Related papers: Automatic Backward Differentiation for American Mo…
Automatic differentiation---the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately---dates to the origin of the computer age. Reverse mode automatic differentiation both antedates and…
This article provides an overview of some of the mathematical principles of Automatic Differentiation (AD). In particular, we summarise different descriptions of the Forward Mode of AD, like the matrix-vector product based approach, the…
In this paper, we present a method for the accurate estimation of the derivative (aka.~sensitivity) of expectations of functions involving an indicator function by combining a stochastic algorithmic differentiation and a regression. The…
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…
Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…
Automatic differentiation, also known as backpropagation, AD, autodiff, or algorithmic differentiation, is a popular technique for computing derivatives of computer programs accurately and efficiently. Sometimes, however, the derivatives…
Monte Carlo methods represent a cornerstone of computer science. They allow to sample high dimensional distribution functions in an efficient way. In this paper we consider the extension of Automatic Differentiation (AD) techniques to Monte…
In this paper we take a look at Automatic Differentiation through the eyes of Tensor and Operational Calculus. This work is best consumed as supplementary material for learning tensor and operational calculus by those already familiar with…
Recent theoretical work on automatic differentiation (autodiff) has focused on characteristics such as correctness and efficiency while assuming that all derivatives are automatically generated by autodiff using program transformation, with…
Automatic differentiation (AD) in reverse mode (RAD) is a central component of deep learning and other uses of large-scale optimization. Commonly used RAD algorithms such as backpropagation, however, are complex and stateful, hindering deep…
Automatic differentiation is involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic…
En este trabajo se presenta una propuesta para realizar Diferenciaci\'on Autom\'atica Anidada utilizando cualquier biblioteca de Diferenciaci\'on Autom\'atica que permita sobrecarga de operadores. Para calcular las derivadas anidadas en una…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
En este trabajo se presenta una propuesta para realizar Diferenciaci\'on Autom\'atica Anidada utilizando cualquier biblioteca de Diferenciaci\'on Autom\'atica que permita sobrecarga de operadores. Para calcular las derivadas anidadas en una…
Automatic differentiation (AD) is a technique for computing the derivative of a function represented by a program. This technique is considered as the de-facto standard for computing the differentiation in many machine learning and…
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…
Various software efforts embrace the idea that object oriented programming enables a convenient implementation of the chain rule, facilitating so-called automatic differentiation via backpropagation. Such frameworks have no mechanism for…
Automatic differentiation (AD) has driven recent advances in machine learning, including deep neural networks and Hamiltonian Markov Chain Monte Carlo methods. Partially observed nonlinear stochastic dynamical systems have proved resistant…
We propose and study a weakly convergent variant of the forward--backward algorithm for solving structured monotone inclusion problems. Our algorithm features a per-iteration deviation vector which provides additional degrees of freedom.…
Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic…