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Natural spatiotemporal processes can be highly non-stationary in many ways, e.g. the low-level non-stationarity such as spatial correlations or temporal dependencies of local pixel values; and the high-level variations such as the…
Let $\mathbf {X}=\{X_t, t=1,2,... \}$ be a stationary Gaussian random process, with mean $EX_t=\mu$ and covariance function $\gamma(\tau)=E(X_t-\mu)(X_{t+\tau}-\mu)$. Let $f(\lambda)$ be the corresponding spectral density; a stationary…
We consider a purely fractionally deferenced process driven by a periodically time-varying long memory parameter. We will build an estimate for the vector parameters using the minimum Hellinger distance estimation. The results are…
This paper investigates bootstrap-based bias correction of semiparametric estimators of the long memory parameter, $d$, in fractionally integrated processes. The re-sampling method involves the application of the sieve bootstrap to data…
Processing spatial data is a key component in many learning tasks for autonomous driving such as motion forecasting, multi-agent simulation, and planning. Prior works have demonstrated the value in using SE(2) invariant network…
This paper contributes to the multivariate analysis of marked spatio-temporal point process data by introducing different partial point characteristics and extending the spatial dependence graph model formalism. Our approach yields a…
Inferring parameters of macro-kinetic growth models, typically represented by Ordinary Differential Equations (ODE), from the experimental data is a crucial step in bioprocess engineering. Conventionally, estimates of the parameters are…
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…
In regular dynamics, discrete maps are model presentations of discrete dynamical systems, and they may approximate continuous dynamical systems. Maps are used to investigate general properties of dynamical systems and to model various…
Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for…
For autonomous service robots to successfully perform long horizon tasks in the real world, they must act intelligently in partially observable environments. Most Task and Motion Planning approaches assume full observability of their state…
With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…
Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods…
We consider a time series $X=\{X_k, k\in\mathbb{Z}\}$ with memory parameter $d\in\mathbb{R}$. This time series is either stationary or can be made stationary after differencing a finite number of times. We study the "Local Whittle Wavelet…
This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential,…
Bisimulation metric is a robust behavioural semantics for probabilistic processes. Given any SOS specification of probabilistic processes, we provide a method to compute for each operator of the language its respective metric…
This article develops nonparametric cointegrating regression models with endogeneity and semi-long memory. We assume that semi-long memory is produced in the regressor process by tempering of random shock coefficients. The fundamental…
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we consider is employed…
Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…
The paper presents two representative classes of Impulsive Fractional Differential Equations defined with generalized Caputo\'s derivative, with fixed lower limit and changing lower limit, respectively. Memory principle is studied and…