Related papers: Block-adaptive Cross Approximation of Discrete Int…
In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
In this paper, we propose the inexact alternating minimization algorithm (inexact AMA), which allows inexact iterations in the algorithm, and its accelerated variant, called the inexact fast alternating minimization algorithm (inexact…
This paper proposes scalable and fast algorithms for solving the Robust PCA problem, namely recovering a low-rank matrix with an unknown fraction of its entries being arbitrarily corrupted. This problem arises in many applications, such as…
Block-coordinate descent algorithms and alternating minimization methods are fundamental optimization algorithms and an important primitive in large-scale optimization and machine learning. While various block-coordinate-descent-type…
Adaptive cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems involving a shifted Hessian in the spirit of the Levenberg-Marquardt and trust-region methods. The standard approach consists in…
This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block structured hierarchical…
We present Accelerated Cyclic Reduction (ACR), a distributed-memory fast direct solver for rank-compressible block tridiagonal linear systems arising from the discretization of elliptic operators, developed here for three dimensions.…
We present a novel matrix-parametrized frugal splitting algorithm which finds the zero of a sum of maximal monotone and cocoercive operators composed with linear selection operators. We also develop a semidefinite programming framework for…
Block Coordinate Update (BCU) methods enjoy low per-update computational complexity because every time only one or a few block variables would need to be updated among possibly a large number of blocks. They are also easily parallelized and…
Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and…
We consider a mixed analog-to-digital converter (ADC) based architecture for direction of arrival (DOA) estimation using a uniform linear array (ULA). We derive the Cram{\'e}r-Rao bound (CRB) of the DOA under the optimal time-varying…
We introduce an extension of the Difference of Convex Algorithm (DCA) in the form of a randomized block coordinate approach for problems with separable structure. For $n$ coordinate-blocks and $k$ iterations, our main result proves a…
The accelerated proximal point algorithm (APPA), also known as "Catalyst", is a well-established reduction from convex optimization to approximate proximal point computation (i.e., regularized minimization). This reduction is conceptually…
Algorithms that promise to leverage resources of quantum computers efficiently to accelerate the finite element method have emerged. However, the finite element method is usually incorporated into a high-level numerical scheme which allows…
Neural operators have achieved promising performance on partial differential equations (PDEs), but most existing models are built on fixed Eulerian coordinates. This mismatch between evolving physical structures and static coordinates…
Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often…
Block coordinate descent is an optimization paradigm that iteratively updates one block of variables at a time, making it quite amenable to big data applications due to its scalability and performance. Its convergence behavior has been…
In this paper, we modify the adaptive cubic regularization method for large-scale unconstrained optimization problem by using a real positive definite scalar matrix to approximate the exact Hessian. Combining with the nonmonotone technique,…
Accurate value estimates are important for off-policy reinforcement learning. Algorithms based on temporal difference learning typically are prone to an over- or underestimation bias building up over time. In this paper, we propose a…