Proposes a new method for nonlinear Bayesian updates using ensemble kernel regression.
problem Nonlinear and non-Gaussian Bayesian updates for complex systems.
method Combines Kalman filtering for observed components and kernel density estimation for unobserved components, with subsampling and clustering.
result Reduces estimation errors in highly nonlinear scenarios compared to standard linear updates.
We analyze SA with Markovian data and nonlinear updates, overcoming prior limitations.
problem Analyzing stochastic approximation with Markovian data and nonlinear updates.
method Fine-grained analysis of SA iterates and Markovian data, leveraging smoothness and recurrence properties.
result Established weak convergence and precise asymptotic bias of SA iterates.
We investigate finite-time decoupled convergence in nonlinear two-time-scale stochastic approximation.
problem Achieving decoupled convergence in nonlinear two-time-scale stochastic approximation.
method Nested local linearity assumption, suitable step size selection, convergence analysis of matrix cross term, fourth-order moment convergence rates.
result Finite-time decoupled convergence rates can be achieved in nonlinear two-time-scale stochastic approximation with proper step size selection.
Novel method for nonlinear data assimilation using Langevin sampling.
problem Nonlinear data assimilation challenges in Bayesian filtering.
method Score-based sequential Langevin sampling (SSLS) with dynamic models and annealing.
result Asymptotic stability and error bounds for local posterior sampling.
This paper analyzes a simplified strategy for nonlinear control using local linear models and iLQR updates.
problem Nonlinear policy optimization in control systems.
method Iterative estimation of local linear models and iLQR-like policy updates.
result Demonstrates polynomial sample complexity and overcomes exponential problem horizon dependence.
We consider filtering in high-dimensional non-Gaussian state-space models with intractable transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in space and time. We propose a novel filtering methodology that harnesses transportation of measures, convex optimization, and ideas from proba…
Unified framework for analyzing batch updating methods with noisy gradients.
problem Analyzing convergence of batch updating methods with noisy gradients and approximations.
method Unified framework using convergence of stochastic processes.
result Establishes a general theorem for most known convergence results.
A new filter reduces density fitting to a linear solve, improving performance on nonlinear systems.
problem Nonlinear Bayesian filtering challenges in representing belief distributions.
method Combines score matching with Stein's identity to avoid partition function evaluation.
result The Score Kalman Filter (SKF) outperforms existing methods on nonlinear systems.
A new numerical scheme approximates nonlinear filtering densities for noisy and partial measurements.
problem Approximating nonlinear filtering densities for noisy and partial measurements.
method Deep splitting scheme applied to the Fokker--Planck equation followed by Bayes' formula.
result Convergence rate established for the numerical scheme under parabolic Hörmander condition.
Bayesian model updating uses VAEs to approximate likelihood with small data.
problem Approximating likelihood for small data sets in structural analysis.
method Uses multimodal VAEs to approximate likelihood, suitable for high-dimensional correlated observations.
result Demonstrates computational efficiency and accuracy compared to original VAE approach.
We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance-optimality (A-optimality) criterion, known in the classical theory of experimental design and applied here to quantum …
New nonlinear smoothers improve state estimation in chaotic systems.
problem Improving state estimation in chaotic dynamical systems with non-Gaussian behavior.
method Developed nonlinear backward ensemble transport smoothers with parameterization and regularization of transport maps.
result Nonlinear smoothers yield lower estimation error than conventional methods for comparable model evaluations.
This paper focuses on coordinate update methods, which are useful for solving problems involving large or high-dimensional datasets. They decompose a problem into simple subproblems, where each updates one, or a small block of, variables while fixing others. These methods can deal with linear and nonlinear mappings, sm…
A new ML-based filter improves data assimilation for nonlinear systems.
problem Improving data assimilation for nonlinear systems using ensemble methods.
method Developed a machine learning-based conditional mean filter (ML-EnCMF) integrating ANN and linear functions.
result ML-EnCMF outperforms EnKF and likelihood-based EnCMF in nonlinear systems.
A recent theoretical analysis shows the equivalence between non-negative matrix factorization (NMF) and spectral clustering based approach to subspace clustering. As NMF and many of its variants are essentially linear, we introduce a nonlinear NMF with explicit orthogonality and derive general kernel-based orthogonal m…
This paper introduces a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. This new model not only generalizes the commonly used linear mixing model, but also allows for possible nonlinear effects to be easily handled, relying on mild assumptions regarding…
DeepRSCN models nonlinear systems using stochastic configurations.
problem Modeling nonlinear dynamic systems efficiently.
method Incrementally constructed deep reservoir computing framework with random parameters and online weight updates.
result DeepRSCN outperforms single-layer networks in efficiency, learning, and generalization.
