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This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…

Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…

This paper deals with inference and prediction for multiple correlated time series, where one has also the choice of using a candidate pool of contemporaneous predictors for each target series. Starting with a structural model for the…

We formulate a recursive estimation problem for multiple dynamical systems coupled through a low dimensional stochastic input, and we propose an efficient sub-optimal solution. The suggested approach is an approximation of the Kalman filter…

Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…

The typical multi-task learning methods for spatio-temporal data prediction involve low-rank tensor computation. However, such a method have relatively weak performance when the task number is small, and we cannot integrate it into…

Irregular multivariate time series forecasting is critical in many real-world applications, where time series are irregularly sampled and exhibit dynamically evolving missingness patterns. Although existing methods perform well in offline…

We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…

With the advent of Big Data, nowadays in many applications databases containing large quantities of similar time series are available. Forecasting time series in these domains with traditional univariate forecasting procedures leaves great…

Solving semiparametric models can be computationally challenging because the dimension of parameter space may grow large with increasing sample size. Classical Newton's method becomes quite slow and unstable with intensive calculation of…

In this paper, we focus on batch state estimation for linear systems. This problem is important in applications such as environmental field estimation, robotic navigation, and target tracking. Its difficulty lies on that limited operational…

This paper is concerned with the problem of distributed Kalman filtering in a network of interconnected subsystems with distributed control protocols. We consider networks, which can be either homogeneous or heterogeneous, of linear…

Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…

In this article, we present a structured Kalman filter associated with the transformation matrix for observable Kalman canonical decomposition from conventional Kalman filter (CKF) in order to generate a more accurate time scale. The…

We introduce the inverse Kalman filter, which enables exact matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with linear computational cost. We integrate the inverse Kalman…

For time-dependent problems with high-contrast multiscale coefficients, the time step size for explicit methods is affected by the magnitude of the coefficient parameter. With a suitable construction of multiscale space, one can achieve a…

We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…

Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…

Parameters of the mathematical model describing many practical dynamical systems are prone to vary due to aging or renewal, wear and tear, as well as changes in environmental or service conditions. These variabilities will adversely affect…

This paper considers an approximate dynamic matrix factor model that accounts for the time series nature of the data by explicitly modelling the time evolution of the factors. We study estimation of the model parameters based on the…