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Aiming for a systematic feature-extraction from time series, we introduce the iterated-sums signature over arbitrary commutative semirings. The case of the tropical semiring is a central, and our motivating example. It leads to features of…

Document reconstruction constitutes a significant facet of document analysis and recognition, a field that has been progressively accruing interest within the scholarly community. A multitude of these researchers employ an array of document…

As the amount of digital devices suspected of containing digital evidence increases, case backlogs for digital investigations are also increasing in many organizations. To ensure timely investigation of requests, this work proposes the use…

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…

In this paper we extend previous work of Galleas and the author to elliptic SOS models. We demonstrate that the dynamical reflection algebra can be exploited to obtain a functional equation characterizing the partition function of an…

The partially separable functions (PSF) model is commonly adopted in dynamic MRI reconstruction, as is the underlying signal model in many reconstruction methods including the ones relying on low-rank assumptions. Even though the PSF model…

Compositional data, such as regional shares of economic sectors or property transactions, are central to understanding structural change in economic systems across space and time. This paper introduces a spatiotemporal multivariate…

In this paper we suggest two continuous-time models which exhibit an autoregressive structure. We obtain existence and uniqueness results and study the structure of the solution processes. One of the models, which corresponds to general…

Due to the influence of imaging equipment and complex imaging environments, most images in daily life have features of intensity inhomogeneity and noise. Therefore, many scholars have designed many image segmentation algorithms to address…

We introduce the notion of property signatures, a representation for programs and program specifications meant for consumption by machine learning algorithms. Given a function with input type $\tau_{in}$ and output type $\tau_{out}$, a…

In finance, economics and many other fields, observations in a matrix form are often generated over time. For example, a set of key economic indicators are regularly reported in different countries every quarter. The observations at each…

Simulation models of complex dynamics in the natural and social sciences commonly lack a tractable likelihood function, rendering traditional likelihood-based statistical inference impossible. Recent advances in machine learning have…

The Forward-Forward (FF) algorithm presents a compelling, bio-inspired alternative to backpropagation. However, while efficient in training, it has a computationally prohibitive inference process that requires a separate forward pass for…

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.…

In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical…

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…

INteger Auto-Regressive (INAR) processes are usually defined by specifying the innovations and the operator, which often leads to difficulties in deriving marginal properties of the process. In many practical situations, a major modeling…

Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on…

The purpose of the present paper is to investigate on a class of spherical functional autoregressive processes in order to introduce and study LASSO (Least Absolute Shrinkage and Selection Operator) type estimators for the corresponding…

Functional autoregressive (FAR) models provide a fundamental framework for analyzing temporally dependent functional data. However, the infinite-dimensional nature of the underlying Hilbert space introduces intrinsic ill-posedness, as the…