Related papers: Local regression on path spaces with signature met…

In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…

This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The…

Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted…

Suppose that $\gamma$ and $\sigma$ are two continuous bounded variation paths which take values in a finite-dimensional inner product space $V$. Recent papers have introduced the truncated and the untruncated signature kernel of $\gamma$…

Simulation models often lack tractable likelihood functions, making likelihood-free inference methods indispensable. Approximate Bayesian computation generates likelihood-free posterior samples by comparing simulated and observed data…

Identifying optimal collective variables to model transformations, using atomic-scale simulations, is a long-standing challenge. We propose a new method for the generation, optimization, and comparison of collective variables, which can be…

The signature of a path is a non-commutative power series whose coefficients are given by certain iterated integrals over the path coordinates. This series almost uniquely characterizes the path up to translation and reparameterization.…

Randomised signature has been proposed as a flexible and easily implementable alternative to the well-established path signature. In this article, we employ randomised signature to introduce a generative model for financial time series data…

Nonlinear and delayed effects of covariates often render time series forecasting challenging. To this end, we propose a novel forecasting framework based on ridge regression with signature features calculated on sliding windows. These…

We develop a rough-path framework for two-parameter rough differential equations on rectangular and simplicial domains, motivated by the signature kernel and Schwinger--Dyson kernel equations. The theory is formulated in spaces of jointly…

Bifurcating autoregressive processes, which can be seen as an adaptation of au-toregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify…

Freight transportation marketplace rates are typically challenging to forecast accurately. In this work, we have developed a novel statistical technique based on signature transforms and have built a predictive and adaptive model to…

The signature kernel is a recent state-of-the-art tool for analyzing high-dimensional sequential data, valued for its theoretical guarantees and strong empirical performance. In this paper, we present a novel method for efficiently…

A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the…

We discuss nonparametric tests for parametric specifications of regression quantiles. The test is based on the comparison of parametric and nonparametric fits of these quantiles. The nonparametric fit is a Nadaraya-Watson quantile smoothing…

Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…

Signatures provide a succinct description of certain features of paths in a reparametrization invariant way. We propose a method for classifying shapes based on signatures, and compare it to current approaches based on the SRV transform and…

Signature kernels, inner products of path signatures, underpin several machine learning algorithms for multivariate time series analysis. For bounded variation paths, signature kernels were recently shown to solve a Goursat PDE. However,…

In this article we introduce the insertion method for reconstructing the path from its signature, i.e. inverting the signature of a path. For this purpose, we prove that a converging upper bound exists for the difference between the…

We introduce a general method to prove uniform in bandwidth consistency of kernel-type function estimators. Examples include the kernel density estimator, the Nadaraya-Watson regression estimator and the conditional empirical process. Our…