CRII: CIF: New Directions in Learning from Data with Faulty Correspondence

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Contemporary data acquisition and analysis frequently involves the integration of multiple pieces of information about a common set of entities into a single comprehensive data set. In the absence of unique identifiers, merging corresponding fragments of data can be demanding and error-prone. This challenge is encountered in various settings covering applications in engineering such as sensor networks as well as in the work of government data analytics. In this project, it is explored to what extent functional relationships between different data sets can be leveraged to resolve potential ambiguities in the process of data integration. This question is also relevant to data confidentiality in situations in which an adversary tries to disclose sensitive information from anonymized data by using auxiliary data sources.The objective of the project is the development and statistical analysis of computationally feasible methods to safeguard downstream statistical analysis against errors in data linkage and to restore missing or faulty correspondences. In this context, linear regression in the presence of an unknown permutation is of central interest. One specific direction of research is the use of prior knowledge about the underlying permutation as commonly available in applications with the goal to sidestep computational barriers and to reduce the occurrent of ill-posed problems in statistical estimation. Emphasis will be placed on the characterization of the fundamental limits of recovery. Making advances in this regard will entail the use of tools from various areas including the theory of assignment problems, nonlinear optimization, high-dimensional and robust statistical inference, and random matrix theory. Results of the conducted research can potentially impact related problems such as regression under unknown linear transform, including blind deconvolution, and inference for permutations, as found in ranking, seriation, or graph matching.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.