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Sparse PCA with Oracle Property
Quanquan Gu, Zhaoran Wang, Han Liu
In this paper, we study the estimation of the -dimensional sparse principal subspace of covariance matrix in the high-dimensional setting. We aim to recover the oracle princ…
More Supervision, Less Computation: Statistical-Computational Tradeoffs in Weakly Supervised Learning
Xinyang Yi, Zhaoran Wang, Zhuoran Yang +2
We consider the weakly supervised binary classification problem where the labels are randomly flipped with probability . Although there exist numerous algorithms for this pro…
Homotopy Parametric Simplex Method for Sparse Learning
Haotian Pang, Robert Vanderbei, Han Liu +1
High dimensional sparse learning has imposed a great computational challenge to large scale data analysis. In this paper, we are interested in a broad class of sparse learning appr…
Symmetry, Saddle Points, and Global Optimization Landscape of Nonconvex Matrix Factorization
Xingguo Li, Junwei Lu, Raman Arora +4
We propose a general theory for studying the \xl{landscape} of nonconvex \xl{optimization} with underlying symmetric structures \tz{for a class of machine learning problems (e.g.,…
Nonconvex Sparse Learning via Stochastic Optimization with Progressive Variance Reduction
Xingguo Li, Raman Arora, Han Liu +2
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which t…