Optimal Transport for Machine Learners
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important tool in machine learning, especially for designing and evaluating generative models. These course notes cover the fundamental mathematical aspects of OT, including the Monge and Kantorovich formulations, Brenier's theorem, the dual and dynamic formulations, the Bures metric on Gaussian distributions, and gradient flows. It also introduces numerical methods such as linear programming, semi-discrete solvers, and entropic regularization. Applications in machine learning include topics like training neural networks via gradient flows, token dynamics in transformers, and the structure of GANs and diffusion models. These notes focus primarily on mathematical content rather than deep learning techniques.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Using Machine Teaching to Identify Optimal Training-Set Attacks on Machine Learners
We investigate a problem at the intersection of machine learning and security: training-set attacks on machine learners. In such attacks an attacker contaminates the training data so that a specific learning algorithm wo…
Bilevel OptimizationregressionRecent Advances in Optimal Transport for Machine Learning
Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new …
reinforcement-learningTransfer LearningThe Teaching Dimension of Linear Learners
Teaching dimension is a learning theoretic quantity that specifies the minimum training set size to teach a target model to a learner. Previous studies on teaching dimension focused on version-space learners which mainta…
regressionTeaching to Learn: Sequential Teaching of Agents with Inner States
In sequential machine teaching, a teacher's objective is to provide the optimal sequence of inputs to sequential learners in order to guide them towards the best model. In this paper we extend this setting from current s…
Meta-LearningRobust Generalization with Adaptive Optimal Transport Priors for Decision-Focused Learning
Few-shot learning requires models to generalize under limited supervision while remaining robust to distribution shifts. Existing Sinkhorn Distributionally Robust Optimization (DRO) methods provide theoretical guarantees…
Few-Shot Learning