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Changepoints are a very common feature of Big Data that arrive in the form of a data stream. In this paper, we study high-dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the…

Multivariate time series forecasting is essential in domains such as finance, transportation, climate, and energy. However, existing patch-based methods typically adopt fixed-length segmentation, overlooking the heterogeneity of local…

Temporal data, obtained in the setting where it is only possible to observe one time point per experiment, is widely used in different research fields, yet remains insufficiently addressed from the statistical point of view. Such data often…

This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the…

Temporal data, notably time series and spatio-temporal data, are prevalent in real-world applications. They capture dynamic system measurements and are produced in vast quantities by both physical and virtual sensors. Analyzing these data…

Functional time series (FTS) data have become increasingly available in real-world applications. Research on such data typically focuses on two objectives: curve reconstruction and forecasting, both of which require efficient dimension…

Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice of the…

Power systems operate under uncertainty originating from multiple factors that are impossible to account for deterministically. Distributional forecasting is used to control and mitigate risks associated with this uncertainty. Recent…

Within the calibration of material models, often the numerical results of a simulation model $y$ are compared with the experimental measurements $y^*$. Usually, the differences between measurements and simulation are minimized using least…

Deconstructing a time index into time granularities can assist in exploration and automated analysis of large temporal data sets. This paper describes classes of time deconstructions using linear and cyclic time granularities. Linear…

We study the probability distribution function of the long-time values of observables being time-evolved by Hamiltonians modeling clean and disordered one-dimensional chains of many spin-1/2 particles. In particular, we analyze the return…

Time series data have grown at an explosive rate in numerous domains and have stimulated a surge of time series modeling research. A comprehensive comparison of different time series models, for a considered data analytics task, provides…

We propose the first comprehensive treatment of high-dimensional time series factor models with multiple change-points in their second-order structure. We operate under the most flexible definition of piecewise stationarity, and estimate…

Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…

Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…

In the last years there has been a considerable increase in the availability of continuous sensor measurements in a wide range of application domains, such as Location-Based Services (LBS), medical monitoring systems, manufacturing plants…

Our predictions for particle physics processes are realized in a chain of complex simulators. They allow us to generate high-fidelity simulated data, but they are not well-suited for inference on the theory parameters with observed data. We…

High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…

Given a pair of multivariate time-series data of the same length and dimensions, an approach is proposed to select variables and time intervals where the two series are significantly different. In applications where one time series is an…

In the era of rapidly increasing amounts of time series data, classification of variable objects has become the main objective of time-domain astronomy. Classification of irregularly sampled time series is particularly difficult because the…