Related papers: Covariance Operator Estimation: Sparsity, Lengthsc…
We develop new stochastic gradient methods for efficiently solving sparse linear regression in a partial attribute observation setting, where learners are only allowed to observe a fixed number of actively chosen attributes per example at…
We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using…
We consider the problem of selecting an optimal set of sensor precisions to estimate the states of a non-linear dynamical system using an Ensemble Kalman filter and an Unscented Kalman filter, which uses random and deterministic ensembles…
In this work, we consider a sensor selection drawn at random by a sampling with replacement policy for a linear time-invariant dynamical system subject to process and measurement noise. We employ the Kalman filter to estimate the state of…
Contemporary data assimilation often involves millions of prediction variables. The classical Kalman filter is no longer computationally feasible in such a high dimensional context. This problem can often be resolved by exploiting the…
The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…
The sample covariance matrix of a random vector is a good estimate of the true covariance matrix if the sample size is much larger than the length of the vector. In high-dimensional problems, this condition is never met. As a result, in…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
We consider a class of Cox models with time-dependent effects that may be zero over certain unknown time regions or, in short, sparse time-varying effects. The model is particularly useful for biomedical studies as it conveniently depicts…
Repeated measurements are common in many fields, where random variables are observed repeatedly across different subjects. Such data have an underlying hierarchical structure, and it is of interest to learn covariance/correlation at…
The theory of Koopman operators allows to deploy non-parametric machine learning algorithms to predict and analyze complex dynamical systems. Estimators such as principal component regression (PCR) or reduced rank regression (RRR) in kernel…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
Covariance estimation is essential yet underdeveloped for analyzing multivariate functional data. We propose a fast covariance estimation method for multivariate sparse functional data using bivariate penalized splines. The tensor-product…
This paper is concerned with the hard thresholding operator which sets all but the $k$ largest absolute elements of a vector to zero. We establish a {\em tight} bound to quantitatively characterize the deviation of the thresholded solution…
Sparsity constraints on the control inputs of a linear dynamical system naturally arise in several practical applications such as networked control, computer vision, seismic signal processing, and cyber-physical systems. In this work, we…
In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a high-dimensional setting under the assumption that the…
Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…
The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, and non-intrusive nature makes the method appealing in various…
Covariance estimation becomes challenging in the regime where the number p of variables outstrips the number n of samples available to construct the estimate. One way to circumvent this problem is to assume that the covariance matrix is…
This work presents a new variation of the commonly used Least Mean Squares Algorithm (LMS) for the identification of sparse signals with an a-priori known sparsity using a hard threshold operator in every iteration. It examines some useful…