Optimization & Variational Methods

Optimal Mixing Time for Log-Concave Sampling

KLS Conjecture (Kannan–Lovász–Simonovits)

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

Smoothed Complexity of the Simplex Method

Posed by Spielman & Teng (implicit) (2004)

Global Landscape of Non-Convex Matrix Sensing

Minimax Rate for Wasserstein Distance Estimation in High Dimensions

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

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

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

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

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

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