Proposes a new method to enhance neural learning by maximizing information gain.
problem Improving neural learning by selecting key variables to maximize information gain.
method Adaptive Ensemble Kalman Filter to quantify uncertainty and maximize information gain.
result The proposed method enables the neural network to learn more effectively from stochastic systems.
HKF uses neural networks to adapt Kalman filters for dynamic channel tracking.
problem Tracking channels with varying dynamics and Doppler values.
method Combines Kalman filters with hypernetworks for dynamic adaptation.
result HKF achieves up to 2dB gain over Kalman filters at high Doppler values.
A new EnKF method for elliptic PDEs reduces dimensionality for accurate state estimation.
problem Elliptic PDEs in fluid flows make traditional EnKF regularization ineffective.
method Low-rank factorization of the Kalman gain based on the Jacobian spectrum.
result Inference can be performed in a low-dimensional subspace of the state space.
The paper develops Kalman filters for unknown systems with sample complexity bounds.
problem Designing Kalman filters for systems with unknown parameters and noise.
method Combines system identification with Kalman filter design, ensuring robustness and sub-optimality guarantees.
result Proves sub-optimality guarantees for both Certainty Equivalent and robust Kalman filters with sample complexity bounds.
Gradient-free framework for Bayesian experimental design in complex systems.
problem Optimal experimental design in systems where gradient information is unavailable.
method Combines EKI and ALDI for optimization and sampling, with approximations for scalable utility estimation.
result Demonstrates robust, accurate, and efficient experimental design in various complex systems.
Bayesian design improves accuracy without extra cost.
problem Nested inference in complex systems limits BED accuracy and efficiency.
method Grouped geometric pooled posterior with EKI formulation.
result Improved accuracy and stable estimators at comparable cost.
CG-EnKF and NS-EnKF outperform deep learning-based SF in data assimilation.
problem Data assimilation with non-linear perturbations.
method Two non-linear extensions of EnKF: CG-EnKF and NS-EnKF.
result CG-EnKF and NS-EnKF outperform SF in high-dimensional multiscale data assimilation.
Dynamical models estimate and predict the temporal evolution of physical systems. State Space Models (SSMs) in particular represent the system dynamics with many desirable properties, such as being able to model uncertainty in both the model and measurements, and optimal (in the Bayesian sense) recursive formulations e…
We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic contribution is a novel approximate posterior that can be calculated efficientl…
New method uses EKI for efficient Bayesian inference in high-dimensional problems.
problem Efficient inference for high-dimensional posterior distributions in physics-informed neural networks.
method Ensemble Kalman Inversion (EKI) for high-dimensional posterior inference.
result EKI-based inference provides comparable uncertainty estimates to HMC-based methods but with reduced computational cost.
A simplified Bayesian approach for online sports rating.
problem Rating players/teams based on game outcomes.
method Bayesian approach using Kalman filter principles.
result Known algorithms like Elo and TrueSkill are special cases.
Data assimilation for subsurface flow using latent diffusion models shows that ensemble Kalman methods may overestimate posterior uncertainty, while Monte Carlo sampling is more reliable.
problem Data assimilation for subsurface flow
method Ensemble Kalman smoother and Markov chain Monte Carlo sampling
result Monte Carlo sampling is more reliable than ensemble Kalman methods
A new model detects anomalies in time series data efficiently.
problem Detect anomalies in high-dimensional time series data.
method r-ssGPFA, an unsupervised online anomaly detection model using state space Gaussian processes.
result The model detects anomalies efficiently and is computationally cheaper.
Improved Kalman filter for Stiefel manifold measurements.
problem Improving accuracy in measurements on Stiefel manifolds.
method Generalization of extended Kalman filter for Stiefel manifold-valued measurements.
result Significant improvement over raw measurements.
A new method scales Gaussian process variational autoencoders to handle high-dimensional time series.
problem Scalability issue in Gaussian process variational autoencoders (GPVAEs).
method Introducing Markovian GPs and using Kalman filtering and smoothing for linear time training.
result MGPVAE outperforms existing approaches in various tasks with high scalability.
