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Unsupervised Time series anomaly detection plays a crucial role in applications across industries. However, existing methods face significant challenges due to data distributional shifts across different domains, which are exacerbated by…

Predicting future probable values of model parameters, is an essential pre-requisite for assessing model decision reliability in an uncertain environment. Scenario Analysis is a methodology for modelling uncertainty in water resources…

Concurrent time series commonly arise in various applications, including when monitoring the environment such as in air quality measurement networks, weather stations, oceanographic buoys, or in paleo form such as lake sediments, tree…

Multivariate functional data from a complex system are naturally high-dimensional and have complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar…

Time series models often deal with extreme events and anomalies, both prevalent in real-world datasets. Such models often need to provide careful probabilistic forecasting, which is vital in risk management for extreme events such as…

Independent component analysis (ICA) is a fundamental statistical tool used to reveal hidden generative processes from observed data. However, traditional ICA approaches struggle with the rotational invariance inherent in Gaussian…

Statistical inference is central to many scientific endeavors, yet how it works remains unresolved. Answering this requires a quantitative understanding of the intrinsic interplay between statistical models, inference methods and data…

Linear causal analysis is central to a wide range of important application spanning finance, the physical sciences, and engineering. Much of the existing literature in linear causal analysis operates in the time domain. Unfortunately, the…

We propose an approach for multiple sequence alignment (MSA) derived from the dynamic time warping viewpoint and recent techniques of curve synchronization developed in the context of functional data analysis. Starting from pairwise…

Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…

We prove that a time series satisfying a (linear) multivariate autoregressive moving average (VARMA) model satisfies the same model assumption in the reversed time direction, too, if all innovations are normally distributed. This…

Time series forecasting plays an increasingly important role in modern business decisions. In today's data-rich environment, people often aim to choose the optimal forecasting model for their data. However, identifying the optimal model…

Anomaly detection on multivariate time-series is of great importance in both data mining research and industrial applications. Recent approaches have achieved significant progress in this topic, but there is remaining limitations. One major…

Motivated by risk assessment of coastal flooding, we consider time-consuming simulators with a spatial output. The aim is to perform sensitivity analysis (SA), quantifying the influence of input parameters on the output. There are three…

Principal component analysis (PCA) is a fundamental tool in multivariate statistics, yet its sensitivity to outliers and limitations in distributed environments restrict its effectiveness in modern large-scale applications. To address these…

Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…

When functional data manifest amplitude and phase variations, a commonly-employed framework for analyzing them is to take away the phase variation through a function alignment and then to apply standard tools to the aligned functions. A…

Recent advances in nonlinear Independent Component Analysis (ICA) provide a principled framework for unsupervised feature learning and disentanglement. The central idea in such works is that the latent components are assumed to be…

Recently, researchers have started applying convolutional neural networks (CNNs) with one-dimensional convolutions to clinical tasks involving time-series data. This is due, in part, to their computational efficiency, relative to recurrent…

Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…