Related papers: Nonlinear projective filtering in a data stream
We discuss applications of nonlinear filtering of time series by locally linear phase space projections. Noise can be reduced whenever the error due to the manifold approximation is smaller than the noise in the system. Examples include the…
Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy…
A physical data (such as astrophysical, geophysical, meteorological etc.) may appear as an output of an experiment or it may come out as a signal from a dynamical system or it may contain some sociological, economic or biological…
To estimate the smoothing distribution in a nonlinear state space model, we apply the conditional particle filter with ancestor sampling. This gives an iterative algorithm in a Markov chain Monte Carlo fashion, with asymptotic convergence…
Numerous fields of nonlinear physics, very different in nature, produce signals and images, that share the common feature of being essentially constituted of piecewise homogeneous phases. Analyzing signals and images from corresponding…
Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We…
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…
The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…
In this tutorial we consider the non-linear Bayesian filtering of static parameters in a time-dependent model. We outline the theoretical background and discuss appropriate solvers. We focus on particle-based filters and present Sequential…
Recent works on deep non-linear spatially selective filters demonstrate exceptional enhancement performance with computationally lightweight architectures for stationary speakers of known directions. However, to maintain this performance in…
The Iterative Filtering method is a technique developed recently for the decomposition and analysis of non-stationary and non-linear signals. In this work we propose two alternative formulations of the original algorithm which allows to…
Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…
Testing for nonlinearity is one of the most important preprocessing steps in nonlinear time series analysis. Typically, this is done by means of the linear surrogate data methods. But it is a known fact that the validity of the results…
Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…
This work presents an algorithm for determining the parameters of a nonlinear dynamic model of the respiratory system in patients undergoing assisted ventilation. Using the pressure and flow signals measured at the mouth, the model's…
The robust estimation of dynamically changing features, such as the position of prey, is one of the hallmarks of perception. On an abstract, algorithmic level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing signals…
Actigraphy has been widely used for the analysis of circadian rhythm. Current practice applies regression analysis to data from multiple days to estimate the circadian phase. This paper presents a filtering method for online processing of…
High-dimensional nonlinear dynamical systems including neural networks can be utilized as a computational resource for information processing. In this sense, nonlinear wave systems are good candidate for such a computational resource. Here,…
We propose a method for adaptive nonlinear sequential modeling of vector-time series data. Data is modeled as a nonlinear function of past values corrupted by noise, and the underlying non-linear function is assumed to be approximately…
Particle filters for data assimilation in nonlinear problems use "particles" (replicas of the underlying system) to generate a sequence of probability density functions (pdfs) through a Bayesian process. This can be expensive because a…