Related papers: Introduction to Geodetic Time Series Analysis
We introduce a novel geometry-oriented methodology, based on the emerging tools of topological data analysis, into the change point detection framework. The key rationale is that change points are likely to be associated with changes in…
Robotic systems often operate with uncertainties in their dynamics, for example, unknown inertial properties. Broadly, there are two approaches for controlling uncertain systems: design robust controllers in spite of uncertainty, or…
Safety-critical navigation applications require that estimation errors be reliably quantified and bounded. This can be challenging for linear dynamic systems if the process noise or measurement errors have uncertain time correlation. In…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
We study filtering of multiscale dynamical systems with model error arising from unresolved smaller scale processes. The analysis assumes continuous-time noisy observations of all components of the slow variables alone. For a linear model…
Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…
This article concerns the predictive modeling for spatio-temporal data as well as model interpretation using data information in space and time. We develop a novel approach based on supervised dimension reduction for such data in order to…
Time series analysis is of immense importance in extensive applications, such as weather forecasting, anomaly detection, and action recognition. This paper focuses on temporal variation modeling, which is the common key problem of extensive…
We provide a method to identify system parameters of dynamical systems, called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with…
Parareal is a well-studied algorithm for numerically integrating systems of time-dependent differential equations by parallelising the temporal domain. Given approximate initial values at each temporal sub-interval, the algorithm locates a…
The Gaussian process is a powerful and flexible technique for interpolating spatiotemporal data, especially with its ability to capture complex trends and uncertainty from the input signal. This chapter describes Gaussian processes as an…
We introduce and study a variational framework for the analysis of empirical risk based inference for dynamical systems and ergodic processes. The analysis applies to a two-stage estimation procedure in which (i) the trajectory of an…
We propose a new semi-parametric approach to the joint segmentation of multiple series corrupted by a functional part. This problem appears in particular in geodesy where GPS permanent station coordinate series are affected by undocumented…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as…
Predicting transportation modes from GPS (Global Positioning System) records is a hot topic in the trajectory mining domain. Each GPS record is called a trajectory point and a trajectory is a sequence of these points. Trajectory mining has…
Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…