Related papers: Generalized Conditional Gradient for Sparse Estima…
We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…
Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…
This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly off-the-diagonal and $L^q$-sparse operators with an…
We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…
When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…
In this work, we extend the sparse iterative covariance-based estimator (SPICE), by generalizing the formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. For a given norm, the…
The pathwise coordinate optimization is one of the most important computational frameworks for high dimensional convex and nonconvex sparse learning problems. It differs from the classical coordinate optimization algorithms in three salient…
This paper addresses the challenge of reconstructing full-field structural mode shapes from sparse sensor data. While Gaussian Process Regression (GPR) offers a robust non-parametric framework for spatial interpolation and uncertainty…
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…
Convolutional sparse representation (CSR), shift-invariant model for inverse problems, has gained much attention in the fields of signal/image processing, machine learning and computer vision. The most challenging problems in CSR implies…
Developing suitable approximate models for analyzing and simulating complex nonlinear systems is practically important. This paper aims at exploring the skill of a rich class of nonlinear stochastic models, known as the conditional Gaussian…
Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…
In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized…
We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…
Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…
We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…
Cooperative online scalar field mapping is an important task for multi-robot systems. Gaussian process regression is widely used to construct a map that represents spatial information with confidence intervals. However, it is difficult to…
Systematic Generalization refers to a learning algorithm's ability to extrapolate learned behavior to unseen situations that are distinct but semantically similar to its training data. As shown in recent work, state-of-the-art deep learning…
In this paper, we estimate the high dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We revisit the sparse column-wise inverse operator (SCIO) estimator \cite{liu2015fast} and derive its…
We propose a new fast algorithm to estimate any sparse generalized linear model with convex or non-convex separable penalties. Our algorithm is able to solve problems with millions of samples and features in seconds, by relying on…