相关论文: A Data-Consistent Approach to Ensemble Filtering

In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in…

Critical decisions frequently rely on high-dimensional output from complex computer simulation models that show intricate cross-variable, spatial and temporal dependence structures, with weather and climate predictions being key examples.…

This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter,…

Integrable differential identities, together with ensemble-specific initial conditions, provide an effective approach for the characterisation of relevant observables and state functions in random matrix theory. We develop this approach for…

This paper presents a novel probabilistic forecasting method called ensemble conformalized quantile regression (EnCQR). EnCQR constructs distribution-free and approximately marginally valid prediction intervals (PIs), which are suitable for…

Decomposing prediction uncertainty into aleatoric (irreducible) and epistemic (reducible) components is critical for the reliable deployment of machine learning systems. While the mutual information between the response variable and model…

Ensemble learning is a classical learning method utilizing a group of weak learners to form a strong learner, which aims to increase the accuracy of the model. Recently, brain-inspired hyperdimensional computing (HDC) becomes an emerging…

The ensemble Gaussian mixture filter combines the simplicity and power of Gaussian mixture models with the provable convergence and power of particle filters. The quality of the ensemble Gaussian mixture filter heavily depends on the choice…

A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…

Many real-world problems require one to estimate parameters of interest, in a Bayesian framework, from data that are collected sequentially in time. Conventional methods for sampling from posterior distributions, such as {Markov Chain Monte…

In this paper, we revisit the inconsistency problem of EKF-based cooperative localization (CL) from the perspective of system decomposition. By transforming the linearized system used by the standard EKF into its Kalman observable canonical…

The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control--to--observable inverse problems. In this context, the EnKF is known as Ensemble Kalman Inversion (EKI). In…

Principal component analysis (PCA) is traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-$k$ projection. These steps can be computationally costly in high-dimensional and…

Data assimilation (DA) for compressible flows with shocks is challenging because many classical DA methods generate spurious oscillations and nonphysical features near uncertain shocks. We focus here on the ensemble Kalman filter (EnKF). We…

Quantum principal component analysis (QPCA) ignited a new development toward quantum machine learning algorithms. Initially showcasing as an active way for analyzing a quantum system using the quantum state itself, QPCA also found potential…

The knockoff filter introduced by Barber and Cand\`es 2016 is an elegant framework for controlling the false discovery rate in variable selection. While empirical results indicate that this methodology is not too conservative, there is no…

Collaborative filtering (CF) and content-based filtering (CBF) have widely been used in information filtering applications. Both approaches have their strengths and weaknesses which is why researchers have developed hybrid systems. This…

In a recent methodological paper, we showed how to learn chaotic dynamics along with the state trajectory from sequentially acquired observations, using local ensemble Kalman filters. Here, we more systematically investigate the possibility…

We investigate random spatially coupled low-density parity-check (SC-LDPC) code ensembles over finite fields. Under different variable-node edge-spreading rules, the random Tanner graphs of several coupled ensembles are defined by multiple…

The Ensemble Kalman Filter (EnKF) is a widely used method for data assimilation in high-dimensional systems, with an ensemble update step equivalent to an empirical version of the Matheron update popular in Gaussian process regression -- a…