Debkumar De - Academia.edu (original) (raw)
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Papers by Debkumar De
arXiv (Cornell University), Oct 27, 2020
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of depe... more Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear seemingly unrelated regression framework. We propose a joint predictor and graph selection model and develop an efficient collapsed Gibbs sampler algorithm to search the joint model space. Furthermore, we investigate its theoretical variable selection properties. We demonstrate our method on a variety of simulated data, concluding with a real data set from the TCPA project.
Estimating model parameters in dynamic model continues to be challenge. In my dissertation, we ha... more Estimating model parameters in dynamic model continues to be challenge. In my dissertation, we have introduced a Stochastic Approximation based parameter estimation approach under Ensemble Kalman Filter setup. Asymptotic properties of the resultant estimates are discussed here. We have compared our proposed method to current methods via simulation studies. We have demonstrated predictive performance of our proposed method on a large spatio-temporal data. In my other topic, we presented a method for simultaneous estimation of regression parameters and the covariance matrix, developed for a nonparametric Seemingly Unrelated Regression problem. This is a very flexible modeling technique that essentially performs a sparse high-dimensional multiple predictor(p), multiple responses(q) regression where the responses may be correlated. Such data appear abundantly in the fields of genomics, finance and econometrics. We illustrate and compare performances of our proposed techniques with previous analyses using both simulated and real multivariate data arising in econometrics and government. I would also like to thank Prof. Mohsen Pourahmadi for always patiently answering my silly questions, and giving me sound advice. Additionally, I would like to thank Prof. Akhil Datta-Gupta whose insightful comments have been extremely helpful. Prof. Anindya Bhadra and Prof. Anirban Bhattacharya's inputs also have been of invaluable help and I thank them profusely. Finally, I would like to take this formal opportunity to thank my parents and my wife for their continuous encouragement and unflinching support.
arXiv: Methodology, 2020
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of depe... more Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear seemingly unrelated regression framework. We propose a joint predictor and graph selection model and develop an efficient collapsed Gibbs sampler algorithm to search the joint model space. Furthermore, we investigate its theoretical variable selection properties. We demonstrate our method on a variety of simulated data, concluding with a real data set from the TCPA project.
arXiv (Cornell University), Oct 27, 2020
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of depe... more Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear seemingly unrelated regression framework. We propose a joint predictor and graph selection model and develop an efficient collapsed Gibbs sampler algorithm to search the joint model space. Furthermore, we investigate its theoretical variable selection properties. We demonstrate our method on a variety of simulated data, concluding with a real data set from the TCPA project.
Estimating model parameters in dynamic model continues to be challenge. In my dissertation, we ha... more Estimating model parameters in dynamic model continues to be challenge. In my dissertation, we have introduced a Stochastic Approximation based parameter estimation approach under Ensemble Kalman Filter setup. Asymptotic properties of the resultant estimates are discussed here. We have compared our proposed method to current methods via simulation studies. We have demonstrated predictive performance of our proposed method on a large spatio-temporal data. In my other topic, we presented a method for simultaneous estimation of regression parameters and the covariance matrix, developed for a nonparametric Seemingly Unrelated Regression problem. This is a very flexible modeling technique that essentially performs a sparse high-dimensional multiple predictor(p), multiple responses(q) regression where the responses may be correlated. Such data appear abundantly in the fields of genomics, finance and econometrics. We illustrate and compare performances of our proposed techniques with previous analyses using both simulated and real multivariate data arising in econometrics and government. I would also like to thank Prof. Mohsen Pourahmadi for always patiently answering my silly questions, and giving me sound advice. Additionally, I would like to thank Prof. Akhil Datta-Gupta whose insightful comments have been extremely helpful. Prof. Anindya Bhadra and Prof. Anirban Bhattacharya's inputs also have been of invaluable help and I thank them profusely. Finally, I would like to take this formal opportunity to thank my parents and my wife for their continuous encouragement and unflinching support.
arXiv: Methodology, 2020
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of depe... more Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear seemingly unrelated regression framework. We propose a joint predictor and graph selection model and develop an efficient collapsed Gibbs sampler algorithm to search the joint model space. Furthermore, we investigate its theoretical variable selection properties. We demonstrate our method on a variety of simulated data, concluding with a real data set from the TCPA project.