Mathematical Statistics

Minimax-Optimal Sparse PCA: Computational–Statistical Gap

Posed by Berthet & Rigollet (formalized) (2013)

Gaussian Correlation Inequality: Optimal Extensions

Posed by Various (post-Royen) (2014)

Optimal Mixing Time for Log-Concave Sampling

Tight PAC-Bayes Bounds for Deep Neural Networks

Optimal Distribution-Free Prediction Intervals

Universality for Wigner Matrices: Optimal Moment Conditions

Minimax Rate for Wasserstein Distance Estimation in High Dimensions

Uniform Inference for High-Dimensional Linear Models

Exact Recovery Threshold in Multi-Community SBM

Adaptive Minimax Nonparametric Hypothesis Testing

Computational Threshold for Tensor PCA

Posed by Richard & Montanari (2014)

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

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

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

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

Remove logarithmic gaps in minimax sample complexity for matrix normal covariance estimation

Sourced from the work of Rafael Mendes de Oliveira, William Cole Franks, Akshay Ramachandran, Michael Walter

Full minimax characterization for tensor normal factor estimation beyond the largest factor

Sourced from the work of Rafael Mendes de Oliveira, William Cole Franks, Akshay Ramachandran, Michael Walter

Optimal guarantees in the low-sample tensor regime (below constant-Frobenius threshold)

Sourced from the work of Rafael Mendes de Oliveira, William Cole Franks, Akshay Ramachandran, Michael Walter

Exact information-theoretic detection threshold for correlated SBM vs Erdos-Renyi pair

Sourced from the work of Guanyi Chen, Jian Ding, Shuyang Gong, Zhangsong Li

General-$k$ threshold for testing correlated SBMs against independent SBMs

Sourced from the work of Guanyi Chen, Jian Ding, Shuyang Gong, Zhangsong Li

From low-degree hardness to unconditional polynomial-time hardness

Sourced from the work of Guanyi Chen, Jian Ding, Shuyang Gong, Zhangsong Li

Remove the Polylogarithmic Gap to Exact Minimax Optimality

Sourced from the work of Kaizheng Wang

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

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

Multiple change-point inference for piecewise constant diffusivity

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

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

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

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

Sourced from the work of Sourav Chatterjee, Timothy Sudijono

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

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

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

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

Polynomial-time minimax robust mean estimation under star-shaped constraints

Sourced from the work of Akshay Prasadan, Matey Neykov

Sharp minimax behavior as contamination approaches the breakdown boundary $\epsilon\uparrow 1/2$

Sourced from the work of Akshay Prasadan, Matey Neykov

Information-theoretic limits under heavy-tailed (non-sub-Gaussian) noise

Sourced from the work of Akshay Prasadan, Matey Neykov

Optimal Break-Point Estimation Rate in Grouped Time-Varying Network VAR

Sourced from the work of Degui Li, Bin Peng, Songqiao Tang, Wei Biao Wu

Full Multiple-Break Theory for Latent Group Structure and Coefficients

Sourced from the work of Degui Li, Bin Peng, Songqiao Tang, Wei Biao Wu

Finite-sample optimal FDR-FNR frontier under the two-group model

Sourced from the work of Yutong Nie, Yihong Wu

Optimal FDR-FNR tradeoff beyond independent two-group mixtures

Sourced from the work of Yutong Nie, Yihong Wu

Asymptotic Normality of Spectrum-Aware Debiasing Beyond Right-Rotationally Invariant Designs

Sourced from the work of Yufan Li, Pragya Sur

Theory for Debiased PCR Under General Covariate Models

Sourced from the work of Yufan Li, Pragya Sur

Overparameterized optimal subsample size for infinite-ensemble subagging

Sourced from the work of Takuya Koriyama, Pratik Patil, Jin-Hong Du, Kai Tan, Pierre C. Bellec

Nonasymptotic guarantees for bagged regularized M-estimators

Sourced from the work of Takuya Koriyama, Pratik Patil, Jin-Hong Du, Kai Tan, Pierre C. Bellec

