Related papers: A theoretical contribution to the fast implementat…
In some significant applications such as data forecasting, the locations of missing entries cannot obey any non-degenerate distributions, questioning the validity of the prevalent assumption that the missing data is randomly chosen…
Low-rank matrix approximation is one of the central concepts in machine learning, with applications in dimension reduction, de-noising, multivariate statistical methodology, and many more. A recent extension to LRMA is called low-rank…
We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…
This paper introduces a novel method for the automatic detection and handling of nonlinearities in a generic transformation. A nonlinearity index that exploits second order Taylor expansions and polynomial bounding techniques is first…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
We present a supervised dimensionality reduction technique called Convex Linear Discriminant Analysis (ConvexLDA). The proposed model optimizes a multi-objective cost function by balancing two complementary terms. The first term pulls the…
In this paper, we propose two new algorithms for transduction with Matrix Completion (MC) problem. The joint MC and prediction tasks are addressed simultaneously to enhance the accuracy, i.e., the label matrix is concatenated to the data…
We study the singularity probability of n*n random matrices with i.i.d. entries from highly biased discrete distributions. We obtain sharp non-asymptotic bounds for this probability and derive estimates on the least singular values. Our…
Data sets in the form of binary matrices are ubiquitous across scientific domains, and researchers are often interested in identifying and quantifying noteworthy structure. One approach is to compare the observed data to that which might be…
We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With $O(r^3 \kappa^2 n \log n)$ random…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…
This paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces. This generalizes the standard low-rank matrix completion…
This study is concerned with the problem of partial state estimation for linear time-invariant (LTI) distributed state-space systems. A necessary and sufficient condition is established in terms of a simple rank criterion involving the…
Dimension reduction plays a pivotal role in analysing high-dimensional data. However, observations with missing values present serious difficulties in directly applying standard dimension reduction techniques. As a large number of dimension…
Researchers and practitioners operating on a limited budget face the cost-performance trade-off dilemma. The challenging decision often centers on whether to use a large LLM with better performance or a smaller one with reduced costs. This…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
An iterative algorithm is adopted to construct approximate representations of matrices describing the scattering properties of arbitrary objects. The method is based on the implicit evaluation of scattering responses from iteratively…
Randomized algorithms in numerical linear algebra can be fast, scalable and robust. This paper examines the effect of sketching on the right singular vectors corresponding to the smallest singular values of a tall-skinny matrix. We analyze…
Autonomous motion planning is challenging in multi-obstacle environments due to nonconvex collision avoidance constraints. Directly applying numerical solvers to these nonconvex formulations fails to exploit the constraint structures,…
The missing data problem has been broadly studied in the last few decades and has various applications in different areas such as statistics or bioinformatics. Even though many methods have been developed to tackle this challenge, most of…