|Recovering Structure of Noisy Data through Hypothesis Testing
|Minoh Jeong, University of Minnesota, United States; Alex Dytso, Princeton University, United States; Martina Cardone, University of Minnesota, United States; H. Vincent Poor, Princeton University, United States
|E.6: Hypothesis Testing II
|Detection and Estimation
|Click here to download the manuscript
|Click here to watch in the Virtual Symposium
|This paper considers a noisy data structure recovery problem. Specifically, the goal is to investigate the following question: Given a noisy observation of the data, according to which permutation was the original data sorted? The main focus is on scenarios where data is generated according to an isotropic Gaussian distribution, and the perturbation consists of adding Gaussian noise with diagonal scalar covariance matrix. This problem is posed within a hypothesis testing framework. First, the optimal decision criterion is characterized and shown to be identical to the hypothesis of the observation. Then, by leveraging the structure of the optimal decision criterion, the probability of error is characterized. Finally, the logarithmic behavior (i.e., the exponent) of the probability of error is derived in the regime where the dimension of the data goes to infinity.