Extension beyond convex differentiable-loss framework

Sourced from the work of Takuya Koriyama, Pratik Patil, Jin-Hong Du, Kai Tan, Pierre C. Bellec

Sparsistent Estimation for Constrained Extremal Graphical Lasso

Sourced from the work of Sebastian Engelke, Michael Lalancette, Stanislav Volgushev

Valid Uncertainty Quantification for Extremal Graph Structure

Sourced from the work of Sebastian Engelke, Michael Lalancette, Stanislav Volgushev

Goodness-of-Fit Test for the H\"usler--Reiss Domain of Attraction

Sourced from the work of Sebastian Engelke, Michael Lalancette, Stanislav Volgushev

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

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

Complete Generic Identifiability in Cyclic LiNGAM with General Confounding

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

Full Causal Graph Recovery Under Arbitrary Nonlinear Latent Confounding

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

Provable Estimation Procedures Under the New Identifiability Criterion

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

State evolution for gradient descent beyond the mean-field scaling

Sourced from the work of Qiyang Han, Xiaocong Xu

Sharp characterization of misspecification robustness for debiased GD inference

Sourced from the work of Qiyang Han, Xiaocong Xu

Uniform risk dominance of transformed Moore-Penrose estimators

Sourced from the work of Taras Bodnar, Nestor Parolya

Non-asymptotic oracle inequalities for fully data-driven generalized-inverse shrinkage

Sourced from the work of Taras Bodnar, Nestor Parolya

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

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

Optimal adaptation beyond compact manifolds

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

Generalization-error estimation beyond Gaussian designs

Sourced from the work of Pierre C Bellec, Kai Tan

Early-stopping optimality without a U-shape risk assumption

Sourced from the work of Pierre C Bellec, Kai Tan

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

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

Beyond smooth finite-dimensional targets in unified semiparametric data fusion

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

Non-asymptotic AMP distributional theory beyond polynomially many iterations

Sourced from the work of Gen Li, Yuting Wei

Characterize adaptive distribution classes where two-point rates are attainable

Sourced from the work of Spencer Compton, Gregory Valiant

Remove polylogarithmic slack in attainable two-point rates

Sourced from the work of Spencer Compton, Gregory Valiant

Sharp boundary for attainability in finite-sample location models

Sourced from the work of Spencer Compton, Gregory Valiant

Remove polylogarithmic dimension factors in high-dimensional Berry--Esseen bounds for $m$-dependent sums

Sourced from the work of Heejong Bong, Arun Kumar Kuchibhotla, Alessandro Rinaldo

Complete optimality characterization in the independent-vector specialization under minimal moments

Sourced from the work of Heejong Bong, Arun Kumar Kuchibhotla, Alessandro Rinaldo

Polynomial-time warm initialization at statistically optimal thresholds

Sourced from the work of Wanteng Ma, Dong Xia

Sharp computational lower bounds for valid inference in the intermediate regime

Sourced from the work of Wanteng Ma, Dong Xia

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

Sourced from the work of Wanteng Ma, Dong Xia

Lower-bound the spanning-tree polynomial to sharpen Gaussian \(\chi^2\) bounds

Sourced from the work of Yanjun Han, Jonathan Niles-Weed

Exploit structure of the overlap matrix beyond trace/spectral gap

Sourced from the work of Yanjun Han, Jonathan Niles-Weed

Critical SNR for outlier emergence at fixed summary statistics

Sourced from the work of Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang, Aukosh Jagannath

Small-SNR no-outlier regime and monotonicity in SNR

Sourced from the work of Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang, Aukosh Jagannath

Sharp dynamic emergence thresholds for XOR/multilayer GMM classification

Sourced from the work of Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang, Aukosh Jagannath

Outlier theory beyond non-degeneracy/invertibility assumptions (ReLU and zero diagonal entries)

Sourced from the work of Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang, Aukosh Jagannath

Outlier characterization for unbounded link functions (e.g., phase retrieval)

Sourced from the work of Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang, Aukosh Jagannath