Related papers: Interaction Hard Thresholding: Consistent Sparse Q…
Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…
In this paper, we present modifications of the iterative hard thresholding (IHT) method for recovery of jointly row-sparse and low-rank matrices. In particular a Riemannian version of IHT is considered which significantly reduces…
We consider the problem of learning a high-dimensional multi-task regression model, under sparsity constraints induced by presence of grouping structures on the input covariates and on the output predictors. This problem is primarily…
We focus on the high-dimensional linear regression problem, where the algorithmic goal is to efficiently infer an unknown feature vector $\beta^*\in\mathbb{R}^p$ from its linear measurements, using a small number $n$ of samples. Unlike most…
The Binary Iterative Hard Thresholding (BIHT) algorithm is a popular reconstruction method for one-bit compressed sensing due to its simplicity and fast empirical convergence. There have been several works about BIHT but a theoretical…
This paper is concerned with the design of algorithms based on systems of interacting particles to represent, approximate, and learn the optimal control law for reinforcement learning (RL). The primary contribution is that convergence rates…
Estimation of a sparse spectral precision matrix, the inverse of a spectral density matrix, is a canonical problem in frequency-domain analysis of high-dimensional time series (HDTS), with applications in neurosciences and environmental…
We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…
Recent work in Deep Learning has re-imagined the representation of data as functions mapping from a coordinate space to an underlying continuous signal. When such functions are approximated by neural networks this introduces a compelling…
In the machine learning era, sparsity continues to attract significant interest due to the benefits it provides to learning models. Algorithms aiming to optimise the \(\ell_0\)- and \(\ell_1\)-norm are the common choices to achieve…
Sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. However, such a problem is difficult to solve since it is NP-hard. Existing solutions are primarily based on convex…
In recent studies on sparse modeling, non-convex penalties have received considerable attentions due to their superiorities on sparsity-inducing over the convex counterparts. Compared with the convex optimization approaches, however, the…
This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank…
Consider a two-class classification problem where the number of features is much larger than the sample size. The features are masked by Gaussian noise with mean zero and covariance matrix $\Sigma$, where the precision matrix…
We study a new linear up to quadratic time algorithm for linear regression in the absence of strong assumptions on the underlying distributions of samples, and in the presence of outliers. The goal is to design a procedure which comes with…
Sparse-reward domains are challenging for reinforcement learning algorithms since significant exploration is needed before encountering reward for the first time. Hierarchical reinforcement learning can facilitate exploration by reducing…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Iterative thresholding algorithms seek to optimize a differentiable objective function over a sparsity or rank constraint by alternating between gradient steps that reduce the objective, and thresholding steps that enforce the constraint.…
The core of a good model is in its ability to focus only on important information that reflects the basic patterns and consistencies, thus pulling out a clear, noise-free signal from the dataset. This necessitates using a simplified model…
In scientific fields such as quantum computing, physics, chemistry, and machine learning, high dimensional data are typically represented using sparse tensors. Tensor contraction is a popular operation on tensors to exploit meaning or alter…