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The safety concern for unmanned systems, namely the concern for the potential casualty caused by system abnormalities, has been a bottleneck for their development, especially in populated areas. Evidently, the collision between the unmanned…

Matrix splitting iteration methods play a vital role in solving large sparse linear systems. Their performance heavily depends on the splitting parameters, however, the approach of selecting optimal splitting parameters has not been well…

When fitting statistical models, some predictors are often found to be correlated with each other, and functioning together. Many group variable selection methods are developed to select the groups of predictors that are closely related to…

Forecasting driving behavior or other sensor measurements is an essential component of autonomous driving systems. Often real-world multivariate time series data is hard to model because the underlying dynamics are nonlinear and the…

We provide some basic and sensible definitions of different types of digital twins and recommendations on when and how to use them. Following up on our recent publication of the Learning Causal Digital Twin, this article reports on a…

We consider the problem of multivariate regression in a setting where the relevant predictors could be shared among different responses. We propose an algorithm which decomposes the coefficient matrix into the product of a long matrix and a…

Ensemble Kalman methods were initially developed to solve nonlinear data assimilation problems in oceanography, but are now popular in applications far beyond their original use cases. Of particular interest is climate model calibration. As…

Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…

Ensemble Kalman inversion is a parallelizable derivative-free method to solve inverse problems. The method uses an ensemble that follows the Kalman update formula iteratively to solve an optimization problem. The ensemble size is crucial to…

Time series analysis by state-space models is widely used in forecasting and extracting unobservable components like level, slope, and seasonality, along with explanatory variables. However, their reliance on traditional Kalman filtering…

Data mining, particularly the analysis of multivariate time series data, plays a crucial role in extracting insights from complex systems and supporting informed decision-making across diverse domains. However, assessing the similarity of…

The unscented Kalman filter is an algorithm capable of handling nonlinear scenarios. Uncertainty in process noise covariance may decrease the filter estimation performance or even lead to its divergence. Therefore, it is important to adjust…

In this paper, We propose a new style panel data factor stochastic volatility model with observable factors and unobservable factors based on the multivariate stochastic volatility model, which is mainly composed of three parts, such as the…

State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms.…

This study proposes a novel method for forecasting a scalar variable based on high-dimensional predictors that is applicable to various data distributions. In the literature, one of the popular approaches for forecasting with many…

We investigate the parameter estimation of regression models with fixed group effects, when the group variable is missing while group related variables are available. This problem involves clustering to infer the missing group variable…

In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signal's amplitude…

Uncertainty is an essential consideration for time series forecasting tasks. In this work, we specifically focus on quantifying the uncertainty of traffic forecasting. To achieve this, we develop Deep Spatio-Temporal Uncertainty…

This work embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and noisy discrete-time observations. The signal dynamics is…

Time series analysis is the process of building a model using statistical techniques to represent characteristics of time series data. Processing and forecasting huge time series data is a challenging task. This paper presents Approximation…