Enhances RSCNs with hybrid regularization for nonlinear dynamics.
problem Modeling nonlinear dynamic systems with uncertainties.
method Recurrent stochastic configuration networks with hybrid regularization.
result The method outperforms other models in nonlinear system identification and industrial tasks.
Newton's method tackles nonlinear mappings into vector bundles with connections and retractions.
problem Finding zeros of mappings from a manifold into a vector bundle.
method Local convergence using differentiability concepts, Banach space Riemannian distance, and affine covariant damping strategy.
result Illustrated application to generalized non-symmetric eigenvalue problems.
Study tackles nonlinear factor models with unknown monotone links from incomplete and noisy data.
problem Learning nonlinear factor models with unknown monotone links from incomplete and noisy data.
method Formulated as joint recovery of low-rank factors, loadings, and nonlinear link function; proposed BCD algorithm with regularization.
result Established convergence guarantees and sublinear regret bounds for link-function updates.
AdaKoop efficiently models nonlinear dynamics from nonstationary data streams.
problem Capturing nonlinear dynamics in nonstationary data streams with computational efficiency.
method Koopman operator theory and probabilistic framework for streaming data.
result AdaKoop outperforms state-of-the-art methods in real-time forecasting accuracy and efficiency.
An incremental/online state dynamic learning method is proposed for identification of the nonlinear Gaussian state space models. The method embeds the stochastic variational sparse Gaussian process as the probabilistic state dynamic model inside a particle filter framework. Model updating is done at measurement sample …
A major goal of unsupervised learning is to discover data representations that are useful for subsequent tasks, without access to supervised labels during training. Typically, this involves minimizing a surrogate objective, such as the negative log likelihood of a generative model, with the hope that representations us…
COLoKe adapts Koopman embeddings online, reducing overfitting and improving long-term predictions.
problem Online adaptation of Koopman embeddings to avoid overfitting and maintain long-term predictive accuracy.
method Combines deep feature learning with multistep prediction consistency in a lifted space, using a conformal-style mechanism for selective updates.
result Empirically effective in reducing overfitting and maintaining long-term predictive accuracy.
Flexible nonlinear Hawkes processes for time-varying systems.
problem Limited expressive ability of classic Hawkes processes.
method Flexible state-switching Hawkes processes with latent variable augmentation for Bayesian inference.
result Superior performance compared to state-of-the-art competitors.
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty. We propose that these uncertainties can be estimated from (conditioned on) past…
This paper finds a new method for decomposing insurer profits and losses.
problem Nonlinear balance sheets make it hard to attribute changes to risk factors.
method An axiomatic approach leading to infinitesimal sequential updating (ISU) decompositions.
result ISU decompositions are more general and applicable beyond insurance.
Two-Timescale EM Methods improve EM for nonconvex models.
problem Nonconvex latent variable models are challenging for EM.
method Two-stage stochastic updates to handle nonconvex optimization.
result Global convergence for nonconvex objective functions.
Bayesian framework improves robustness in nonlinear regression models.
problem Measurement error, model misspecification, and distributional misspecification in regression analyses.
method Joint Dirichlet process prior on latent covariate-response distribution, updating with posterior pseudo-samples.
result Improved stability and consistency in estimators under increasing measurement error.
New algorithm optimizes nonlinear SDEs online with convergence guarantees.
problem Optimizing nonlinear stochastic differential equations (SDEs) is computationally challenging.
method Forward propagation algorithm that solves an SDE derived using forward differentiation.
result Convergence theorem for nonlinear dissipative SDEs with bounds on stochastic fluctuations.
Multiview analysis aims at extracting shared latent components from data samples that are acquired in different domains, e.g., image, text, and audio. Classic multiview analysis, e.g., canonical correlation analysis (CCA), tackles this problem via matching the linearly transformed views in a certain latent domain. More…
Proposes LAE-EnKF for improved nonlinear data assimilation.
problem Performance of EnKF deteriorates for strongly nonlinear dynamics.
method Reformulates assimilation in a learned latent space with linear dynamics.
result LAE-EnKF yields more accurate and stable assimilation.
