Nonparametric input estimation in physiological systems: problems, methods, and case studies
Automatica (Journal of IFAC)
Bayesian Function Learning Using MCMC Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Finite-dimensional approximation of Gaussian processes
Proceedings of the 1998 conference on Advances in neural information processing systems II
Exploiting generative models in discriminative classifiers
Proceedings of the 1998 conference on Advances in neural information processing systems II
Training Support Vector Machines: an Application to Face Detection
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Brief Explicit formulas for LMI-based H2 filtering and deconvolution
Automatica (Journal of IFAC)
Brief Regularization networks for inverse problems: A state-space approach
Automatica (Journal of IFAC)
Wavelet-based image estimation: an empirical Bayes approach using Jeffrey's noninformative prior
IEEE Transactions on Image Processing
Regularization networks: fast weight calculation via Kalman filtering
IEEE Transactions on Neural Networks
Optimal smoothing of non-linear dynamic systems via Monte Carlo Markov chains
Automatica (Journal of IFAC)
Wavelet estimation by Bayesian thresholding and model selection
Automatica (Journal of IFAC)
A new kernel-based approach for linear system identification
Automatica (Journal of IFAC)
Prediction error identification of linear systems: A nonparametric Gaussian regression approach
Automatica (Journal of IFAC)
Distributed parametric and nonparametric regression with on-line performance bounds computation
Automatica (Journal of IFAC)
Estimation of building occupancy levels through environmental signals deconvolution
Proceedings of the 5th ACM Workshop on Embedded Systems For Energy-Efficient Buildings
The Journal of Machine Learning Research
| Hi-index | 22.15 |
We consider the semi-blind deconvolution problem; i.e., estimating an unknown input function to a linear dynamical system using a finite set of linearly related measurements where the dynamical system is known up to some system parameters. Without further assumptions, this problem is often ill-posed and ill-conditioned. We overcome this difficulty by modeling the unknown input as a realization of a stochastic process with a covariance that is known up to some finite set of covariance parameters. We first present an empirical Bayes method where the unknown parameters are estimated by maximizing the marginal likelihood/posterior and subsequently the input is reconstructed via a Tikhonov estimator (with the parameters set to their point estimates). Next, we introduce a Bayesian method that recovers the posterior probability distribution, and hence the minimum variance estimates, for both the unknown parameters and the unknown input function. Both of these methods use the eigenfunctions of the random process covariance to obtain an efficient representation of the unknown input function and its probability distributions. Simulated case studies are used to test the two methods and compare their relative performance.