Deep density methods improve filtering in high-dimensional systems.
problem Nonlinear filtering in high-dimensional systems.
method Two deep density methods based on Feynman-Kac formulas and neural networks.
result Logarithmic deep backward stochastic differential equation filter outperforms classical methods in high dimensions.
FGD reduces noisy gradient variance in SGD for neural networks.
problem Noisy and unreliable gradient estimation in SGD for deep learning.
method Solves an adaptive filtering problem to consistently estimate the local gradient.
result Significantly reduces gradient variance and accelerates convergence.
A novel method reduces dimensionality for filtering SRNs with observed variables.
problem Challenges in estimating hidden state variables in SRNs with limited observations.
method Filtered Markovian Projection (Filtered MP) for dimensionality reduction in filtering.
result Filtered MP guarantees consistency and superior computational efficiency in high dimensions.
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.
This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the one generated by the asset prices, and the unobservable processes will be modeled …
Develops inverse unscented Kalman filter for non-linear systems.
problem Estimating defender's state in adversarial settings.
method Formulated inverse unscented Kalman filter (I-UKF) and reproducing kernel Hilbert space-based UKF (RKHS-UKF).
result Proposed filters are conservative estimators with upper-bounded error covariance.
A new Bayesian filtering method speeds up stochastic Newton optimization.
problem Minimizing log-convex functions using stochastic methods.
method Contextualizes the problem as Bayesian inference, applying Bayesian filtering to update estimates.
result Establishes conditions for diminishing effect of older observations, akin to momentum.
This paper presents the construction of a particle filter, which incorporates elements inspired by genetic algorithms, in order to achieve accelerated adaptation of the estimated posterior distribution to changes in model parameters. Specifically, the filter is designed for the situation where the subsequent data in on…
In this study, we develop a deterministic nonlinear filtering algorithm based on a high-dimensional version of Kitagawa (1987) to evaluate the likelihood function of models that allow for stochastic volatility and jumps whose arrival intensity is also stochastic. We show numerically that the deterministic filtering met…
Paper uses averaging from many particle filters to approximate posterior predictive distributions.
problem Approximating posterior predictive distributions efficiently and accurately.
method Particle swarm filter algorithm that averages many particle filter approximations.
result Law of large numbers and central limit theorem support the method's effectiveness.
Particle MCMC involves using a particle filter within an MCMC algorithm. For inference of a model which involves an unobserved stochastic process, the standard implementation uses the particle filter to propose new values for the stochastic process, and MCMC moves to propose new values for the parameters. We show how p…
Adaptive Heston model calibration using PCRLB and switching filters.
problem Estimating volatility in stochastic volatility models like Heston.
method Bayesian filtering (EKF, UKF, PF) with PCRLB for parameter estimation.
result Adaptive estimation of Heston model parameters improves volatility estimation.
Paper addresses fault-tolerance in distributed machine learning with stochastic gradient descent.
problem Fault-tolerance in distributed stochastic gradient descent (D-SGD) for machine learning.
method Proposes norm-based comparative gradient elimination (CGE) to robustify D-SGD against Byzantine faulty agents.
result CGE guarantees fault-tolerance against a bounded fraction of Byzantine agents under standard stochastic assumptions.
This paper presents a new approach for filter design based on stochastic distances and tests between distributions. A window is defined around each pixel, overlapping samples are compared and only those which pass a goodness-of-fit test are used to compute the filtered value. The technique is applied to intensity SAR d…
New deep learning method approximates Benes filter model.
problem Approximating high-dimensional SPDEs for filtering.
method Deep learning mesh-free neural network representation.
result First study of neural network method for Benes model.
Method uses deep learning to estimate traffic intensity.
problem Estimating stochastic intensity of traffic processes.
method Deep neural networks for nonlinear filtering.
result Deep learning method accurately estimates traffic intensity.
This work analyzes the stability of graph filters under large perturbations.
problem Stability of graph filters under large edge rewires.
method Proves a bound on stability using frequency response and community structure.
result Graph filter stability depends on perturbation to community structure.
Binary Stochastic Filtering (BSF), the algorithm for feature selection and neuron pruning is proposed in this work. The method defines filtering layer which penalizes amount of the information involved in the training process. This information could be the input data or output of the previous layer, which directly lead…
Improved volatility estimation using SV-PF-RNN.
problem Estimating true volatility in the presence of market noise.
method SV-PF-RNN: hybrid neural network and particle filter architecture.
result SV-PF-RNN outperforms basic particle filter.
Gradient filters track moving parameters under noisy data and misspecification.
problem Tracking multidimensional time-varying parameters under noisy observations and model misspecification.
method Gradient-based filters update parameters using the gradient of a postulated objective function, evaluated at either the predicted or updated parameters.
result Novel sufficient conditions for exponential stability of the filtered parameter path, and finite-sample and asymptotic mean squared error bounds.
We use GANs and signatures to approximate conditional laws in filtering and prediction of diffusion processes.
problem Approximating conditional laws for diffusion processes with noisy observations.
method Conditional GANs combined with signatures for approximation.
result Efficient approximation of conditional laws for diffusion processes.
We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method for the optimal filter infinite dimensional Stochastic Partial Differential Equation (SPDE), based on the direct L2 metric and on a family o…
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.
