相关论文: Path Imputation Strategies for Signature Models of…

We introduce a novel modeling approach for time series imputation and forecasting, tailored to address the challenges often encountered in real-world data, such as irregular samples, missing data, or unaligned measurements from multiple…

Time series are all around in real-world applications. However, unexpected accidents for example broken sensors or missing of the signals will cause missing values in time series, making the data hard to be utilized. It then does harm to…

Path signatures are powerful nonparametric tools for time series analysis, shown to form a universal and characteristic feature map for Euclidean valued time series data. We lift the theory of path signatures to the setting of Lie group…

Gaussian Processes (\textbf{GPs}) are flexible non-parametric models with strong probabilistic interpretation. While being a standard choice for performing inference on time series, GPs have few techniques to work in a streaming setting.…

The 'signature method' refers to a collection of feature extraction techniques for multivariate time series, derived from the theory of controlled differential equations. There is a great deal of flexibility as to how this method can be…

Sequential and temporal data arise in many fields of research, such as quantitative finance, medicine, or computer vision. A novel approach for sequential learning, called the signature method and rooted in rough path theory, is considered.…

The interface between stochastic analysis and machine learning is a rapidly evolving field, with path signatures - iterated integrals that provide faithful, hierarchical representations of paths - offering a principled and universal feature…

We propose a novel generative model for multivariate discrete-time time series data. Drawing inspiration from the construction of neural spline flows, our algorithm incorporates linear transformations and the signature transform as a…

Path signatures have been proposed as a powerful representation of paths that efficiently captures the path's analytic and geometric characteristics, having useful algebraic properties including fast concatenation of paths through tensor…

Signatures are iterated path integrals of continuous and discrete-time processes, and their universal nonlinearity linearizes the problem of feature selection in time series data analysis. This paper studies the consistency of signature…

Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot…

Recent work on simultaneous trajectory estimation and mapping (STEAM) for mobile robots has found success by representing the trajectory as a Gaussian process. Gaussian processes can represent a continuous-time trajectory, elegantly handle…

Dealing with missing values and incomplete time series is a labor-intensive, tedious, inevitable task when handling data coming from real-world applications. Effective spatio-temporal representations would allow imputation methods to…

Path signatures embed trajectories into tensor algebra and constitute a universal, non-parametric representation of paths; however, in the standard form, they collapse temporal structure into a single global object, which limits their…

Recent years have witnessed a growing interest for time series foundation models, with a strong emphasis on the forecasting task. Yet, the crucial task of out-of-domain imputation of missing values remains largely underexplored. We propose…

Many finance, physics, and engineering phenomena are modeled by continuous-time dynamical systems driven by highly irregular (stochastic) inputs. A powerful tool to perform time series analysis in this context is rooted in rough path theory…

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…

We bring the theory of rough paths to the study of non-parametric statistics on streamed data. We discuss the problem of regression where the input variable is a stream of information, and the dependent response is also (potentially) a…

Time series imputation is one of the most challenge problems and has broad applications in various fields like health care and the Internet of Things. Existing methods mainly aim to model the temporally latent dependencies and the…

Signal processing and machine learning algorithms for data supported over graphs, require the knowledge of the graph topology. Unless this information is given by the physics of the problem (e.g., water supply networks, power grids), the…