Variational And Information Flows In Machine Learning And Optimal Transport
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Variational and Information Flows in Machine Learning and Optimal Transport
This book is based on lectures given at the Mathematisches Forschungsinstitut Oberwolfach on “Computational Variational Flows in Machine Learning and Optimal Transport”. Variational and stochastic flows on measure spaces are ubiquitous in machine learning and generative modeling. Optimal transport and diffeomorphic flows provide powerful frameworks to analyze such trajectories of distributions with elegant notions from differential geometry, such as geodesics, gradient and Hamiltonian flows. Recently, mean field control and mean field games offered a general optimal control variational view on learning problems. The four independent chapters in this book address the question of how the presented tools lead us to better understanding and further development of machine learning and generative models.
Variational and Information Flows in Machine Learning and Optimal Transport
This book is based on lectures given at the Mathematisches Forschungsinstitut Oberwolfach on “Computational Variational Flows in Machine Learning and Optimal Transport”. Variational and stochastic flows on measure spaces are ubiquitous in machine learning and generative modeling. Optimal transport and diffeomorphic flows provide powerful frameworks to analyze such trajectories of distributions with elegant notions from differential geometry, such as geodesics, gradient and Hamiltonian flows. Recently, mean field control and mean field games offered a general optimal control variational view on learning problems. The four independent chapters in this book address the question of how the presented tools lead us to better understanding and further development of machine learning and generative models.
Information Bottleneck
The celebrated information bottleneck (IB) principle of Tishby et al. has recently enjoyed renewed attention due to its application in the area of deep learning. This collection investigates the IB principle in this new context. The individual chapters in this collection: • provide novel insights into the functional properties of the IB; • discuss the IB principle (and its derivates) as an objective for training multi-layer machine learning structures such as neural networks and decision trees; and • offer a new perspective on neural network learning via the lens of the IB framework. Our collection thus contributes to a better understanding of the IB principle specifically for deep learning and, more generally, of information–theoretic cost functions in machine learning. This paves the way toward explainable artificial intelligence.