Related papers: Eigenvector spatial filtering for large data sets:…

Large-scale association analysis between multivariate responses and predictors is of great practical importance, as exemplified by modern business applications including social media marketing and crisis management. Despite the rapid…

Extended Kalman Filter (EKF) has been a popular approach to localization a mobile robot. However, the performance of the EKF and the quality of the estimation depends on the correct a priori knowledge of process and measurement noise…

We present the FastEMRIWaveforms (FEW) package, a collection of tools to build and analyze extreme mass ratio inspiral (EMRI) waveforms. Here, we expand on the Physical Review Letter that introduced the first fast and accurate…

In this paper, we present a novel approach to geostatistical filtering which tackles two challenges encountered when applying this method to complex spatial datasets: modeling the non-stationarity of the data while still being able to work…

Data-driven methods are emerging as efficient alternatives to traditional numerical forecasting, offering fast inference and lower computational cost. Yet, for complex systems, long-term accuracy often deteriorates due to error…

As a fundamental task in natural language processing, word embedding converts each word into a representation in a vector space. A challenge with word embedding is that as the vocabulary grows, the vector space's dimension increases, which…

Markov random fields (MRFs) are invaluable tools across diverse fields, and spatiotemporal MRFs (STMRFs) amplify their effectiveness by integrating spatial and temporal dimensions. However, modeling spatiotemporal data introduces additional…

Data assimilation plays a pivotal role in understanding and predicting turbulent systems within geoscience and weather forecasting, where data assimilation is used to address three fundamental challenges, i.e., high-dimensionality,…

We discuss certain basic features of the equation-free (EF) approach to modeling and computation for complex/multiscale systems. We focus on links between the equation-free approach and tools from systems and control theory (design of…

Effective feature selection is essential for high-dimensional data analysis and machine learning. Unsupervised feature selection (UFS) aims to simultaneously cluster data and identify the most discriminative features. Most existing UFS…

This work introduces a new, distributed implementation of the Ensemble Kalman Filter (EnKF) that allows for non-sequential assimilation of large datasets in high-dimensional problems. The traditional EnKF algorithm is computationally…

We focus in this work on the estimation of the first $k$ eigenvectors of any graph Laplacian using filtering of Gaussian random signals. We prove that we only need $k$ such signals to be able to exactly recover as many of the smallest…

This paper introduces a structured, adaptive-length deep representation called Neural Eigenmap. Unlike prior spectral methods such as Laplacian Eigenmap that operate in a nonparametric manner, Neural Eigenmap leverages NeuralEF to…

The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnKF originated as a version of the Kalman…

Estimating the probability of rare failure events is an essential step in the reliability assessment of engineering systems. Computing this failure probability for complex non-linear systems is challenging, and has recently spurred the…

Data selection is designed to accelerate learning with preserved performance. To achieve this, a fundamental thought is to identify informative data samples with significant contributions to the training. In this work, we propose…

The extended Kalman filter (EKF) is a cornerstone of nonlinear state estimation, yet its performance is fundamentally limited by noise-model mismatch and linearization errors. We develop a residual-aware distributionally robust EKF that…

The particle filter (PF) and the ensemble Kalman filter (EnKF) are widely used for approximate inference in state-space models. From a Bayesian perspective, these algorithms represent the prior by an ensemble of particles and update it to…

The effective sample size quantifies the amount of independent information contained in a dataset, accounting for redundancy due to correlation between observations. While widely used in geostatistics for scalar data, its extension to…

Deep convolutional neural networks achieve remarkable performance by exhaustively processing dense spatial feature maps, yet this brute-force strategy introduces significant computational redundancy and encourages reliance on spurious…