Related papers: Sum-of-Squares Lower Bounds for Sparse PCA

We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…

We consider the high-dimensional inference problem where the signal is a low-rank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large…

We consider sparse variants of the classical Learning Parities with random Noise (LPN) problem. Our main contribution is a new algorithmic framework that provides learning algorithms against low-noise for both Learning Sparse Parities…

In the literature, there are a few researches to design some parameters in the Proximal Point Algorithm (PPA), especially for the multi-objective convex optimizations. Introducing some parameters to PPA can make it more flexible and…

Decoders are a critical component of fault-tolerant quantum computing. They must identify errors based on syndrome measurements to correct quantum states. While finding the optimal correction is NP-hard and thus extremely difficult,…

Classification with a sparsity constraint on the solution plays a central role in many high dimensional machine learning applications. In some cases, the features can be grouped together so that entire subsets of features can be selected or…

Principal component regression (PCR) is a widely used two-stage procedure: principal component analysis (PCA), followed by regression in which the selected principal components are regarded as new explanatory variables in the model. Note…

In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…

We study a cutting-plane method for semidefinite optimization problems (SDOs), and supply a proof of the method's convergence, under a boundedness assumption. By relating the method's rate of convergence to an initial outer approximation's…

We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to…

This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…

The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…

Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the $\ell_1$-norm. However, several important learning applications cannot benefit from this approach as…

This paper investigates some theoretical properties of the Partial Least Square (PLS) method. We focus our attention on the single component case, that provides a useful framework to understand the underlying mechanism. We provide a…

Inspired by recent work on convex formulations of clustering (Lashkari & Golland, 2008; Nowozin & Bakir, 2008) we investigate a new formulation of the Sparse Coding Problem (Olshausen & Field, 1997). In sparse coding we attempt to…

Randomized algorithms can be used to speed up the analysis of large datasets. In this paper, we develop a unified methodology for statistical inference via randomized sketching or projections in two of the most fundamental problems in…

We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized…

The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…

Since the introduction of the lasso in regression, various sparse methods have been developed in an unsupervised context like sparse principal component analysis (s-PCA), sparse canonical correlation analysis (s-CCA) and sparse singular…