Related papers: Stable Recovery Of Sparse Vectors From Random Sinu…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
This paper considers reconstructing a spectrally sparse signal from a small number of randomly observed time-domain samples. The signal of interest is a linear combination of complex sinusoids at $R$ distinct frequencies. The frequencies…
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…
For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…
Inverse inference, or "brain reading", is a recent paradigm for analyzing functional magnetic resonance imaging (fMRI) data, based on pattern recognition and statistical learning. By predicting some cognitive variables related to brain…
In this paper, we provide a general methodology to draw statistical inferences on individual signal coordinates or linear combinations of them in sparse phase retrieval. Given an initial estimator for the targeting parameter (some simple…
We present a pursuit-like algorithm that we call the "superset method" for recovery of sparse vectors from consecutive Fourier measurements in the super-resolution regime. The algorithm has a subspace identification step that hinges on the…
We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…
We propose a pivotal method for estimating high-dimensional sparse linear regression models, where the overall number of regressors $p$ is large, possibly much larger than $n$, but only $s$ regressors are significant. The method is a…
A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…
We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…
Sparse regression and variable selection for large-scale data have been rapidly developed in the past decades. This work focuses on sparse ridge regression, which enforces the sparsity by use of the L0 norm. We first prove that the…
Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…
In the Network Inference problem, one seeks to recover the edges of an unknown graph from the observations of cascades propagating over this graph. In this paper, we approach this problem from the sparse recovery perspective. We introduce a…
In presence of sparse noise we propose kernel regression for predicting output vectors which are smooth over a given graph. Sparse noise models the training outputs being corrupted either with missing samples or large perturbations. The…
A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…
We examine in this paper the problem of image registration from the new perspective where images are given by sparse approximations in parametric dictionaries of geometric functions. We propose a registration algorithm that looks for an…
Big data has become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt…
In this paper, we study the problem of sparse mixed linear regression on an unlabeled dataset that is generated from linear measurements from two different regression parameter vectors. Since the data is unlabeled, our task is not only to…