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We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…
Predicting future operational risk losses gives rise to a significant challenge due to the heterogeneous and time-dependent structures present in real-world data. Furthermore, stress test exercises require examining the relationship with…
When environmental interaction is expensive, model-based reinforcement learning offers a solution by planning ahead and avoiding costly mistakes. Model-based agents typically learn a single-step transition model. In this paper, we propose a…
In this paper, we consider the problem of event classification with multi-variate time series data consisting of heterogeneous (continuous and categorical) variables. The complex temporal dependencies between the variables combined with…
In the burgeoning ecosystem of Internet of Things, multivariate time series (MTS) data has become ubiquitous, highlighting the fundamental role of time series forecasting across numerous applications. The crucial challenge of long-term MTS…
Multivariate time series present challenges to standard machine learning techniques, as they are often unlabeled, high dimensional, noisy, and contain missing data. To address this, we propose T-Rep, a self-supervised method to learn time…
Variational formulations of time-dependent PDEs in space and time yield $(d+1)$-dimensional problems to be solved numerically. This increases the number of unknowns as well as the storage amount. On the other hand, this approach enables…
Multivariate time series data suffer from the problem of missing values, which hinders the application of many analytical methods. To achieve the accurate imputation of these missing values, exploiting inter-correlation by employing the…
Correlation matrices contain a wide variety of spatio-temporal information about a dynamical system. Predicting correlation matrices from partial time series information of a few nodes characterizes the spatio-temporal dynamics of the…
For the application of MPC design in on-line regulation or tracking control problems, several studies have attempted to develop an accurate model, and realize adequate uncertainty description of linear or non-linear plants of the processes.…
Multivariate time series forecasting poses an ongoing challenge across various disciplines. Time series data often exhibit diverse intra-series and inter-series correlations, contributing to intricate and interwoven dependencies that have…
A foundation model is a machine learning model trained on a large and diverse set of data, typically using self-supervised learning-based pre-training techniques, that can be adapted to various downstream tasks. However, current research on…
Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical…
This paper gives an overview on how to develop a dense and deep neural network for making a time series prediction. First, the history and cornerstones in Artificial Intelligence and Machine Learning will be presented. After a short…
This paper studies sequence modeling for prediction tasks with long range dependencies. We propose a new formulation for state space models (SSMs) based on learning linear dynamical systems with the spectral filtering algorithm (Hazan et…
Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…
Data is essential to performing time series analysis utilizing machine learning approaches, whether for classic models or today's large language models. A good time-series dataset is advantageous for the model's accuracy, robustness, and…
Many methods for time-series forecasting are known in classical statistics, such as autoregression, moving averages, and exponential smoothing. The DeepAR framework is a novel, recent approach for time-series forecasting based on deep…
The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models…
We present Timer-XL, a causal Transformer for unified time series forecasting. To uniformly predict multidimensional time series, we generalize next token prediction, predominantly adopted for 1D token sequences, to multivariate next token…