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The main goal in this manuscript is to present a class of functions satisfying a certain orthogonality property for which there also exists a three term recurrence formula. This class of functions, which can be considered as an extension to…
This article introduces the GNAR package, which fits, predicts, and simulates from a powerful new class of generalised network autoregressive processes. Such processes consist of a multivariate time series along with a real, or inferred,…
We introduce a new methodology to conduct simultaneous inference of the nonparametric component in partially linear time series regression models where the nonparametric part is a multivariate unknown function. In particular, we construct a…
We introduce the novel concept of hypercomplex iterated function system (IFS) on the complete metric space $(\mathbb{A}_{n+1}^k,d)$ and define its hypercomplex attractor. Systems of hypercomplex function systems arising from hypercomplex…
The signature of a path can be described as its full non-commutative exponential. Following T. Lyons we regard its expectation, the expected signature, as path space analogue of the classical moment generating function. The logarithm…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
When observations are curves over some natural time interval, the field of functional data analysis comes into play. Functional linear processes account for temporal dependence in the data. The prediction problem for functional linear…
Recent progress in controllable image generation and editing is largely driven by diffusion-based methods. Although diffusion models perform exceptionally well in specific tasks with tailored designs, establishing a unified model is still…
Feature engineering is a crucial step in the process of predictive modeling. It involves the transformation of given feature space, typically using mathematical functions, with the objective of reducing the modeling error for a given…
We study nonparametric regression and classification for path-valued data. We introduce a functional Nadaraya-Watson estimator that combines the signature transform from rough path theory with local kernel regression. The signature…
Humans and animals show remarkable flexibility in adjusting their behaviour when their goals, or rewards in the environment change. While such flexibility is a hallmark of intelligent behaviour, these multi-task scenarios remain an…
It is known that the Barlow-Proschan index of a system with i.i.d. component lifetimes coincides with the Shapley value, a concept introduced earlier in cooperative game theory. Due to a result by Owen, this index can be computed…
Physical motions are inherently continuous, and higher camera frame rates typically contribute to improved smoothness and temporal coherence. For the first time, we explore continuous representations of human motion sequences, featuring the…
In this paper we consider the problem of proving properties of infinite behaviour of formalisms suitable to describe (infinite state) systems with recursion and parallelism. As a formal setting, we consider the framework of Process…
Heteroskedasticity is a common feature of financial time series and is commonly addressed in the model building process through the use of ARCH and GARCH processes. More recently multivariate variants of these processes have been in the…
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…
In this work, a novel Dynamic Movement Primitive (DMP) formulation is proposed which supports reversibility, i.e. backwards reproduction of a learned trajectory. Apart from sharing all favourable properties of the original DMP, decoupling…
Existing digital sensors capture images at fixed spatial and spectral resolutions (e.g., RGB, multispectral, and hyperspectral images), and each combination requires bespoke machine learning models. Neural Implicit Functions partially…
A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…
This thesis deals with the specification and construction of syntax and operational semantics of a programming language. We work with a general notion of signature for specifying objects of a given category as initial objects in a suitable…