Related papers: Random projections: data perturbation for classifi…

In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…

We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are…

For classification problems, feature extraction is a crucial process which aims to find a suitable data representation that increases the performance of the machine learning algorithm. According to the curse of dimensionality theorem, the…

With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…

Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…

We develop a randomized Newton method capable of solving learning problems with huge dimensional feature spaces, which is a common setting in applications such as medical imaging, genomics and seismology. Our method leverages randomized…

Ptychography is a popular technique to achieve diffraction limited resolution images of a two or three dimensional sample using high frame rate detectors. We introduce a relaxation of common projection algorithms to account for…

We analyze a random projection method for adjacency matrices, studying its utility in representing sparse graphs. We show that these random projections retain the functionality of their underlying adjacency matrices while having extra…

Random Projection (RP) technique has been widely applied in many scenarios because it can reduce high-dimensional features into low-dimensional space within short time and meet the need of real-time analysis of massive data. There is an…

A random vector whose norm and overlap (inner product with an independent copy) concentrates is shown to have random low-dimensional projections that are approximately random Gaussians. Conversely, asymptotically random Gaussian projections…

Classical extragradient schemes and their stochastic counterpart represent a cornerstone for resolving monotone variational inequality problems. Yet, such schemes have a per-iteration complexity of two projections onto a convex set and…

We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…

Machine learning techniques always aim to reduce the generalized prediction error. In order to reduce it, ensemble methods present a good approach combining several models that results in a greater forecasting capacity. The Random Machines…

In this work we collect and compare to each other many different numerical methods for regularized regression problem and for the problem of projection on a hyperplane. Such problems arise, for example, as a subproblem of demand matrix…

The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of…

Sketching techniques have become popular for scaling up machine learning algorithms by reducing the sample size or dimensionality of massive data sets, while still maintaining the statistical power of big data. In this paper, we study…

In these notes we discuss tools and concepts that emerge when studying high-dimensional random landscapes, i.e., random functions on high-dimensional spaces. As an illustrative example, we consider an inference problem in two forms:…

Taking projections of high-dimensional data is a common analytical and visualisation technique in statistics for working with high-dimensional problems. Sectioning, or slicing, through high dimensions is less common, but can be useful for…

Joint sparsity offers powerful structural cues for feature selection, especially for variables that are expected to demonstrate a "grouped" behavior. Such behavior is commonly modeled via group-lasso, multitask lasso, and related methods…