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Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral characteristics of these time series data.…

Industrial Multivariate Time Series (MTS) is a critical view of the industrial field for people to understand the state of machines. However, due to data collection difficulty and privacy concerns, available data for building industrial…

Causal inference in a nonlinear system of multivariate timeseries is instrumental in disentangling the intricate web of relationships among variables, enabling us to make more accurate predictions and gain deeper insights into real-world…

Large language models (LLMs) have demonstrated their effectiveness in multivariate time series classification (MTSC). Effective adaptation of LLMs for MTSC necessitates informative data representations. Existing LLM-based methods directly…

Early and accurate detection of anomalies in time series data is critical, given the significant risks associated with false or missed detections. While MLP-based mixer models have shown promise in time series analysis, they lack a…

Anomaly detection in multivariate time series is a central challenge in industrial monitoring, as failures frequently arise from complex temporal dynamics and cross-sensor interactions. While recent deep learning models, including graph…

The goal of this paper is to study a distributed version of the gradient temporal-difference (GTD) learning algorithm for a class of multi-agent Markov decision processes (MDPs). The temporal-difference (TD) learning is a reinforcement…

We provide a new estimation method for conditional moment models via the martingale difference divergence (MDD).Our MDD-based estimation method is formed in the framework of a continuum of unconditional moment restrictions. Unlike the…

Extracting causal connections can advance interpretable AI and machine learning. Granger causality (GC) is a robust statistical method for estimating directed influences (DC) between signals. While GC has been widely applied to analysing…

We develop a multivariate functional autoregressive model (MFAR), which captures the cross-correlation among multiple functional time series and thus improves forecast accuracy. We estimate the parameters under the Bayesian dynamic linear…

Multivariate time series forecasting is extensively studied throughout the years with ubiquitous applications in areas such as finance, traffic, environment, etc. Still, concerns have been raised on traditional methods for incapable of…

The availability of relational data can offer new insights into the functioning of the economy. Nevertheless, modeling the dynamics in network data with multiple types of relationships is still a challenging issue. Stochastic block models…

We study the problem of automatically discovering Granger causal relations from observational multivariate time-series data.Vector autoregressive (VAR) models have been time-tested for this problem, including Bayesian variants and more…

Despite recent progress in time-series foundation models, challenges persist in improving representation learning and adapting to diverse downstream tasks. We introduce a General Time-series Model (GTM), which advances representation…

That physiological oscillations of various frequencies are present in fMRI signals is the rule, not the exception. Herein, we propose a novel theoretical framework, spatio-temporal Granger causality, which allows us to more reliably and…

We study modeling and inference with the Elliptical Gamma Distribution (EGD). We consider maximum likelihood (ML) estimation for EGD scatter matrices, a task for which we develop new fixed-point algorithms. Our algorithms are efficient and…

While time series diffusion models have received considerable focus from many recent works, the performance of existing models remains highly unstable. Factors limiting time series diffusion models include insufficient time series datasets…

Identifying directed interactions between species from time series of their population densities has many uses in ecology. This key statistical task is equivalent to causal time series inference, which connects to the Granger causality (GC)…

Multivariate time series data for real-world applications typically contain a significant amount of missing values. The dominant approach for classification with such missing values is to impute them heuristically with specific values…

Temporal point process as the stochastic process on continuous domain of time is commonly used to model the asynchronous event sequence featuring with occurrence timestamps. Thanks to the strong expressivity of deep neural networks, they…