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Improvement of time series forecasting accuracy through combining multiple models is an important as well as a dynamic area of research. As a result, various forecasts combination methods have been developed in literature. However, most of…

The Linear Parameter-Varying (LPV) framework provides a modeling and control design toolchain to address nonlinear (NL) system behavior via linear surrogate models. Despite major research effort on LPV data-driven modeling, a key…

Implicit neural representations (INRs) have recently emerged as a powerful tool that provides an accurate and resolution-independent encoding of data. Their robustness as general approximators has been shown in a wide variety of data…

In recent years, the modeling and analysis of interval-valued time series have garnered significant attention in the fields of econometrics and statistics. However, the existing literature primarily focuses on regression tasks while…

We study the problem of modelling high-dimensional, heavy-tailed time series data via a factor-adjusted vector autoregressive (VAR) model, which simultaneously accounts for pervasive co-movements of the variables by a handful of factors, as…

Many real-life applications involve simultaneously forecasting multiple time series that are hierarchically related via aggregation or disaggregation operations. For instance, commercial organizations often want to forecast inventories…

Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main aim of this paper is to develop a parametric identification strategy that delivers accurate and…

Dependence between nodes in a network is an important concept that pervades many areas including finance, politics, sociology, genomics and the brain sciences. One way to characterize dependence between components of a multivariate time…

We address a three-tier numerical framework based on manifold learning for the forecasting of high-dimensional time series. At the first step, we embed the time series into a reduced low-dimensional space using a nonlinear manifold learning…

We propose an efficient inference method for switching nonlinear dynamical systems. The key idea is to learn an inference network which can be used as a proposal distribution for the continuous latent variables, while performing exact…

Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning…

High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series,…

This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this…

Recently deep neural networks demonstrate competitive performances in classification and regression tasks for many temporal or sequential data. However, it is still hard to understand the classification mechanisms of temporal deep neural…

There exists recent work in computer vision, named VAR, that proposes a new autoregressive paradigm for image generation. Diverging from the vanilla next-token prediction, VAR structurally reformulates the image generation into a coarse to…

We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…

This paper presents a novel online identification algorithm for nonlinear regression models. The online identification problem is challenging due to the presence of nonlinear structure in the models. Previous works usually ignore the…

Models with a large number of latent variables are often used to fully utilize the information in big or complex data. However, they can be difficult to estimate using standard approaches, and variational inference methods are a popular…

Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications, including machine learning, but can be very difficult as…

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…