Related papers: Sharp Variable Selection of a Sparse Submatrix in …
Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in…
A sparse precision matrix can be directly translated into a sparse Gaussian graphical model under the assumption that the data follow a joint normal distribution. This neat property makes high-dimensional precision matrix estimation very…
We consider the following basic inference problem: there is an unknown high-dimensional vector $w \in \mathbb{R}^n$, and an algorithm is given access to labeled pairs $(x,y)$ where $x \in \mathbb{R}^n$ is a measurement and $y = w \cdot x +…
We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…
Varying coefficient models have numerous applications in a wide scope of scientific areas. While enjoying nice interpretability, they also allow flexibility in modeling dynamic impacts of the covariates. But, in the new era of big data, it…
Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…
Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…
The performance of Orthogonal Matching Pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the…
We investigate the sub-Gaussian property for almost surely bounded random variables. If sub-Gaussianity per se is de facto ensured by the bounded support of said random variables, then exciting research avenues remain open. Among these…
Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of…
Consider the standard Gaussian linear regression model $Y=X\theta+\epsilon$, where $Y\in R^n$ is a response vector and $ X\in R^{n*p}$ is a design matrix. Numerous work have been devoted to building efficient estimators of $\theta$ when $p$…
Let A be an n by m matrix with m>n, and suppose that the underdetermined linear system As=x admits a sparse solution s0 for which ||s0||_0 < 1/2 spark(A). Such a sparse solution is unique due to a well-known uniqueness theorem. Suppose now…
We study sparse principal components analysis in high dimensions, where $p$ (the number of variables) can be much larger than $n$ (the number of observations), and analyze the problem of estimating the subspace spanned by the principal…
We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured…
We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
We study the problem of selecting a subset of k random variables from a large set, in order to obtain the best linear prediction of another variable of interest. This problem can be viewed in the context of both feature selection and sparse…
Many problems require the selection of a subset of variables from a full set of optimization variables. The computational complexity of an exhaustive search over all possible subsets of variables is, however, prohibitively expensive,…