In the past decade, sparse principal component analysis has emerged as an archetypal
problem for illustrating statistical-computational tradeoffs. This trend has largely been driven …

It is well known that Sparse PCA (Sparse Principal Component Analysis) is NP-hard to solve
exactly on worst-case instances. What is the complexity of solving Sparse PCA …

We study a variant of the sparse PCA (principal component analysis) problem in the “hard”
regime, where the inference task is possible yet no polynomial-time algorithm is known to …

This paper establishes a statistical versus computational trade-offfor solving a basic high-
dimensional machine learning problem via a basic convex relaxation method. Specifically …

In sparse principal component analysis we are given noisy observations of a low-rank matrix
of dimension n× p and seek to reconstruct it under additional sparsity assumptions. In …

We study the question of learning a sparse multivariate polynomial over the real domain. In
particular, for some unknown polynomial f (x) of degree-d and k monomials, we show how to …

We give a reduction from clique to establish that sparse Principal Components Analysis
(sparse PCA) is NP-hard. Using our reduction, we exclude a fully polynomial time …

Abstract Principal Components Analysis (PCA) is a dimension-reduction technique widely
used in machine learning and statistics. However, due to the dependence of the principal …

We provide statistical and computational analysis of sparse Principal Component Analysis
(PCA) in high dimensions. The sparse PCA problem is highly nonconvex in nature …

We study the computational cost of recovering a unit-norm sparse principal component x∈
R n planted in a random matrix, in either the Wigner or Wishart spiked model (observing …