estimation
University of Texas at Austin
Optimal Deterministic Multicalibration and Omniprediction
Jun 18, 2026Georgy Noarov, Aaron RothMinimax Estimation Model Calibration
University of Pennsylvania
A Complexity Measure for Active Learning in Multi-group Mean Estimation
Jun 12, 2026Abdellah Aznag, Rachel Cummings, Adam N. ElmachtoubMulti-Armed Bandits Active Learning
Department of Industrial Engineering and Operations Research & Data Science Institute, Columbia University
Pointwise Complexity for Gaussian Fields: Upper Envelopes, Algorithmic Lower Bounds, and Separation
Jun 6, 2026Yunbei XuGaussian Processes Minimax Estimation
National University of Singapore
A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space
Jun 5, 2026Munsik KimMinimax Estimation Spatiotemporal Forecasting
Improved Distribution Estimation in $\ell_\infty$
May 28, 2026Doron Cohen, Aryeh Kontorovich, Yonatan LivshitzMinimax Estimation
Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Reward Transfer from Inverse Reinforcement Learning: A Coupled Minimax Approach
May 27, 2026Guang-Yuan Hao, Lars van der Laan, Aurélien Bibaut +1Reinforcement Learning Minimax Estimation
Cornell Tech, Cornell University · Netflix Research · Department of Statistics, University of Washington
Minimax Limits of k-Fold Cross-Validation via Majority
May 25, 2026Ido Nachum, Rüdiger Urbanke, Thomas WeinbergerMinimax Estimation Statistical Learning Theory
University of Haifa, Haifa, Israel. · EPFL, Lausanne, Switzerland.
Instance-Optimal Estimation with Multiple LLM Judges on a Budget
May 22, 2026Junghyun Lee, Sanghwa Kim, Yassir Jedra +2Parameter Estimation LLM Evaluation
KAIST AI · ICL EEE · KTH EECS
Extended Wasserstein-GAN Approach to Causal Distribution Learning: Density-Free Estimation and Minimax Optimality
May 11, 2026Shu Tamano, Masaaki ImaizumiCausal Effect Estimation Causal Counterfactual Generation
1The University of Tokyo · 2Japan Institute for Health Security · 3RIKEN Center for Advanced Intelligence Project +1
The Minimax Rate of Perturbed Second-Order Calibration
May 8, 2026Kamil Ciosek, Banafsheh Rafiee, Sina Ghiassian +1Post-Hoc Calibration Minimax Estimation
Spotify
ConquerNet: Convolution-Smoothed Quantile ReLU Neural Networks with Minimax Guarantees
May 7, 2026Tianpai Luo, Fangwei Wu, Weichi WuQuantile Regression Minimax Estimation
Department of Statistics and Data Science Tsinghua University Beijing, 100084, China
Direct Estimation of Schrödinger Bridge Time-Series Drifts: Finite-Sample, Asymptotic, and Adaptive Guarantees
May 6, 2026Othmane Mazhar, Huyên PhamParameter Estimation Schrödinger Bridges
LPSM, Sorbonne Université and Université Paris Cité · École Polytechnique, CMAP
Information-theoretic Limits of Learning and Estimation
May 6, 2026Abbas El Gamal, Maxim RaginskyInformation-Theoretic Generalization Bounds Minimax Estimation
Stanford University* · UIUC**
Optimal Estimation of Watermark Proportions in Hybrid AI-Human Texts
Jun 27, 2025Xiang Li, Garrett Wen, Weiqing He +3Text Watermarking Minimax Estimation
University of Pennsylvania · Yale University

Jun 30, 2026, math.STJ/K move · Enter open · S save

Sample Complexities of Estimating Gumbel--Max Watermark Proportions with and without Reduction to Pivotal Statistics

Shuwen Chai, Qiaosen Wang

Northwestern University · University of Chicago

Minimax Estimation LLM Watermarking

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Watermarking promises statistical traceability of large language model (LLM) uses, but real documents rarely arrive as purely human-written or purely LLM-generated. This motivates a quantitative question beyond detection: what proportion of a document is generated from a pre-specified watermarked LLM? We study this watermark proportion estimation problem under the Gumbel--max watermarking mechanism, treating the next-token prediction distributions as unknown and arbitrary nuisance parameters subject to a non-degeneracy condition. We compare two observation regimes: in the full observation regime, the estimator observes the pseudorandom vector and the selected token at each position; in the more prevalent setting of pivotal reduction, it observes only a scalar pivot, which follows a one-dimensional Uniform--Beta mixture distribution. Under pivotal reduction, we develop a Laguerre-polynomial estimator and establish a matching information-theoretic lower bound for the sample complexity. For full observation, we introduce an event-counting estimator and show a matching lower bound, yielding a substantially smaller sample complexity. As our results imply, although reducing to pivotal statistics is an elegant and prevalent choice, it is not always sample-efficient for estimating the proportion of watermarks.

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