Probability Theory

Gaussian Correlation Inequality: Optimal Extensions

Posed by Various (post-Royen) (2014)

Optimal Mixing Time for Log-Concave Sampling

KLS Conjecture (Kannan–Lovász–Simonovits)

Posed by Ravi Kannan, László Lovász, Miklós Simonovits (1995)

Universality for Wigner Matrices: Optimal Moment Conditions

Cover Time of Random Walk on General Graphs

Posed by Peter Winkler, David Zuckerman (1996)

Minimax Rate for Wasserstein Distance Estimation in High Dimensions

Exact Recovery Threshold in Multi-Community SBM

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

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

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

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

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

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