Related papers: Gaussian processes based data augmentation and exp…
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…
The expected signature maps a collection of data streams to a lower dimensional representation, with a remarkable property: the resulting feature tensor can fully characterize the data generating distribution. This "model-free" embedding…
In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural…
The expected supremum of a Gaussian process indexed by the image of an index set under a function class is bounded in terms of separate properties of the index set and the function class. The bound is relevant to the estimation of nonlinear…
The signature kernel is a kernel between time series of arbitrary length and comes with strong theoretical guarantees from stochastic analysis. It has found applications in machine learning such as covariance functions for Gaussian…
Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture…
The concept of signatures and expected signatures is vital in data science, especially for sequential data analysis. The signature transform, a Cartan type development, translates paths into high-dimensional feature vectors, capturing their…
We provide an introduction to the topic of path signatures as means of feature extraction for machine learning from data streams. The article stresses the mathematical theory underlying the signature methodology, highlighting the conceptual…
In this paper, we consider the problem of extraction of most informative features from time series that are regarded as observed values of stochastic processes satisfying the It{\^{o}} stochastic differential equations with unknown random…
A new approach for feature extraction from time series is proposed in this paper. This approach consists of a specific regression model incorporating a discrete hidden logistic process. The model parameters are estimated by the maximum…
The signature of a sample path is a formal series of iterated integrals along the path. The expected signature of a stochastic process gives a summary of the process that is especially useful for studying stochastic differential equations…
Feature-based time series representations have attracted substantial attention in a wide range of time series analysis methods. Recently, the use of time series features for forecast model averaging has been an emerging research focus in…
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…
We develop a Bayesian approach to learning from sequential data by using Gaussian processes (GPs) with so-called signature kernels as covariance functions. This allows to make sequences of different length comparable and to rely on strong…
The expected signature kernel arises in statistical learning tasks as a similarity measure of probability measures on path space. Computing this kernel for known classes of stochastic processes is an important problem that, in particular,…
Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it…
In this study, we examine if engineered topological features can distinguish time series sampled from different stochastic processes with different noise characteristics, in both balanced and unbalanced sampling schemes. We compare our…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
We introduce a novel edge tracing algorithm using Gaussian process regression. Our edge-based segmentation algorithm models an edge of interest using Gaussian process regression and iteratively searches the image for edge pixels in a…
The signature of a path is an essential object in the theory of rough paths. The signature representation of the data stream can recover standard statistics, e.g. the moments of the data stream. The classification of random walks indicates…