The article improves prediction by aggregating Kalman recursions online.
problem Improving expert aggregation in prediction models.
method Using exponential weights and state-space models to aggregate Kalman recursions.
result New algorithms outperform existing methods in Kalman recursion expert aggregation.
Parallel-in-time solver reduces ODE simulation time from linear to logarithmic.
problem Efficiently solving ordinary differential equations (ODEs) with reduced computational cost.
method Formulated a parallel-in-time probabilistic numerical ODE solver using time-parallel formulation of iterated extended Kalman smoothers.
result Reduces span cost from linear to logarithmic in the number of time steps.
Paper analyzes ensemble Kalman updates for effective dimension and localization.
problem Why small ensemble sizes work well in inverse problems and data assimilation.
method Non-asymptotic analysis of ensemble Kalman updates, focusing on effective dimension and localization.
result Rigorously explains why a small ensemble size is sufficient when prior covariance has moderate effective dimension.
In this paper, we revisit the Kalman filter theory. After giving the intuition on a simplified financial markets example, we revisit the maths underlying it. We then show that Kalman filter can be presented in a very different fashion using graphical models. This enables us to establish the connection between Kalman fi…
Illustrates interleaved learning with Kalman Filter for linear least squares.
problem Improving machine learning algorithms through interleaved learning.
method Simple statistical and optimization framework based on Kalman Filter.
result Demonstrates the effectiveness of interleaved learning.
Graph Kalman filters adapt classical filters to graph data.
problem Adapting classical Kalman filters to graph data.
method Generalizes Kalman filters to attributed graphs, learning state-transition and readout functions end-to-end.
result Adapted Kalman filters can predict graph outputs.
Recursive KalmanNet combines neural networks with Kalman filters for precise state estimation.
problem State estimation in systems with noisy measurements and non-Gaussian noise.
method Recursive KalmanNet uses a recurrent neural network to estimate states with consistent error covariance, optimizing for Gaussian negative log-likelihood.
result Recursive KalmanNet outperforms conventional Kalman filters and deep learning-based estimators in non-Gaussian noise conditions.
Paper introduces EnDKF for more accurate pose tracking.
problem Accurate pose tracking with directional uncertainty.
method EnDKF integrates unit-quaternion attitude representation for better directional uncertainty capture.
result Significant reduction in error compared to traditional methods.
The extended Kalman filter is perhaps the most standard tool to estimate in real time the state of a dynamical system from noisy measurements of some function of the system, with extensive practical applications (such as position tracking via GPS). While the plain Kalman filter for linear systems is well-understood, th…
The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman filter have been proposed that incorporate linear approximations to nonlinear m…
This paper proves long-time accuracy of ensemble Kalman filters for chaotic and machine-learned systems.
problem Ensuring long-term accuracy of ensemble Kalman filters for complex dynamical systems.
method Established conditions for long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems.
result Ensemble Kalman filters maintain small estimation error over long time horizons for chaotic and machine-learned systems.
A Kalman filter reduces valuation risk in business valuation models.
problem Reducing valuation risk in business valuation models.
method Recursive FCFF model with Kalman filtering to adjust WACC.
result Significant reduction in valuation risk by implementing Kalman filter.
Transformers can approximate Kalman Filtering in linear systems with small error.
problem Approximating Kalman Filtering using Transformers for linear dynamical systems.
method Two-step reduction: 1) Softmax self-attention block approximates Nadaraya-Watson kernel smoothing, 2) This estimator approximates Kalman Filter.
result Constructs a Transformer that implements the Kalman Filter with small additive error, uniformly bounded in time.
The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems wi…
Two proofs of Kalman Theorem using flows of vector fields.
problem Classical result of Control Theory (Kalman Theorem).
method Two proofs using flows of vector fields.
result New criteria for local controllability of non-linear systems.
Proposes a framework to handle missing data in traffic forecasting with sensor blackouts.
problem Missing data in traffic forecasting due to sensor blackouts, especially when correlated with traffic conditions.
method Latent state-space framework that models traffic dynamics and sensor dropout probabilities.
result Improves traffic forecasting by reducing blackout imputation RMSE from 7.02 to 4.23, with MNAR modeling providing additional gains.
