Jul 12, 2020
Unlabeled linear regression, or “linear regression with an unknown permutation”, has attracted increasing attentions due to its applications in linkage record and de-anonymization. However, its computation proves to be cumbersome and all existing algorithms require considerable time in the high dimensional regime. This paper proposes a one-step estimator which are optimal from both the computational and statistical sense. From the computational perspective, our estimator exhibits the same order of computational time as that of the oracle case, where the covariates are known in advance and only the permutation needs recovery. From the statistical perspective, when comparing with the necessary conditions for permutation recovery, our requirement on signal-to-noise ratio () agrees up to Ologlog n difference in certain regimes. Numerical experiments have also been provided to corroborate the above claims.
The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.
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