Related papers: Effective Dimension Adaptive Sketching Methods for…

In this paper, we study a fast approximation method for {\it large-scale high-dimensional} sparse least-squares regression problem by exploiting the Johnson-Lindenstrauss (JL) transforms, which embed a set of high-dimensional vectors into a…

Stochastic optimisation problems minimise expectations of random cost functions. We use 'optimise then discretise' method to solve stochastic optimisation. In our approach, accurate quadrature methods are required to calculate the…

We present iDARR, a scalable iterative Data-Adaptive RKHS Regularization method, for solving ill-posed linear inverse problems. The method searches for solutions in subspaces where the true solution can be identified, with the data-adaptive…

We consider the bound-constrained global optimization of functions with low effective dimensionality, that are constant along an (unknown) linear subspace and only vary over the effective (complement) subspace. We aim to implicitly explore…

This paper addresses the optimization problem of minimizing non-convex continuous functions, which is relevant in the context of high-dimensional machine learning applications characterized by over-parametrization. We analyze a randomized…

High-fidelity 3D reconstruction of common indoor scenes is crucial for VR and AR applications. 3D Gaussian splatting, a novel differentiable rendering technique, has achieved state-of-the-art novel view synthesis results with high rendering…

We present a random-subspace variant of cubic regularization algorithm that chooses the size of the subspace adaptively, based on the rank of the projected second derivative matrix. Iteratively, our variant only requires access to…

In this paper, we develop a new accelerated stochastic gradient method for efficiently solving the convex regularized empirical risk minimization problem in mini-batch settings. The use of mini-batches is becoming a golden standard in the…

3D reconstruction from multi-view images is one of the fundamental challenges in computer vision and graphics. Recently, 3D Gaussian Splatting (3DGS) has emerged as a promising technique capable of real-time rendering with high-quality 3D…

Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…

Sketching is a probabilistic data compression technique that has been largely developed in the computer science community. Numerical operations on big datasets can be intolerably slow; sketching algorithms address this issue by generating a…

Stochastic gradient descent is a canonical tool for addressing stochastic optimization problems, and forms the bedrock of modern machine learning and statistics. In this work, we seek to balance the fact that attenuating step-size is…

We consider stochastic variational inequality problems where the mapping is monotone over a compact convex set. We present two robust variants of stochastic extragradient algorithms for solving such problems. Of these, the first scheme…

We investigate the unconstrained global optimization of functions with low effective dimensionality, that are constant along certain (unknown) linear subspaces. Extending the technique of random subspace embeddings in [Wang et al., Bayesian…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…

We consider distributed optimization problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We develop unbiased parameter averaging methods for randomized second order optimization…

We study the problem of residual error estimation for matrix and vector norms using a linear sketch. Such estimates can be used, for example, to quickly assess how useful a more expensive low-rank approximation computation will be. The…

In this work, we propose an efficient two-metric adaptive projection method for solving the $\ell_1$-norm minimization problem. Our approach is inspired by the two-metric projection method, a simple yet elegant algorithm proposed by…

In this paper, we present GASG21 (Grassmannian Adaptive Stochastic Gradient for $L_{2,1}$ norm minimization), an adaptive stochastic gradient algorithm to robustly recover the low-rank subspace from a large matrix. In the presence of column…

We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…