12 papers
One-Shot Generative Flows: Existence and Obstructions
Panos Tsimpos, Daniel Sharp, Youssef Marzouk
We study dynamic measure transport for generative modeling, focusing on transport maps that connect a source measure to a target measure by integrating a velocity field…
Weighted quantization using MMD: From mean field to mean shift via gradient flows
Ayoub Belhadji, Daniel Sharp, Youssef Marzouk
Approximating a probability distribution using a set of particles is a fundamental problem in machine learning and statistics, with applications including clustering and quantizati…
Data Curation for Machine Learning Interatomic Potentials by Determinantal Point Processes
Joanna Zou, Youssef Marzouk
The development of machine learning interatomic potentials faces a critical computational bottleneck with the generation and labeling of useful training datasets. We present a nove…
Generative Modeling through Koopman Spectral Analysis: An Operator-Theoretic Perspective
Yuanchao Xu, Fengyi Li, Masahiro Fujisawa +3
We propose Koopman Spectral Wasserstein Gradient Descent (KSWGD), a particle-based generative modeling framework that learns the Langevin generator via Koopman theory and integrate…
Conformal Prediction for Generative Models via Adaptive Cluster-Based Density Estimation
Qidong Yang, Qianyu Julie Zhu, Jonathan Giezendanner +3
Conditional generative models map input variables to complex, high-dimensional distributions, enabling realistic sample generation in a diverse set of domains. A critical challenge…
Sharp detection of low-dimensional structure in probability measures via dimensional logarithmic Sobolev inequalities
Matthew T. C. Li, Tiangang Cui, Fengyi Li +2
Identifying low-dimensional structure in high-dimensional probability measures is an essential pre-processing step for efficient sampling. We introduce a method for identifying and…