Learning Theory

MSC 68Q32

Computational learning theory, statistical learning, PAC learning, online learning, information-theoretic limits.

29 problems

UnsolvedMajor

Tight PAC-Bayes Bounds for Deep Neural Networks

Learning TheoryMathematical Statistics
UnsolvedNotable

Optimal Distribution-Free Prediction Intervals

Mathematical StatisticsLearning Theory
UnsolvedNotable

Global Landscape of Non-Convex Matrix Sensing

Optimization & Variational MethodsLearning Theory
UnsolvedNotable

Exact Recovery Threshold in Multi-Community SBM

Mathematical StatisticsProbability TheoryLearning Theory
UnsolvedMajor

Computational Threshold for Tensor PCA

Mathematical StatisticsLearning TheoryTheoretical Computer Science

Posed by Richard & Montanari (2014)

Unsolved

Sharp minimax rate for central-space estimation in the low-signal SIR regime

Mathematical StatisticsLearning Theory

Sourced from the work of Dongming Huang, Songtao Tian, Qian Lin

Unsolved

Universality of exponential decay of the $d$-th SIR eigenvalue

Mathematical StatisticsLearning Theory

Sourced from the work of Dongming Huang, Songtao Tian, Qian Lin

Unsolved

Remove the Polylogarithmic Gap to Exact Minimax Optimality

Mathematical StatisticsLearning TheoryInformation Theory

Sourced from the work of Kaizheng Wang

UnsolvedNotable

Local-asymptotic limit law with unknown diffusivity levels under vanishing jump

Mathematical StatisticsProbability TheoryLearning Theory

Sourced from the work of Markus Reiß, Claudia Strauch, Lukas Trottner

Unsolved

Multiple change-point inference for piecewise constant diffusivity

Mathematical StatisticsProbability TheoryLearning Theory

Sourced from the work of Markus Reiß, Claudia Strauch, Lukas Trottner

Unsolved

Higher-dimensional change-set (interface) estimation for discontinuous diffusivity

Mathematical StatisticsProbability TheoryLearning Theory

Sourced from the work of Markus Reiß, Claudia Strauch, Lukas Trottner

Unsolved

Rigorous tempered-overfitting guarantees for MDL ReLU interpolators under label noise

Learning TheoryMathematical StatisticsProbability Theory

Sourced from the work of Sourav Chatterjee, Timothy Sudijono

Unsolved

Does the score-matched optimal convex estimator attain the full semiparametric efficiency bound?

Mathematical StatisticsLearning TheoryOptimization & Variational Methods

Sourced from the work of Oliver Y. Feng, Yu-Chun Kao, Min Xu, Richard J. Samworth

Unsolved

Quantify and characterize the efficiency gap induced by convex-loss restriction for non-log-concave errors

Mathematical StatisticsLearning TheoryOptimization & Variational Methods

Sourced from the work of Oliver Y. Feng, Yu-Chun Kao, Min Xu, Richard J. Samworth

Unsolved

Finite-sample error-rate control and power guarantees under the linear subspace model

Mathematical StatisticsLearning TheoryInformation Theory

Sourced from the work of Amitay Eldar, Keren Mor Waknin, Samuel Davenport, Tamir Bendory, Armin Schwartzman, Yoel Shkolnisky

Unsolved

Complete Generic Identifiability in Cyclic LiNGAM with General Confounding

Mathematical StatisticsProbability TheoryLearning Theory

Sourced from the work of Daniele Tramontano, Jalal Etesami, Mathias Drton

Unsolved

Full Causal Graph Recovery Under Arbitrary Nonlinear Latent Confounding

Mathematical StatisticsProbability TheoryLearning Theory

Sourced from the work of Daniele Tramontano, Jalal Etesami, Mathias Drton

Unsolved

Provable Estimation Procedures Under the New Identifiability Criterion

Mathematical StatisticsProbability TheoryLearning Theory

Sourced from the work of Daniele Tramontano, Jalal Etesami, Mathias Drton

Unsolved

State evolution for gradient descent beyond the mean-field scaling

Mathematical StatisticsOptimization & Variational MethodsLearning Theory

Sourced from the work of Qiyang Han, Xiaocong Xu

Unsolved

Sharp characterization of misspecification robustness for debiased GD inference

Mathematical StatisticsOptimization & Variational MethodsLearning Theory

Sourced from the work of Qiyang Han, Xiaocong Xu

Unsolved

Log-factor-free adaptive contraction on general Minkowski-dimensional domains

Mathematical StatisticsLearning TheoryInformation Theory

Sourced from the work of Tao Tang, Xiuyuan Cheng, Nan Wu, David Dunson

Unsolved

Optimal adaptation beyond compact manifolds

Mathematical StatisticsLearning TheoryInformation Theory

Sourced from the work of Tao Tang, Xiuyuan Cheng, Nan Wu, David Dunson

Unsolved

Generalization-error estimation beyond Gaussian designs

Mathematical StatisticsOptimization & Variational MethodsLearning Theory

Sourced from the work of Pierre C Bellec, Kai Tan

Unsolved

Early-stopping optimality without a U-shape risk assumption

Mathematical StatisticsOptimization & Variational MethodsLearning Theory

Sourced from the work of Pierre C Bellec, Kai Tan

Unsolved

Machine-learning debiased efficient estimation under generalized data-fusion alignments

Mathematical StatisticsLearning TheoryInformation Theory

Sourced from the work of Ellen Sandra Graham, Marco Carone, Andrea Rotnitzky

Unsolved

Beyond smooth finite-dimensional targets in unified semiparametric data fusion

Mathematical StatisticsLearning TheoryInformation Theory

Sourced from the work of Ellen Sandra Graham, Marco Carone, Andrea Rotnitzky

UnsolvedNotable

Polynomial-time warm initialization at statistically optimal thresholds

Mathematical StatisticsProbability TheoryLearning Theory

Sourced from the work of Wanteng Ma, Dong Xia

Unsolved

Sharp computational lower bounds for valid inference in the intermediate regime

Mathematical StatisticsProbability TheoryLearning Theory

Sourced from the work of Wanteng Ma, Dong Xia

Unsolved

General-rank intrinsic Cramér–Rao lower bound on Tucker manifolds

Mathematical StatisticsProbability TheoryLearning Theory

Sourced from the work of Wanteng Ma, Dong Xia