Related papers: Finite time large deviations via matrix product st…
High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology. To achieve significant dimension reduction while preserving the intrinsic matrix…
A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307…
Dynamic time warping constitutes a major tool for analyzing time series. In particular, computing a mean series of a given sample of series in dynamic time warping spaces (by minimizing the Fr\'echet function) is a challenging computational…
Temporal-difference (TD) networks are a class of predictive state representations that use well-established TD methods to learn models of partially observable dynamical systems. Previous research with TD networks has dealt only with…
We compute the joint large deviation rate functional in the limit of large time for the current flowing through the edges of a finite graph on which a boundary-driven system of stochastic particles evolves with zero-range dynamics.This…
We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed…
Utilization of multiple trajectories of a dynamical system model provides us with several benefits in approximation of time series. For short term predictions a high accuracy can be achieved via switches to new trajectory at any time.…
We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear…
We build on a previous statistical model for distributed systems and formulate it in a way that the deterministic and stochastic processes within the system are clearly separable. We show how internal fluctuations can be analysed in a…
We present a method to extend the finite element library FEniCS to solve problems with domains in dimensions above three by constructing tensor product finite elements. This methodology only requires that the high dimensional domain is…
We solve two problems related to the fluctuations of time-integrated functionals of Markov diffusions, used in physics to model nonequilibrium systems. In the first we derive and illustrate the appropriate boundary conditions on the…
Deciding the best future execution time is a critical task in many business activities while evolving time series forecasting, and optimal timing strategy provides such a solution, which is driven by observed data. This solution has plenty…
Temporal difference learning (TD) is a simple iterative algorithm used to estimate the value function corresponding to a given policy in a Markov decision process. Although TD is one of the most widely used algorithms in reinforcement…
We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We…
Real world evolves in continuous time but computations are done from finite samples. Therefore, we study algorithms using finite observations in continuous-time linear dynamical systems. We first study the system identification problem, and…
For minimization problems without 2nd derivative information, methods that estimate Hessian matrices can be very effective. However, conventional techniques generate dense matrices that are prohibitive for large problems. Limited-memory…
Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…
Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors.…
We explore how matrix bootstrap techniques can be used to constrain matrix and tensor models at finite $N$, where $N$ is the dimension of the matrix/tensor, taking a Gaussian model with a quartic interaction as example. For matrix models,…
Stationary states of stochastic models, which have $N$ states per site, in matrix product form are considered. First we give a necessary condition for the existence of a finite $M$-dimensional matrix product state for any ${N,M}$. Second,…