This paper develops a Bayesian procedure for estimation and forecasting of the volatility of multivariate time series. The foundation of this work is the matrix-variate dynamic linear model, for the volatility of which we adopt a multiplicative stochastic evolution, using Wishart and singular multivariate beta distributions. A diagonal matrix of discount factors is employed in order to discount...

Stochastic gradient optimization is a class of widely used algorithms for training machine learning models. To optimize an objective, it uses the noisy gradient computed from the random data samples instead of the true gradient computed from the entire dataset. However, when the variance of the noisy gradient is large, the algorithm might spend much time bouncing around, leading to slower conve...

Adaptive Monte Carlo methods are simulation efficiency improvement techniques designed to adaptively tune simulation estimators. Most of the work on adaptive Monte Carlo methods has been devoted to adaptively tuning importance sampling schemes. We instead focus on adaptive methods based on control variate schemes. We introduce two adaptive control variate methods, and develop their asymptotic p...

We present a general control variate method for Monte Carlo estimation of the expectations of the functionals of Lévy processes. It is based on fast numerical inversion of the cumulative distribution functions and exploits the strong correlation between the increments of the original process and Brownian motion. In the suggested control variate framework, a similar functional of Brownian motion...

Integration of rich sensor technologies with everyday applications, such as gesture recognition and health monitoring, has raised the importance of the ability to e‚ectively search and analyze multivariate time series data. Consequently, various time series distance measures (such as Euclidean distance, edit distance, and dynamic time warping) have been extended from uni-variate to multi-variat...

Matrix-variate observations are frequently encountered in many contemporary statistical problems due to a rising need to organize and analyze data with structured information. In this paper, we propose a novel sparse matrix graphical model for this type of statistical problems. By penalizing respectively two precision matrices corresponding to the rows and columns, our method yields a sparse ma...