Related papers: Linear Processes for Functional Data

In recent years, Large Language Models (LLMs) have emerged as a prominent area of interest across various research domains, including Process Mining (PM). Current applications in PM have predominantly centered on prompt engineering…

Time series prediction covers a vast field of every-day statistical applications in medical, environmental and economic domains. In this paper we develop nonparametric prediction strategies based on the combination of a set of 'experts' and…

The idea of functional programming has played a big role in shaping today's landscape of mainstream programming languages. Another concept that dominates the current programming style is Dijkstra's structured programming. Both concepts have…

In this paper, we consider function-indexed normalized weighted integrated periodograms for equidistantly sampled multivariate continuous-time state space models which are multivariate continuous-time ARMA processes. Thereby, the sampling…

We live in a world driven by data. The amount of it outgrows anyone's ability to oversee it or even observe its scope. Along with all the advances in the space of data management, there is still a significant lack of formalism and…

The continued success of Large Language Models (LLMs) and other generative artificial intelligence approaches highlights the advantages that large information corpora can have over rigidly defined symbolic models, but also serves as a…

Classical automata theory is far more capable of modeling complex digital systems than is widely acknowledged in the ``formal methods'' literature. This paper takes a second look at automata theory methods that were mostly developed in the…

Partial observations of continuous time-series dynamics at arbitrary time stamps exist in many disciplines. Fitting this type of data using statistical models with continuous dynamics is not only promising at an intuitive level but also has…

Time series data is being used everywhere, from sales records to patients' health evolution metrics. The ability to deal with this data has become a necessity, and time series analysis and forecasting are used for the same. Every Machine…

Real-world problems of operations research are typically high-dimensional and combinatorial. Linear programs are generally used to formulate and efficiently solve these large decision problems. However, in multi-period decision problems, we…

The field of Machine Learning has changed significantly since the 1970s. However, its most basic principle, Empirical Risk Minimization (ERM), remains unchanged. We propose Functional Risk Minimization~(FRM), a general framework where…

Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…

Time series analysis is pivotal in domains like financial forecasting and biomedical monitoring, yet traditional methods are constrained by limited nonlinear feature representation and long-term dependency capture. The emergence of Large…

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…

The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares…

Time series analysis stands as a focal point within the data mining community, serving as a cornerstone for extracting valuable insights crucial to a myriad of real-world applications. Recent advances in Foundation Models (FMs) have…

When regularity lemmas were first developed in the 1970s, they were described as results that promise a partition of any graph into a ``small'' number of parts, such that the graph looks ``similar'' to a random graph on its edge subsets…

Random processes with stationary increments and intrinsic random processes are two concepts commonly used to deal with non-stationary random processes. They are broader classes than stationary random processes and conceptually closely…

Process analytics is an umbrella of data-driven techniques which includes making predictions for individual process instances or overall process models. At the instance level, various novel techniques have been recently devised, tackling…

Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…