From symmetry to geometry: Tractable nonconvex problems

Y Zhang, Q Qu, J Wright - arxiv preprint arxiv:2007.06753, 2020 - arxiv.org
As science and engineering have become increasingly data-driven, the role of optimization
has expanded to touch almost every stage of the data analysis pipeline, from signal and …

Leave-one-out singular subspace perturbation analysis for spectral clustering

AY Zhang, HY Zhou - The Annals of Statistics, 2024 - projecteuclid.org
In the supplement [46], we first provide the proof of Theorem 2.3 in Appendix A, followed by
the proofs of results of Section 3.4 in Appendix B. The proof of Theorem 3.3 is given in …

Clustering a mixture of gaussians with unknown covariance

D Davis, M Diaz, K Wang - arxiv preprint arxiv:2110.01602, 2021 - arxiv.org
We investigate a clustering problem with data from a mixture of Gaussians that share a
common but unknown, and potentially ill-conditioned, covariance matrix. We start by …

Statistical-computational trade-offs in tensor pca and related problems via communication complexity

R Dudeja, D Hsu - The Annals of Statistics, 2024 - projecteuclid.org
Statistical-computational trade-offs in tensor PCA and related problems via communication
complexity Page 1 The Annals of Statistics 2024, Vol. 52, No. 1, 131–156 https://doi.org/10.1214/23-AOS2331 …

High-dimensional estimation, basis assets, and the adaptive multi-factor model

L Zhu, S Basu, RA Jarrow, MT Wells - Quarterly Journal of Finance, 2020 - World Scientific
The paper proposes a new algorithm for the high-dimensional financial data—the
Groupwise Interpretable Basis Selection (GIBS) algorithm, to estimate a new Adaptive Multi …

A new variational model for shape graph registration with partial matching constraints

Y Sukurdeep, M Bauer, N Charon - SIAM Journal on Imaging Sciences, 2022 - SIAM
This paper introduces a new extension of Riemannian elastic curve matching to a general
class of geometric structures, which we call (weighted) shape graphs, that allows for shape …

Optimal clustering in anisotropic gaussian mixture models

X Chen, AY Zhang - ar** strict saddle points of the Moreau envelope in nonsmooth optimization
D Davis, M Díaz, D Drusvyatskiy - SIAM Journal on Optimization, 2022 - SIAM
Recent work has shown that stochastically perturbed gradient methods can efficiently
escape strict saddle points of smooth functions. We extend this body of work to nonsmooth …

Clustering structure of microstructure measures

L Zhu, N Sun, MT Wells - arxiv preprint arxiv:2107.02283, 2021 - arxiv.org
This paper builds the clustering model of measures of market microstructure features which
are popular in predicting stock returns. In a 10-second time-frequency, we study the …

Achieving optimal clustering in Gaussian mixture models with anisotropic covariance structures

X Chen, AY Zhang - The Thirty-eighth Annual Conference on Neural …, 2024 - openreview.net
We study clustering under anisotropic Gaussian Mixture Models (GMMs), where covariance
matrices from different clusters are unknown and are not necessarily the identity matrix. We …