Related papers: Empirical sparse regression on quadratic manifolds
Generative graph models struggle to scale due to the need to predict the existence or type of edges between all node pairs. To address the resulting quadratic complexity, existing scalable models often impose restrictive assumptions such as…
Non-negative signals form an important class of sparse signals. Many algorithms have already beenproposed to recover such non-negative representations, where greedy and convex relaxed algorithms are among the most popular methods. The…
We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may…
Accurate and concise governing equations are crucial for understanding system dynamics. Recently, data-driven methods such as sparse regression have been employed to automatically uncover governing equations from data, representing a…
We propose a new \textit{quadratic programming-based} method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying…
In this document, we present key findings in structured matrix approximation theory, with applications to the regressive representation of dynamic financial processes. Initially, we explore a comprehensive approach involving generic…
Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies.…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…
We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…
In this paper we develop a novel approach for estimating large and sparse dynamic factor models using variational inference, also allowing for missing data. Inspired by Bayesian variable selection, we apply slab-and-spike priors onto the…
We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of the sparse Poisson regression model. To provide approximate conjugacy in the model, the likelihood is approximated by a quadratic function, yielding…
Although various distributed machine learning schemes have been proposed recently for pure linear models and fully nonparametric models, little attention has been paid on distributed optimization for semi-paramemetric models with…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…
We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…
Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address…