7 papers
Learning Probabilistic Filters with Strictly Proper Scoring Rules
Eviatar Bach, Ricardo Baptista, Jochen Bröcker +2
Bayesian filtering of partially and noisily observed dynamical systems seeks to infer the evolving conditional distribution of the state of a dynamical system, given observations,…
Quantitative Wasserstein Propagation of Chaos for Transport Ensemble Filters
Frederic J. N. Jorgensen, Ricardo Baptista, Franca Hoffmann +1
We develop a general probabilistic framework for analyzing propagation of chaos in transport ensemble filters (TEFs), a broad class of interacting particle systems that are used to…
Large Language Models: A Mathematical Formulation
Ricardo Baptista, Andrew Stuart, Son Tran
Large language models (LLMs) process and predict sequences containing text to answer questions, and address tasks including document summarization, providing recommendations, writi…
Learning Enhanced Ensemble Filters
Eviatar Bach, Ricardo Baptista, Edoardo Calvello +2
The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state-observation space. The ensemble Kalman filter (EnKF) approximates thi…
Machine Learning for Inverse Problems and Data Assimilation
Eviatar Bach, Ricardo Baptista, Daniel Sanz-Alonso +1
The aim of this book is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is…
A Mathematical Perspective On Contrastive Learning
Ricardo Baptista, Andrew M. Stuart, Son Tran
Multimodal contrastive learning is a methodology for linking different data modalities; the canonical example is linking image and text data. The methodology is typically framed as…