Related papers: Inference on low-rank data matrices with applicati…
Probe-level models have led to improved performance in microarray studies but the various sources of probe-level contamination are still poorly understood. Data-driven analysis of probe performance can be used to quantify the uncertainty in…
This paper develops a general framework for conducting inference on the rank of an unknown matrix $\Pi_0$. A defining feature of our setup is the null hypothesis of the form $\mathrm H_0: \mathrm{rank}(\Pi_0)\le r$. The problem is of first…
Class prediction is an important application of microarray gene expression data analysis. The high-dimensionality of microarray data, where number of genes (variables) is very large compared to the number of samples (obser- vations), makes…
Quality of microarray gene expression data has emerged as a new research topic. As in other areas, microarray quality is assessed by comparing suitable numerical summaries across microarrays, so that outliers and trends can be visualized,…
Motivation: Microarray data has been recently been shown to be efficacious in distinguishing closely related cell types that often appear in the diagnosis of cancer. It is useful to determine the minimum number of genes needed to do such a…
This paper develops new methods to recover the missing entries of a high-rank or even full-rank matrix when the intrinsic dimension of the data is low compared to the ambient dimension. Specifically, we assume that the columns of a matrix…
Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings…
This paper investigates statistical inference for noisy matrix completion in a semi-supervised model when auxiliary covariates are available. The model consists of two parts. One part is a low-rank matrix induced by unobserved latent…
There exist many high-dimensional data in real-world applications such as biology, computer vision, and social networks. Feature selection approaches are devised to confront with high-dimensional data challenges with the aim of efficient…
We consider the recovery of a low rank and jointly sparse matrix from under sampled measurements of its columns. This problem is highly relevant in the recovery of dynamic MRI data with high spatio-temporal resolution, where each column of…
We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…
Matrix completion has become an extremely important technique as data scientists are routinely faced with large, incomplete datasets on which they wish to perform statistical inferences. We investigate how error introduced via matrix…
The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…
Many real world datasets subsume a linear or non-linear low-rank structure in a very low-dimensional space. Unfortunately, one often has very little or no information about the geometry of the space, resulting in a highly under-determined…
DNA microarray gene-expression data has been widely used to identify cancerous gene signatures. Microarray can increase the accuracy of cancer diagnosis and prognosis. However, analyzing the large amount of gene expression data from…
Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we…
We consider the problem of matrix column subset selection, which selects a subset of columns from an input matrix such that the input can be well approximated by the span of the selected columns. Column subset selection has been applied to…
One of the most popular tools for large scale gene expression studies are high-density oligonucleotide (GeneChip(R)) arrays. These currently have 16-20 small probe cells (``features'') for evaluating the transcript abundance of each gene.…