A new arXiv paper by Daniel Busbib delves into the complex optimization landscape of Toeplitz covariance estimation. The research utilizes an overparameterized Carathéodory representation to analyze the problem, demonstrating that optimizing only amplitudes can lead to errors. The study proves that this nonlinear parameterization does not introduce additional stationary points, ensuring that stationary points of the Toeplitz maximum-likelihood problem correspond to stationary points of the overall problem. Furthermore, the paper shows that gradient descent converges to the true covariance in the population setting and to the unique maximum likelihood estimate under specific conditions, without requiring overparameterization. AI
IMPACT Provides theoretical insights into optimization challenges in signal processing and machine learning.
RANK_REASON The cluster contains a single academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=1.0]
- arXiv
- Carathéodory
- Daniel Busbib
- Gaussian function
- Gradient-based auto-tuning for machine learning and deep learning models
- Newton-Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems
- Toeplitz
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