AuON is a linear-time optimizer that improves upon Muon's performance without approximate orthogonal matrices.
problem High memory and computational costs of orthogonal momentum updates.
method AuON uses normalized nonlinear scaling and a 'emergency brake' to handle exploding attention logits.
result AuON achieves strong performance without approximate orthogonal matrices, preserving structural alignment and reconditioning.
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…
Algorithm recovers factors of rank-1 matrices from noisy measurements.
problem Estimating factors of a rank-1 matrix from nonlinearly transformed and noisy measurements.
method Alternating minimization with random initialization and analysis of empirical error recursion.
result Algorithm converges geometrically fast from random initialization, with sharp guarantees.
In this work, we highlight a connection between the incremental proximal method and stochastic filters. We begin by showing that the proximal operators coincide, and hence can be realized with, Bayes updates. We give the explicit form of the updates for the linear regression problem and show that there is a one-to-one …
A new flow-based Bayesian filter tackles high-dimensional nonlinear stochastic systems.
problem Bayesian filtering for high-dimensional nonlinear systems is challenging due to non-Gaussian distributions and computational limitations.
method Integrates normalizing flows to construct a latent linear state-space model with efficient density estimation and sampling.
result Demonstrates superior accuracy and efficiency in numerical experiments.
We consider the fully decentralized machine learning scenario where many users with personal datasets collaborate to learn models through local peer-to-peer exchanges, without a central coordinator. We propose to train personalized models that leverage a collaboration graph describing the relationships between user per…
EnSF improves accuracy in tracking high-dimensional nonlinear systems.
problem Low accuracy in high-dimensional, nonlinear filtering problems.
method Score-based diffusion model, mini-batch Monte Carlo estimator.
result EnSF outperforms state-of-the-art methods in tracking high-dimensional systems.
Parallelizes feedforward computation using nonlinear equation solving.
problem Sequential nature of feedforward computation limits parallelization.
method Frame feedforward computation as solving nonlinear equations; use Jacobi or Gauss-Seidel methods for parallel updates.
result Accelerates feedforward computation with reduced parallelizable iterations.
Extends return extrapolation to nonlinear, asymmetric functions under stochastic volatility.
problem Behavioral anomalies in portfolio choice under stochastic volatility.
method Smooth, nonlinear, asymmetric extrapolation function; CRRA investor; Heston stochastic volatility; Hamilton-Jacobi-Bellman equation; Numerical solutions (finite-difference ADI, deep learning-driven iterative).
result Saturation acts as an endogenous correction mechanism, reducing welfare loss.
This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive system of ordinary differential equations (ODEs) for the relevant conditional distri…
Proposes variational Gaussian approximations for solving the Kushner equation.
problem Solving the Kushner equation for state estimation with observations.
method Tractable variational Gaussian approximations of proximal losses based on Wasserstein and Fisher metrics.
result The proposed method leads to a Gaussian flow consistent with Kalman-Bucy and Riccati flows.
Kernel-based Bayesian filter for nonlinear systems using infinite-dimensional operators.
problem Modeling and predicting nonlinear dynamical systems.
method Functional Bayesian perspective, reproducing kernel Hilbert space, Gaussian kernel.
result Effective approximation and accurate results for nonlinear systems.
New convergence bounds for online learning with heavy-tailed noise.
problem Learning on streaming data with heavy-tailed noise.
method Nonlinear stochastic gradient descent (SGD) for non-convex and strongly convex costs.
result Strong convergence rates for various nonlinearities and noise distributions.
New decision-theoretic characterization separates belief and decision posteriors.
problem Understanding the conditions under which loss-based updating coincides with Bayesian updating.
method Decision-theoretic approach to distinguish belief and decision posteriors.
result Generalized Bayes coincides with ordinary Bayesian updating only if the loss is proportional to negative log-likelihood.
Augmented KRnet improves flow-based generative modeling by maintaining exact invertibility.
problem Maintaining exact invertibility in flow-based generative models.
method Integrates augmented dimensions into KRnet to achieve full nonlinear updates in two iterations, keeping exact invertibility.
result Augmented KRnet achieves full nonlinear updates in two iterations, maintaining exact invertibility.
We extend return extrapolation to incorporate asymmetry and saturation, finding that asymmetric nonlinear extrapolation leads to lower welfare loss.
problem Optimal portfolio choice under stochastic volatility
method Smooth, nonlinear extrapolation function with sentiment and variance hedging
result Lower welfare loss with asymmetric nonlinear extrapolation