Related papers: Linear Processes for Functional Data
In the last few decades both the volume of high-quality observing data on variable stars and common access to them have boomed; however the standard used methods of data processing and interpretation have lagged behind this progress. The…
Time series data is a collection of chronological observations which is generated by several domains such as medical and financial fields. Over the years, different tasks such as classification, forecasting, and clustering have been…
Accurately predicting industrial aging processes makes it possible to schedule maintenance events further in advance, ensuring a cost-efficient and reliable operation of the plant. So far, these degradation processes were usually described…
Process mining (PM) aims to construct, from event logs, process maps that can help discover, automate, improve, and monitor organizational processes. Robotic process automation (RPA) uses software robots to perform some tasks usually…
The inception of large language models has helped advance state-of-the-art performance on numerous natural language tasks. This has also opened the door for the development of foundation models for other domains and data modalities such as…
Artificial neural networks are simple and efficient machine learning tools. Defined originally in the traditional setting of simple vector data, neural network models have evolved to address more and more difficulties of complex real world…
The explosion of Time Series (TS) data, driven by advancements in technology, necessitates sophisticated analytical methods. Modern management systems increasingly rely on analyzing this data, highlighting the importance of effcient…
The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…
Despite their simplicity, linear models perform well at time series forecasting, even when pitted against deeper and more expensive models. A number of variations to the linear model have been proposed, often including some form of feature…
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…
A conventional linear model for functional data involves expressing a response variable $Y$ in terms of the explanatory function $X(t)$, via the model: $Y=a+\int_I b(t)X(t)dt+\hbox{error}$, where $a$ is a scalar, $b$ is an unknown function…
This report showcases the role of, and future directions for, the field of Randomized Numerical Linear Algebra (RNLA) in a selection of scientific applications. These applications span the domains of imaging, genomics and dynamical systems,…
We introduce the concept of local dyadic stationarity, to account for non-stationary time series, within the framework of Walsh-Fourier analysis. We define and study the time varying dyadic ARMA models (tvDARMA). It is proven that the…
This paper treats functional marked point processes (FMPPs), which are defined as marked point processes where the marks are random elements in some (Polish) function space. Such marks may represent e.g. spatial paths or functions of time.…
We introduce the class of continuous-time autoregressive moving-average (CARMA) processes in Hilbert spaces. As driving noises of these processes we consider Levy processes in Hilbert space. We provide the basic definitions, show relevant…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
Effectively learning from sequential data is a longstanding goal of Artificial Intelligence, especially in the case of long sequences. From the dawn of Machine Learning, several researchers have pursued algorithms and architectures capable…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…
Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…
In this paper, we derive (local) orthogonality graphs for the popular continuous-time state space models, including in particular multivariate continuous-time ARMA (MCARMA) processes. In these (local) orthogonality graphs, vertices…