Related papers: Statistical and computational trade-offs in estima…
Sparse principal component analysis (sPCA) has become one of the most widely used techniques for dimensionality reduction in high-dimensional datasets. The main challenge underlying sPCA is to estimate the first vector of loadings of the…
High-dimensional time series data exist in numerous areas such as finance, genomics, healthcare, and neuroscience. An unavoidable aspect of all such datasets is missing data, and dealing with this issue has been an important focus in…
Under a standard assumption in complexity theory (NP not in P/poly), we demonstrate a gap between the minimax prediction risk for sparse linear regression that can be achieved by polynomial-time algorithms, and that achieved by optimal…
Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly…
Sparse PCA is the optimization problem obtained from PCA by adding a sparsity constraint on the principal components. Sparse PCA is NP-hard and hard to approximate even in the single-component case. In this paper we settle the computational…
The development of cluster computing frameworks has allowed practitioners to scale out various statistical estimation and machine learning algorithms with minimal programming effort. This is especially true for machine learning problems…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…
Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…
We consider the sparse principal component analysis for high-dimensional stationary processes. The standard principal component analysis performs poorly when the dimension of the process is large. We establish the oracle inequalities for…
This paper studies the minimax detection of a small submatrix of elevated mean in a large matrix contaminated by additive Gaussian noise. To investigate the tradeoff between statistical performance and computational cost from a…
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 by a line of research aiming to characterize the…
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…
Estimating a covariance matrix and its associated principal components is a fundamental problem in contemporary statistics. While optimal estimation procedures have been developed with well-understood properties, the increasing demand for…
Maximum likelihood estimators are often of limited practical use due to the intensive computation they require. We propose a family of alternative estimators that maximize a stochastic variation of the composite likelihood function. Each of…
Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely…
Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…
The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine…
The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…
Robustness is a key requirement for widespread deployment of machine learning algorithms, and has received much attention in both statistics and computer science. We study a natural model of robustness for high-dimensional statistical…