Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization

Model error covariance estimation in particle and ensemble Kalman filters using an online expectation-maximization algorithm

The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are not usually known and have to be inferred. Many approaches have been proposed to tackle this problem, including fully Bayesian, likelihood maximization and innovation-based techniques. This work focuses on maximization of the likelihood function via the expectation-maximization (EM) algorithm to infer the model error covariance combined with ensemble Kalman …

Auto-differentiable Ensemble Kalman Filters

Data assimilation is concerned with sequentially estimating a temporally-evolving state. This task, which arises in a wide range of scientific and engineering applications, is particularly challenging when the state is high-dimensional and the state-space dynamics are unknown. This paper introduces a machine learning framework for learning dynamical systems in data assimilation. Our auto-differentiable ensemble Kalman filters (AD-EnKFs) blend ensemble Kalman filters for state recovery with machine learning tools for learning the dynamics. In doing so, AD-EnKFs leverage the ability of ensemble …

Model uncertainty estimation using the expectation maximization algorithm and a particle flow filter

Model error covariances play a central role in the performance of data assimilation methods applied to nonlinear state-space models. However, these covariances are largely unknown in most of the applications. A misspecification of the model error covariance has a strong impact on the computation of the posterior probability density function, leading to unreliable estimations and even to a total failure of the assimilation procedure. In this work, we propose the combination of the Expectation-Maximization algorithm (EM) with an efficient particle filter to estimate the model error covariance, u…

UCSL : A Machine Learning Expectation-Maximization framework for Unsupervised Clustering driven by Supervised Learning

Subtype Discovery consists in finding interpretable and consistent sub-parts of a dataset, which are also relevant to a certain supervised task. From a mathematical point of view, this can be defined as a clustering task driven by supervised learning in order to uncover subgroups in line with the supervised prediction. In this paper, we propose a general Expectation-Maximization ensemble framework entitled UCSL (Unsupervised Clustering driven by Supervised Learning). Our method is generic, it can integrate any clustering method and can be driven by both binary classification and regression. We…

EM-like Learning Chaotic Dynamics from Noisy and Partial Observations

The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for fully-observed systems, {\em i.e.} large signal-to-noise ratios and high-frequency sampling of all system variables, we here address the learning of data-driven representations of chaotic dynamics for partially-observed systems, including significant noise patterns and possibly lower and irregular sampling setting. Instead of considering training losses based on short-t…

FeDXL：用于深度 X-Risk 优化的可证明联邦学习

FeDXL: Provable Federated Learning for Deep X-Risk Optimization

针对分布式 X-risk 优化中目标不可分解与机器间依赖问题，论文提出主动-被动分解框架及两种可证明的 FeDXL 算法，并验证其在深度 AUROC 任务上的有效性。