6 papers
TrIM: Transformed Iterative Mondrian Forests for Gradient-based Dimension Reduction and High-Dimensional Regression
Ricardo Baptista, Eliza O'Reilly, Yangxinyu Xie
We propose a computationally efficient algorithm for gradient-based linear dimension reduction and high-dimensional regression. The algorithm initially computes a Mondrian forest a…
Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting the dots
Théo Bourdais, Pau Batlle, Xianjin Yang +3
Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown f…
Proximal optimal transport divergences
Ricardo Baptista, Panagiota Birmpa, Markos A. Katsoulakis +2
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal…
Neural Approximate Mirror Maps for Constrained Diffusion Models
Berthy T. Feng, Ricardo Baptista, Katherine L. Bouman
Diffusion models excel at creating visually-convincing images, but they often struggle to meet subtle constraints inherent in the training data. Such constraints could be physics-b…
Memorization and Regularization in Generative Diffusion Models
Ricardo Baptista, Agnimitra Dasgupta, Nikola B. Kovachki +2
Diffusion models have emerged as a powerful framework for generative modeling. At the heart of the methodology is score matching: learning gradients of families of log-densities fo…
Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks
Ricardo Baptista, Edoardo Calvello, Matthieu Darcy +3
We consider the use of Gaussian Processes (GPs) or Neural Networks (NNs) to numerically approximate the solutions to nonlinear partial differential equations (PDEs) with rough forc…