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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Generalized Sparse Bayesian Learning And Application To Image Reconstruction, Jan Glaubitz, Anne Gelb, Guohui Song
Generalized Sparse Bayesian Learning And Application To Image Reconstruction, Jan Glaubitz, Anne Gelb, Guohui Song
Mathematics & Statistics Faculty Publications
Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues of robustness due to parameter tuning. Moreover, since the recovery is limited to a point estimate, it is impossible to quantify the uncertainty, which is often desirable. Due to these inherent limitations, a sparse Bayesian learning approach is sometimes adopted to recover a posterior distribution of the unknown. Sparse Bayesian learning assumes that some linear transformation of the unknown is sparse. However, most of the methods developed are …
Robust Testing Of Paired Outcomes Incorporating Covariate Effects In Clustered Data With Informative Cluster Size, Sandipan Dutta
Robust Testing Of Paired Outcomes Incorporating Covariate Effects In Clustered Data With Informative Cluster Size, Sandipan Dutta
Mathematics & Statistics Faculty Publications
Paired outcomes are common in correlated clustered data where the main aim is to compare the distributions of the outcomes in a pair. In such clustered paired data, informative cluster sizes can occur when the number of pairs in a cluster (i.e., a cluster size) is correlated to the paired outcomes or the paired differences. There have been some attempts to develop robust rank-based tests for comparing paired outcomes in such complex clustered data. Most of these existing rank tests developed for paired outcomes in clustered data compare the marginal distributions in a pair and ignore any covariate effect on …
Representer Theorems In Banach Spaces: Minimum Norm Interpolation, Regularized Learning And Semi-Discrete Inverse Problems, Rui Wang, Yusheng Xu
Representer Theorems In Banach Spaces: Minimum Norm Interpolation, Regularized Learning And Semi-Discrete Inverse Problems, Rui Wang, Yusheng Xu
Mathematics & Statistics Faculty Publications
Learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation (MNI) problem, a regularized learning problem or, in general, a semi discrete inverse problem (SDIP), in either Hilbert spaces or Banach spaces. The goal of this paper is to systematically study solutions of these problems in Banach spaces. We aim at obtaining explicit representer theorems for their solutions, on which convenient solution methods can then be developed. For the MNI problem, the explicit representer theorems enable us to express the infimum …
Supervised Classification Using Finite Mixture Copula, Sumen Sen, Norou Diawara
Supervised Classification Using Finite Mixture Copula, Sumen Sen, Norou Diawara
Mathematics & Statistics Faculty Publications
Use of copula for statistical classification is recent and gaining popularity. For example, statistical classification using copula has been proposed for automatic character recognition, medical diagnostic and most recently in data mining. Classical discrimination rules assume normality. But in this data age time, this assumption is often questionable. In fact features of data could be a mixture of discrete and continues random variables. In this paper, mixture copula densities are used to model class conditional distributions. Such types of densities are useful when the marginal densities of the vector of features are not normally distributed and are of a mixed …
The Bivariate Erlang And Its Application In Modeling Recurrence Times Of Kidney Dialysis Data, Norou Diawara, S.H. Sathish Indika, Melva Grant, Edgard M. Maboudou-Tchao
The Bivariate Erlang And Its Application In Modeling Recurrence Times Of Kidney Dialysis Data, Norou Diawara, S.H. Sathish Indika, Melva Grant, Edgard M. Maboudou-Tchao
Mathematics & Statistics Faculty Publications
Recent advances in computer modeling allows us to find closer fits to data. Our emphasis is on the interdependence between occurrence at kidney dialysis. The interdependence between kidney dialysis occurrences is modelled by a bivariate exponential that we propose in this article. The application is shown on the McGilchrist and Aisbett kidney data set with the use of the exponential distribution. The proposed bivariate exponential model has exponential marginal densities, correlated via a latent random variables and with finite probability of simultaneous occurrence. Extension of the model to a bivariate Erlang type distribution with same shape parameter is presented.