Study uses Kalman-Filter to assess market efficiency in major stock markets.
problem Assessing market efficiency in major stock markets.
method Utilizes Kalman-Filter in two stages, assuming a trendline representing true market value.
result Significant portfolio returns in emerging and developed markets.
The Kalman filter and Heston model are used to estimate asset prices and trading performance.
problem Estimating asset prices using stochastic models.
method Kalman filter applied to mean-reverting processes and Heston model with method of moments.
result The Kalman filter and Heston model provide effective methods for estimating asset prices and trading performance.
Paper proves convergence of Kalman filter on Stiefel manifolds with measurement errors.
problem Filtering constant particle with measurement errors on Stiefel manifolds.
method Extended Kalman filter applied to Stiefel manifold-valued observations.
result Convergence of the extended Kalman filter proved for constant system process.
We cast Amari's natural gradient in statistical learning as a specific case of Kalman filtering. Namely, applying an extended Kalman filter to estimate a fixed unknown parameter of a probabilistic model from a series of observations, is rigorously equivalent to estimating this parameter via an online stochastic natural…
In this manuscript we introduce numerical Gaussian process Kalman filtering (GPKF). Numerical Gaussian processes have recently been developed to simulate spatiotemporal models. The contribution of this paper is to embed numerical Gaussian processes into the recursive Kalman filter equations. This embedding enables us t…
Improved Kalman filter for non-linear, non-Gaussian data.
problem Estimating hidden variables with non-linear, non-Gaussian observations.
method Reproduces and extends Burkhart et al.'s discriminative Kalman filter.
result Enhanced filter performance for complex observation models.
In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering an…
Ensemble Kalman methods improve climate model calibration from noisy observations.
problem Calibrating parameters in complex climate models from noisy data.
method Comparing ensemble Kalman methods for efficiency in climate model calibration.
result Ensemble Kalman methods are more efficient and robust for parameter learning in climate models.
Improved stock volume prediction using Kalman Filters with various hidden states.
problem Improving accuracy of intraday trading volume prediction.
method Extended Kalman Filter with various hidden states for different stocks, using cross-validation to determine optimal state number.
result Demonstrated improved accuracy through comparison experiments and numerical analysis.
Enhances linear regression with Kalman filter for loss minimization.
problem Minimizing loss in linear regression models.
method Integrates Kalman filter and SGD for optimal weight updates.
result Develops optimal linear regression equation with minimum area under curve.
In order to integrate uncertainty estimates into deep time-series modelling, Kalman Filters (KFs) (Kalman et al., 1960) have been integrated with deep learning models, however, such approaches typically rely on approximate inference techniques such as variational inference which makes learning more complex and often le…
Paper presents a robust Kalman filter for state estimation.
problem Robust state estimation under process and measurement noise.
method Generalized Bayesian approach to a Weighted Observation Likelihood Filter (WoLF) framework.
result Achieved robust state estimation against both process and measurement noise.
This paper uses Bayesian optimization to efficiently identify stochastic dynamical systems.
problem Efficiently identifying linear stochastic dynamical systems with unknown coefficients and noise variances.
method Adaptive Bayesian optimization with ensemble Gaussian processes (EGP) and Kalman filter recursion.
result BO-based estimator achieves RMSE below the Cramer-Rao bound, improving robustness and consistency.
Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only estimate states that are correlated with the observation. Therefore, sequential esti…
This paper explores estimating chaotic dynamics and parameters using local ensemble Kalman filters.
problem Estimating chaotic dynamics and parameters from observations.
method Local ensemble Kalman filters with covariance and local domain localisation.
result Rigorously updating global parameters using a local domain ensemble Kalman filter.
We investigate the convergence and stability properties of the decoupled extended Kalman filter learning algorithm (DEKF) within the long-short term memory network (LSTM) based online learning framework. For this purpose, we model DEKF as a perturbed extended Kalman filter and derive sufficient conditions for its stabi…
AD-EnKFs use machine learning to improve data assimilation in high-dimensional systems.
problem Data assimilation in high-dimensional, unknown dynamics systems.
method Auto-differentiable ensemble Kalman filters blending machine learning and ensemble Kalman filters.
result AD-EnKFs outperform existing methods in the Lorenz-96 model.