This paper is concerned with sequential filtering based stochastic optimization (FSO) approaches that leverage a probabilistic perspective to implement the incremental proximity method (IPM). The present FSO methods are derived based on the Kalman filter (KF) and the extended KF (EKF). In contrast with typical methods …
This paper presents two approaches for filter design based on stochastic distances for intensity speckle reduction. A window is defined around each pixel, overlapping samples are compared and only those which pass a goodness-of-fit test are used to compute the filtered value. The tests stem from stochastic divergences …
Three situations in which filtering theory is used in mathematical finance are illustrated at different levels of detail. The three problems originate from the following different works: 1) On estimating the stochastic volatility model from observed bilateral exchange rate news, by R. Mahieu, and P. Schotman; 2) A stat…
Transformers can solve complex filtering problems for non-Gaussian signals.
problem Non-linear and non-Markovian filtering problems for conditionally Gaussian signals.
method Continuous-time transformer models called filterformers.
result Filterformers can approximate the conditional law of non-Markovian and conditionally Gaussian signal processes.
This paper presents a new approach for filter design based on stochastic distances and tests between distributions. A window is defined around each pixel, samples are compared and only those which pass a goodness-of-fit test are used to compute the filtered value. The technique is applied to intensity Synthetic Apertur…
Improved model-based estimation through tempered Bayes filter.
problem Improving predictive accuracy in partially-observable stochastic systems.
method Developed tempered Bayes filter combining likelihood and full posterior tempering.
result Tempered Bayes filter achieves improved predictive performance over the Bayes filter baseline.
Geometry arising from two diffusion operators (smooth semi-elliptic, second order differential operators) on different spaces but intertwined by a smooth map is described. Particular cases arise from Riemannian submersions when the operators are Laplace-Beltrami operators, from equivariant operators on the total space …
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 …
We introduce Kalman Gradient Descent, a stochastic optimization algorithm that uses Kalman filtering to adaptively reduce gradient variance in stochastic gradient descent by filtering the gradient estimates. We present both a theoretical analysis of convergence in a non-convex setting and experimental results which dem…
Novel filter uses deep BSDE for nonlinear density approximation.
problem Nonlinear filtering problem.
method Bayesian filter based on deep BSDE and neural networks.
result Theoretical convergence rate confirmed in numerical examples.
New filters improve radar target inference in complex scenarios.
problem Improving radar target inference in highly non-linear system models.
method Developed inverse cubature Kalman filter (I-CKF), inverse quadrature Kalman filter (I-QKF), and inverse cubature-quadrature Kalman filter (I-CQKF) for non-linear systems.
result Numerical experiments show improved estimation accuracy compared to existing methods.
Method learns dynamics from noisy partial observations.
problem Reconstructing stochastic dynamical systems from indirect noisy data.
method Amortized path generation method for nonlinear stochastic filtering.
result Learned conditional path generator quantifies uncertainty.
Unified approach to stochastic control, filtering, and stopping using rough paths.
problem Addressing gaps in classical problems of stochastic control, filtering, and stopping.
method Combining rough path theory with controlled rough paths to provide a pathwise deterministic framework.
result Established rigorous connection between candidate solutions and Hamilton-Jacobi-Bellman equation.
Novel digital twin for complex systems improves performance.
problem Lack of practical implementation details for stochastic nonlinear MDOF systems.
method Decouples time-scales, uses physics-based model, Bayesian filtering, and machine learning.
result Excellent performance of proposed digital twin framework validated by examples.
We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and our proofs only use the definition of ReLU, in contrast with previous works that …
The paper stabilizes PD term structures under forecast uncertainty using a Kalman filter with an anchored observation model.
problem Stable estimation of lifetime PDs under forecast uncertainty.
method Reformulated in state-space framework, introduced an anchored observation model.
result Asymptotic stochastic stability of error dynamics, leading to smoother projections.
A new method for estimating adversarial strategies in nonlinear systems.
problem Inferring an intelligent adversarial agent's strategy in highly nonlinear systems.
method Formulated inverse cognition as a nonlinear Gaussian state-space model and developed an inverse UKF (IUKF) system.
result The estimation error of IUKF converges and closely follows the recursive Cramér-Rao lower bound.
A new multi-factor model improves commodity pricing accuracy.
problem Enhancing accuracy in commodity pricing by integrating multiple risk factors.
method A four-factor model using Kalman filter for simultaneous estimation and state variable filtering.
result The four-factor model outperforms existing models in capturing futures term structures and crude oil pricing.
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.
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation algorithm. Using the probabilistic model, we derive a matrix factorisation algorithm …
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.
Extends nonlinear filtering to predictable jump times.
problem Filtering with jumps in both signal and observation, especially when jump times are known.
method Derive Kushner-Stratonovich and Zakai equations for predictable discontinuities.
result Extends classical nonlinear filtering results to a setting with predictable discontinuities.
MoE-F combines LLMs online for better time-series prediction.
problem Combining multiple LLMs for online time-series prediction.
method Time-adaptive stochastic filtering techniques to combine experts.
result MoE-F achieves 17% absolute and 48.5% relative F1 measure improvement.
A deep learning method solves nonlinear filtering problems efficiently.
problem Nonlinear filtering problem
method Deep splitting method combined with energy-based neural network approximation
result Computational efficiency and performance comparable to Kalman and bootstrap filters
Develops state-space deep Gaussian processes for irregular signals.
problem Solving deep Gaussian process regression problems for irregular signals/functions.
method Represent DGPs as SDEs, solve using state-space filtering and smoothing methods.
result Rich class of priors compatible with irregular signals/functions.