Related papers: Complex trend inference for high-dimensional piece…

This work considers the problem of detecting signals from multiple sequentially observed data streams, where only one stream can be observed at every time instant. The goal is to detect signals as quickly as possible while controlling the…

The high-index saddle dynamics (HiSD) method [J. Yin, L. Zhang, and P. Zhang, {\it SIAM J. Sci. Comput., }41 (2019), pp.A3576-A3595] serves as an efficient tool for computing index-$k$ saddle points and constructing solution landscapes.…

Change detection in multivariate time series has applications in many domains, including health care and network monitoring. A common approach to detect changes is to compare the divergence between the distributions of a reference window…

We develop adaptive time-stepping strategies for It\^o-type stochastic differential equations (SDEs) with jump perturbations. Our approach builds on adaptive strategies for SDEs. Adaptive methods can ensure strong convergence of nonlinear…

The problem of sequential detection of anomalies in multimodal data is considered. The objective is to observe physical sensor data from CCTV cameras, and social media data from Twitter and Instagram to detect anomalous behaviors or events.…

Anomaly detection in surveillance videos is currently a challenge because of the diversity of possible events. We propose a deep convolutional neural network (CNN) that addresses this problem by learning a correspondence between common…

Accurate, long-term forecasting of pedestrian trajectories in highly dynamic and interactive scenes is a long-standing challenge. Recent advances in using data-driven approaches have achieved significant improvements in terms of prediction…

Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null…

As a highly expressive generative model, diffusion models have demonstrated exceptional success across various domains, including image generation, natural language processing, and combinatorial optimization. However, as data distributions…

Online joint estimation of unknown parameters and states in a dynamical system with uncertainty quantification is crucial in many applications. For example, digital twins dynamically update their knowledge of model parameters and states to…

For many real data, long term observation consists of different processes that coexist or occur one after the other. Those processes very often exhibit different statistical properties and thus before the further analysis the observed data…

Stationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus a rather attractive assumption to base statistical analysis on, especially for problems for which less general…

Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult…

Given high-dimensional time series data (e.g., sensor data), how can we detect anomalous events, such as system faults and attacks? More challengingly, how can we do this in a way that captures complex inter-sensor relationships, and…

Visualizing the uncertainty of ensemble simulations is challenging due to the large size and multivariate and temporal features of ensemble data sets. One popular approach to studying the uncertainty of ensembles is analyzing the positional…

Modern power systems with high penetration of inverter-based resources exhibit complex dynamic behaviors that challenge the scalability and generalizability of traditional stability assessment methods. This paper presents a dynamic…

Deep learning-based sequence models are extensively employed in Time Series Anomaly Detection (TSAD) tasks due to their effective sequential modeling capabilities. However, the ability of TSAD is limited by two key challenges: (i) the…

In recent years, change point detection for high dimensional data has become increasingly important in many scientific fields. Most literature develop a variety of separate methods designed for specified models (e.g. mean shift model,…

Accurate pedestrian trajectory prediction is of great importance for downstream tasks such as autonomous driving and mobile robot navigation. Fully investigating the social interactions within the crowd is crucial for accurate pedestrian…

We develop a projected least squares estimator for the change point parameter in a high dimensional time series model with a potential change point. Importantly we work under the setup where the jump size may be near the boundary of the…