Maximum Entropy Kernels for System Identification

A new nonparametric approach for system identification has been recently proposed where the impulse response is modeled as the realization of a zero-mean Gaussian process whose covariance (kernel) has to be estimated from data. In this scheme, quality of the estimates crucially depends on the parametrization of the covariance of the Gaussian process. A family of kernels that have been shown to be particularly effective in the system identification framework is the family of Diagonal/Correlated (DC) kernels. Maximum entropy properties of a related family of kernels, the Tuned/Correlated (TC) kernels, have been recently pointed out in the literature. In this paper we show that maximum entropy properties indeed extend to the whole family of DC kernels. The maximum entropy interpretation can be exploited in conjunction with results on matrix completion problems in the graphical models literature to shed light on the structure of the DC kernel. In particular, we prove that the DC kernel admits a closed-form factorization, inverse and determinant. These results can be exploited both to improve the numerical stability and to reduce the computational complexity associated with the computation of the DC estimator.Comment: Extends results of 2014 IEEE MSC Conference Proceedings (arXiv:1406.5706

A new kernel-based approach to system identification with quantized output data

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data.Comment: 10 pages, 4 figure

Locally Orderless Registration

Image registration is an important tool for medical image analysis and is used to bring images into the same reference frame by warping the coordinate field of one image, such that some similarity measure is minimized. We study similarity in image registration in the context of Locally Orderless Images (LOI), which is the natural way to study density estimates and reveals the 3 fundamental scales: the measurement scale, the intensity scale, and the integration scale. This paper has three main contributions: Firstly, we rephrase a large set of popular similarity measures into a common framework, which we refer to as Locally Orderless Registration, and which makes full use of the features of local histograms. Secondly, we extend the theoretical understanding of the local histograms. Thirdly, we use our framework to compare two state-of-the-art intensity density estimators for image registration: The Parzen Window (PW) and the Generalized Partial Volume (GPV), and we demonstrate their differences on a popular similarity measure, Normalized Mutual Information (NMI). We conclude, that complicated similarity measures such as NMI may be evaluated almost as fast as simple measures such as Sum of Squared Distances (SSD) regardless of the choice of PW and GPV. Also, GPV is an asymmetric measure, and PW is our preferred choice.Comment: submitte