Related papers: Regularized Spatial Maximum Covariance Analysis
Most multivariate outlier detection procedures ignore the spatial dependency of observations, which is present in many real data sets from various application areas. This paper introduces a new outlier detection method that accounts for a…
State-of-the-art methods for solving smooth optimization problems are nonlinear conjugate gradient, low memory BFGS, and Majorize-Minimize (MM) subspace algorithms. The MM subspace algorithm which has been introduced more recently has shown…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a…
In this paper, we focus on the variable selection techniques for a class of semiparametric spatial regression models which allow one to study the effects of explanatory variables in the presence of the spatial information. The spatial…
Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
A polarimetric synthetic aperture radar (PolSAR) system, which uses multiple images acquired with different polarizations in both transmission and reception, has the potential to improve the description and interpretation of the observed…
In optimization routines used for on-line Model Predictive Control (MPC), linear systems of equations are usually solved in each iteration. This is true both for Active Set (AS) methods as well as for Interior Point (IP) methods, and for…
We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…
Dynamic inference problems in autoregressive (AR/ARMA/ARIMA), exponential smoothing, and navigation are often formulated and solved using state-space models (SSM), which allow a range of statistical distributions to inform innovations and…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…
Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…
We propose a general technique for improving alternating optimization (AO) of nonconvex functions. Starting from the solution given by AO, we conduct another sequence of searches over subspaces that are both meaningful to the optimization…
Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can…
We recently developed a new approach to get a stabilized image from a sequence of frames acquired through atmospheric turbulence. The goal of this algorihtm is to remove the geometric distortions due by the atmosphere movements. This method…
Due to spatial dependence -- often characterized as complex and non-linear -- model misspecification is a prevalent and critical issue in spatial data analysis and prediction. As the data, and thus model performance, is heterogeneous,…
A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [11]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic half-space and a slip on…