Frameworks for Generic Robust Inference, Mismeasured Spatial and Network Data, and Nonlinear Dimension Reduction

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This research project will conduct three sub-projects to improve upon existing statistical inference methods. There is a need for more generally applicable easy-to-use simulation-based statistical inference methods that exploit the availability of machine learning and other advanced data processing techniques. This project will develop more broadly applicable simulation-based inference methods. It will enable measurement-error robust inference in models based on spatial or network data. Finally, the project will improve the scalability of nonlinear dimension-reduction techniques. The simulation-based statistical inference methods developed under this project will have significant impact on data science in general. Research efforts increasingly rely on sophisticated data analysis methods where traditional simulation methods fail to provide reliable inference. Studies in the social, medical, and natural sciences increasingly are leveraging the broad availability of spatial or network data as well as high-dimensional data. These fields will be significantly impacted by the methods to be developed. Graduate students will play an important role in the development and implementation of the proposed methods.This project will push the boundary of existing inferential methods via the use of a broad range of novel concepts. The investigator will use the idea of super-sampling, in which an augmented sample, larger than the dataset itself, is generated and optimized to represent the true population. The research will exploit the idea of using neighboring data points in spatial or network data to disentangle the true signal from noise. The project extends that domain of applicability of existing resampling methods that are based on the observed sample or subsets to carefully constructed hypothetical populations larger than the sample. The project also will address the presence of measurement error in spatial or network contexts by viewing neighboring data points as repeated measurements of the true underlying variables of interest. These measurements do not conform to classical frameworks based on statistically independent errors and thus demand dedicated techniques. Finally, the nonlinear dimension-reduction techniques to be used will merge the concepts of optimal transport, entropy maximization, and simulation-based estimation in novel ways. Dimension reduction techniques have applications in fields as diverse as finance, psychology, neurology, data compression, information retrieval and processing, and machine learning.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.