Related papers: A Hitchhiker's Guide to Automatic Differentiation
Anomaly detection (AD) is a task that distinguishes normal and abnormal data, which is important for applying automation technologies of the manufacturing facilities. For MVTec dataset that is a representative AD dataset for industrial…
The alternating direction method of multipliers (ADMM) is a flexible method to solve a large class of convex minimization problems. Particular features are its unconditional convergence with respect to the involved step size and its direct…
Anderson Acceleration (AA) is a popular acceleration technique to enhance the convergence of fixed-point iterations. The analysis of AA approaches typically focuses on the convergence behavior of a corresponding fixed-point residual, while…
Anomaly detection (AD) plays a crucial role in various domains, including cybersecurity, finance, and healthcare, by identifying patterns or events that deviate from normal behaviour. In recent years, significant progress has been made in…
Autodiff refers to the core of the automatic differentiation systems developed in projects like JAX and Dex. Autodiff has recently been formalised in a linear typed calculus by Radul et al in arXiv:2204.10923. Although this formalisation…
Mirror descent uses the mirror function to encode geometry and constraints, improving convergence while preserving feasibility. Accelerated Mirror Descent Methods (Acc-MD) are derived from a discretization of an accelerated mirror ODE…
Phase retrieval is a well known ill-posed inverse problem where one tries to recover images given only the magnitude values of their Fourier transform as input. In recent years, new algorithms based on deep learning have been proposed,…
The alternating direction method of multipliers (ADMM) is an effective method for solving wide fields of convex problems. At each iteration, the classical ADMM solves two subproblems exactly. However, in many applications, it is expensive…
In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain…
Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) can be used to solve convex optimization problems that consist of a sum of two functions. Convergence rate estimates for these algorithms have received…
Despite the great progress of person re-identification (ReID) with the adoption of Convolutional Neural Networks, current ReID models are opaque and only outputs a scalar distance between two persons. There are few methods providing users…
The Forward Search is an iterative algorithm for avoiding outliers in a regression analysis suggested by Hadi and Simonoff (J. Amer. Statist. Assoc. 88 (1993) 1264-1272), see also Atkinson and Riani (Robust Diagnostic Regression Analysis…
We study two procedures (reverse-mode and forward-mode) for computing the gradient of the validation error with respect to the hyperparameters of any iterative learning algorithm such as stochastic gradient descent. These procedures mirror…
This work studies the linear convergence of an accelerated scheme of the Alternating Direction Method of Multipliers (ADMM) for strongly convex and Lipschitz-smooth problems. We use the methodology of expressing the accelerated ADMM as a…
Alternating Directions Implicit (ADI) integration is an operator splitting approach to solve parabolic and elliptic partial differential equations in multiple dimensions based on solving sequentially a set of related one-dimensional…
Black-box explainability methods are popular tools for explaining the decisions of image classifiers. A major drawback of these tools is their reliance on mutants obtained by occluding parts of the input, leading to out-of-distribution…
In this paper we consider from two different aspects the proximal alternating direction method of multipliers (ADMM) in Hilbert spaces. We first consider the application of the proximal ADMM to solve well-posed linearly constrained…
We present a previously unexplored forward-mode differentiation method for Maxwell's equations, with applications in the field of sensitivity analysis. This approach yields exact gradients and is similar to the popular adjoint variable…
In this paper, we propose a new stochastic alternating direction method of multipliers (ADMM) algorithm, which incrementally approximates the full gradient in the linearized ADMM formulation. Besides having a low per-iteration complexity as…
The alternating direction method of multipliers (ADMM) is widely used for solving large-scale semidefinite programs (SDPs), yet on instances with multiple primal-dual optimal solution pairs, it often enters prolonged slow-convergence…