arXiv subjects

Subhadra Dasgupta

Publications and source records attributed to Subhadra Dasgupta.

3 recordsLinked to original sources

arXiv2024

Efficient subsampling for exponential family models

We propose a novel two-stage subsampling algorithm based on optimal design principles. In the first stage, we use a density-based clustering algorithm to identify an approximating design space for the predictors from an initial subsample. Next, we determine an optimal approximate design on this design space. Finally, we use matrix distances such as the Procrustes, Frobenius, and square-root distance to define the remaining subsample, such that its points are "closest" to the support points of the optimal design. Our approach reflects the specific nature of the information matrix as a weighted sum of non-negative definite Fisher information matrices evaluated at the design points and applies to a large class of regression models including models where the Fisher information is of rank larger than $1$.

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arXiv2022

Optimal designs for some bivariate cokriging models

This article focuses on the estimation and design aspects of a bivariate collocated cokriging experiment. For a large class of covariance matrices, a linear dependency criterion is identified, which allows the best linear unbiased estimator of the primary variable in a bivariate collocated cokriging setup to reduce to a univariate kriging estimator. Exact optimal designs for efficient prediction for such simple and ordinary reduced cokriging models with one-dimensional inputs are determined. Designs are found by minimizing the maximum and the integrated prediction variance, where the primary variable is an Ornstein-Uhlenbeck process. For simple and ordinary cokriging models with known covariance parameters, the equispaced design is shown to be optimal for both criterion functions. The more realistic scenario of unknown covariance parameters is addressed by assuming prior distributions on the parameter vector, thus adopting a Bayesian approach to the design problem. The equispaced design is proved to be the Bayesian optimal design for both criteria. The work is motivated by designing an optimal water monitoring system for an Indian river.

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arXiv2022

G-optimal grid designs for kriging models

This work is focused on finding G-optimal designs theoretically for kriging models with two-dimensional inputs and separable exponential covariance structures. For design comparison, the notion of evenness of two-dimensional grid designs is developed. The mathematical relationship between the design and the supremum of the mean squared prediction error ($SMSPE$) function is studied and then optimal designs are explored for both prospective and retrospective design scenarios. In the case of prospective designs, the new design is developed before the experiment is conducted and the regularly spaced grid is shown to be the G-optimal design. The retrospective designs are constructed by adding or deleting points from an already existing design. Deterministic algorithms are developed to find the best possible retrospective designs (which minimizes the $SMSPE$). It is found that a more evenly spread design under the G-optimality criterion leads to the best possible retrospective design. For all the cases of finding the optimal prospective designs and the best possible retrospective designs, both frequentist and Bayesian frameworks have been considered. The proposed methodology for finding retrospective designs is illustrated with a methane flux monitoring design.

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