Related papers: Linear Processes for Functional Data
Process Mining is a branch of Data Science that aims to extract process-related information from event data contained in information systems, that is steadily increasing in amount. Many algorithms, and a general-purpose open source…
We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…
The study of the dynamic behavior of cross-sectional ranks over time for functional data and the ranks of the observed curves at each time point and their temporal evolution can yield valuable insights into the time dynamics of functional…
The object of this paper is to study the asymptotic dependence structure of the linear time series models with infinitely divisible innovations by the use of their characteristic functions. Autoregressive moving-average (ARMA) models and…
The standard approach for studying the periodic ARMA model with coefficients that vary over the seasons is to express it in a vector form. In this paper we introduce an alternative method which views the periodic formulation as a time…
Stationary and ergodic time series can be constructed using an s-vine decomposition based on sets of bivariate copula functions. The extension of such processes to infinite copula sequences is considered and shown to yield a rich class of…
Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or…
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…
When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated…
The study of topology is strictly speaking, a topic in pure mathematics. However in only a few years, Topological Data Analysis (TDA), which refers to methods of utilizing topological features in data (such as connected components, tunnels,…
Continuous-time autoregressive moving average (CARMA) processes have recently been used widely in the modeling of non-uniformly spaced data and as a tool for dealing with high-frequency data of the form $Y_{n\Delta}, n=0,1,2,...$, where…
By using the space of fuzzy numbers, in e.g. [5] have been considered several complete metric spaces (called here {\bf FN}-type spaces) endowed with addition and scalar multiplication, such that the metrics have nice properties but the…
The availability of large amounts of time series data, paired with the performance of deep-learning algorithms on a broad class of problems, has recently led to significant interest in the use of sequence-to-sequence models for time series…
The modeling of time-varying graph signals as stationary time-vertex stochastic processes permits the inference of missing signal values by efficiently employing the correlation patterns of the process across different graph nodes and time…
The process of data mining produces various patterns from a given data source. The most recognized data mining tasks are the process of discovering frequent itemsets, frequent sequential patterns, frequent sequential rules and frequent…
This chapter opens with a review of classic tools for regression, a subset of machine learning that seeks to find relationships between variables. With the advent of scientific machine learning this field has moved from a purely data-driven…
High-Dimensional Dynamic Factor Models are presented in detail: The main assumptions and their motivation, main results, illustrations by means of elementary examples. In particular, the role of singular ARMA models in the theory and…
Automated Planning is one of the main research field of Artificial Intelligence since its beginnings. Research in Automated Planning aims at developing general reasoners (i.e., planners) capable of automatically solve complex problems.…
Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning…
Linear models are a core component for statistical software that analyzes treatment effects. They are used in experimentation platforms where analysis is automated, as well as scientific studies where analysis is done locally and manually.…