Title: | Differential Equations for Machine Learning |
Author(s): | Yıldız, Çağatay |
Date: | 2022 |
Language: | en |
Pages: | 106 + app. 82 |
Department: | Tietotekniikan laitos Department of Computer Science |
ISBN: | 978-952-64-0666-4 (electronic) 978-952-64-0665-7 (printed) |
Series: | Aalto University publication series DOCTORAL THESES, 7/2022 |
ISSN: | 1799-4942 (electronic) 1799-4934 (printed) 1799-4934 (ISSN-L) |
Supervising professor(s): | Lähdesmäki, Harri, Prof., Aalto University, Department of Computer Science, Finland |
Thesis advisor(s): | Lähdesmäki, Harri, Prof., Aalto University, Finland; Heinonen, Markus, Dr., Aalto University, Finland |
Subject: | Computer science |
Keywords: | machine learning, differential equations, neural networks, Gaussian processes |
Archive | yes |
|
|
Abstract:Mechanistic models express novel hypotheses for an observed phenomenon by constructing mathematical formulations of causal mechanisms. As opposed to this modeling paradigm, machine learning approaches learn input-output mappings by complicated and often non-interpretable models. While requiring large chunks of data for successful training and downstream performance,the resulting models can come with universal approximation guarantees. Historically, differential equations (DEs) developed in physics, economics, engineering, and numerous other fields have relied on the principles of mechanistic modeling. Despite providing causality and interpretability that machine learning approaches usually lack, mechanistic differential equation models tend tocarry oversimplified assumptions. In this dissertation, we aim to bring these two worlds together by demonstrating how machine learning problems can be tackled by means of differential equations, and how differential equation models can benefit from modern machine learning tools.
|
|
Description:Defence is held on 18.2.2022 12:15 – 16:15
|
|
Parts:[Publication 1]: Markus Heinonen, Çagatay Yıldız, Henrik Mannerström, Jukka Intosalmi, Harri Lähdesmäki. Learning Unknown ODE Models with Gaussian Processes. In International Conference on Machine Learning, Stockholm, pages 1959–1968, vol.80, July 2018. Full text in Acris/Aaltodoc: http://urn.fi/URN:NBN:fi:aalto-201907304456. [Publication 2]: Çagatay Yıldız, Markus Heinonen, Jukka Intosalmi, Henrik Mannerström, Harri Lähdesmäki. Learning Stochastic Differential Equations with Gaussian Processes without Gradient Matching. In 2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP), Aalborg, September 2018. DOI: 10.1109/MLSP.2018.8516991 View at Publisher [Publication 3]: Çagatay Yıldız, Markus Heinonen, Harri Lähdesmäki. ODE2VAE: Deep Generative Second Order ODEs with Bayesian Neural Networks. In Neural Information Processing Systems, Vancouver, pages 13412–13421, vol.32, December 2019[Publication 4]: Umut Simsekli, Çagatay Yıldız, Than Huy Nguyen, Taylan Cemgil and Gael Richard. Asynchronous Stochastic Quasi-Newton MCMC for Non-Convex Optimization. In International Conference on Machine Learning, Stockholm, pages 4674–4683, vol.80, July 2018. Full ext in Acris/Aaltodoc: http://urn.fi/URN:NBN:fi:aalto-201907304448. [Publication 5]: Çagatay Yıldız, Markus Heinonen, Harri Lähdesmäki. Continuous-Time Model-Based Reinforcement Learning. In International Conference on Machine Learning, Virtual, pages 12009–12018, vol.139, July 2021. Full text in Acris/Aaltodoc: http://urn.fi/URN:NBN:fi:aalto-202108258419. |
|
|
Unless otherwise stated, all rights belong to the author. You may download, display and print this publication for Your own personal use. Commercial use is prohibited.
Page content by: Aalto University Learning Centre | Privacy policy of the service | About this site