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Numerical optimization is a work horse of machine learning that often requires the derivation and computation of gradients and Hessians. For learning problem that are modeled by some loss or likelihood function, the gradients and Hessians are typically derived manually, which is a time consuming and error prone process. Computing gradients (and Hessians) is also an integral part of deep learning frameworks that mostly employ automatic differentiation, aka algorithmic differentiation (typically in reverse mode). At www.MatrixCalculus.org we provide a tool for symbolically computing gradients and Hessians that can be used in the classical setting of loss and likelihood functions, for constrained optimization, but also for deep learning.
Author Information
Sören Laue (Universitaet Jena)
Matthias Mitterreiter (Friedrich Schiller University Jena)
Joachim Giesen (Friedrich-Schiller-Universitat Jena)
More from the Same Authors
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2022 Poster: Convexity Certificates from Hessians »
Julien Klaus · Niklas Merk · Konstantin Wiedom · Sören Laue · Joachim Giesen -
2019 : Posters and Coffee »
Sameer Kumar · Tomasz Kornuta · Oleg Bakhteev · Hui Guan · Xiaomeng Dong · Minsik Cho · Sören Laue · Theodoros Vasiloudis · Andreea Anghel · Erik Wijmans · Zeyuan Shang · Oleksii Kuchaiev · Ji Lin · Susan Zhang · Ligeng Zhu · Beidi Chen · Vinu Joseph · Jialin Ding · Jonathan Raiman · Ahnjae Shin · Vithursan Thangarasa · Anush Sankaran · Akhil Mathur · Martino Dazzi · Markus Löning · Darryl Ho · Emanuel Zgraggen · Supun Nakandala · Tomasz Kornuta · Rita Kuznetsova -
2019 Poster: GENO -- GENeric Optimization for Classical Machine Learning »
Sören Laue · Matthias Mitterreiter · Joachim Giesen -
2019 Demonstration: GENO -- Optimization for Classical Machine Learning Made Fast and Easy »
Sören Laue · Matthias Mitterreiter · Joachim Giesen -
2018 Poster: Computing Higher Order Derivatives of Matrix and Tensor Expressions »
Sören Laue · Matthias Mitterreiter · Joachim Giesen -
2012 Poster: Approximating Concavely Parameterized Optimization Problems »
Joachim Giesen · Jens K Mueller · Sören Laue · Sascha Swiercy -
2012 Oral: Approximating Concavely Parameterized Optimization Problems »
Joachim Giesen · Jens K Mueller · Sören Laue · Sascha Swiercy