Goran Marjanovic
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Goran Marjanovic has a total of 3 co-authors. Here are the top co-authors by number of shared publications:
- Magnus Orn Ulfarsson
Faculty of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland
2 shared publications - Victor Solo
School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, Australia
2 shared publications - Alfred Olivier Hero
University of Michigan
1 shared publication
Latest Publications
- 26 January 2018
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 63 (12) , 4035-4050
Numerical Methods for Stochastic Differential Equations in Matrix Lie Groups Made Simple
A large number of significant applications involve numerical solution of stochastic differential equations (SDE's) evolving in Lie Groups such as SO(3). In the engineering literature the proper formulation of numerical schemes has largely been ignored so that many schemes are flawed i.e. do not guarantee the solution stays in the Lie Group. There is a small mathematics literature but it is not easily accessible. With this in mind we give a directly accessible derivation of numerical schemes for solving SDE's that do not rely on differential geometry or advanced random process theory. In so doing we develop some new results. We illustrate the numerical schemes with simulations.
- 26 January 2018
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 63 (12) , 4035-4050
Numerical Methods for Stochastic Differential Equations in Matrix Lie Groups Made Simple
A large number of significant applications involve numerical solution of stochastic differential equations (SDE's) evolving in Lie Groups such as SO(3). In the engineering literature the proper formulation of numerical schemes has largely been ignored so that many schemes are flawed i.e. do not guarantee the solution stays in the Lie Group. There is a small mathematics literature but it is not easily accessible. With this in mind we give a directly accessible derivation of numerical schemes for solving SDE's that do not rely on differential geometry or advanced random process theory. In so doing we develop some new results. We illustrate the numerical schemes with simulations.
- 1 March 2016
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 4767-4771
Large-scale l0 sparse inverse covariance estimation
There has been significant interest in sparse inverse covariance estimation in areas such as statistics, machine learning, and signal processing. In this problem, the sparse inverse of a covariance matrix of a multivariate normal distribution is estimated. A Penalised Log-Likelihood (PLL) optimisation problem is solved to obtain the matrix estimator, where the penalty is responsible for inducing sparsity. The most natural sparsity promoting penalty is the non-convex l 0 function. Due to speed and memory limitations, the existing algorithms for dealing with the non-convex l 0 PLL problem are unable to be used in high dimensional settings. Here we address this issue by presenting a new block iterative approach for this problem, which can handle large-scale data sizes. Simulations demonstrate that our approach outperforms existing methods for this problem.
- 1 March 2016
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 4767-4771
Large-scale l0 sparse inverse covariance estimation
There has been significant interest in sparse inverse covariance estimation in areas such as statistics, machine learning, and signal processing. In this problem, the sparse inverse of a covariance matrix of a multivariate normal distribution is estimated. A Penalised Log-Likelihood (PLL) optimisation problem is solved to obtain the matrix estimator, where the penalty is responsible for inducing sparsity. The most natural sparsity promoting penalty is the non-convex l 0 function. Due to speed and memory limitations, the existing algorithms for dealing with the non-convex l 0 PLL problem are unable to be used in high dimensional settings. Here we address this issue by presenting a new block iterative approach for this problem, which can handle large-scale data sizes. Simulations demonstrate that our approach outperforms existing methods for this problem.
- Open Access
MIST: L0 Sparse Linear Regression with Momentum
Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the so-called $l_0$ norm. In this paper we develop a Momentumized Iterative Shrinkage Thresholding (MIST) algorithm for minimizing the resulting non-convex criterion and prove its convergence to a local minimizer. Simulations on large data sets show superior performance of the proposed method to other methods.Open AccessMIST: L0 Sparse Linear Regression with Momentum
Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the so-called $l_0$ norm. In this paper we develop a Momentumized Iterative Shrinkage Thresholding (MIST) algorithm for minimizing the resulting non-convex criterion and prove its convergence to a local minimizer. Simulations on large data sets show superior performance of the proposed method to other methods.