Related papers: Estimating Common Principal Components in High Dim…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
We propose a supervised principal component regression method for relating functional responses with high dimensional predictors. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected…
We study a class of optimization problems in which the objective function is given by the sum of a differentiable but possibly nonconvex component and a nondifferentiable convex regularization term. We introduce an auxiliary variable to…
In this paper, we study the problem of decomposing a superposition of a low-rank matrix and a sparse matrix when a relatively few linear measurements are available. This problem arises in many data processing tasks such as aligning multiple…
With the growth of model and data sizes, a broad effort has been made to design pruning techniques that reduce the resource demand of deep learning pipelines, while retaining model performance. In order to reduce both inference and training…
Complexity of the Operations Research Theory tasks can be often diminished in cases that do not require finding the exact solution. For example, forecasting two-dimensional hierarchical time series leads us to the transportation problem…
In this paper we analyze different ways of performing principal component analysis throughout three different approaches: robust covariance and correlation matrix estimation, projection pursuit approach and non-parametric maximum entropy…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…
Multitask learning, i.e. taking advantage of the relatedness of individual tasks in order to improve performance on all of them, is a core challenge in the field of machine learning. We focus on matrix regression tasks where the rank of the…
In this paper, we derive a randomized version of the Mirror-Prox method for solving some structured matrix saddle-point problems, such as the maximal eigenvalue minimization problem. Deterministic first-order schemes, such as Nesterov's…
Despite the prominence of neural network approaches in the field of recommender systems, simple methods such as matrix factorization with quadratic loss are still used in industry for several reasons. These models can be trained with…
In the non-negative matrix factorization (NMF) problem, the input is an $m\times n$ matrix $M$ with non-negative entries and the goal is to factorize it as $M\approx AW$. The $m\times k$ matrix $A$ and the $k\times n$ matrix $W$ are both…
A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
We analyze the consensus based optimization method proposed by Pinnau et al.(2017) in one dimension. We rigorously provide a quantitative error estimate between the consensus point and global minimizer of a given objective function. Our…
Dimension reduction techniques for multivariate time series decompose the observed series into a few useful independent/orthogonal univariate components. We develop a spectral domain method for multivariate second-order stationary time…