Related papers: The Hitchhiker's Guide to Nonlinear Filtering
System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…
When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
Simulating multi-scale phenomena such as turbulent fluid flows is typically computationally very expensive. Filtering the smaller scales allows for using coarse discretizations, however, this requires closure models to account for the…
Unravelling hidden patterns in datasets is a classical problem with many potential applications. In this paper, we present a challenge whose objective is to discover nonlinear relationships in noisy cloud of points. If a set of point…
Identifying the dynamic precompensator that renders a nonlinear control system feedback linearizable is a challenging problem. Researchers have explored the problem -- dynamic feedback linearization -- and produced existence conditions and…
Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods…
Modern recommender systems operate in uniquely dynamic settings: user interests, item pools, and popularity trends shift continuously, and models must adapt in real time without forgetting past preferences. While existing tutorials on…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob's $h$-transforms that are typically intractable.…
Quantification of relations between measured variables of interest by statistical measures of dependence is a common step in analysis of climate data. The term "connectivity" is used in the network context including the study of complex…
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…
In the following article we consider the numerical approximation of the non-linear filter in continuous-time, where the observations and signal follow diffusion processes. Given access to high-frequency, but discrete-time observations, we…
Convolutional Neural Network (CNN) is one of the most important architectures in deep learning. The fundamental building block of a CNN is a trainable filter, represented as a discrete grid, used to perform convolution on discrete input…
The paper considers causal smoothing of the real sequences, i.e.,discrete time processes in a deterministic setting. A family of causal linear time-invariant filters is suggested. These filters approximate the gain decay for some non-causal…
In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…
Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion,…
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…