Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Vector approximate message passing (VAMP) is a computationally simple approach to the recovery of a signal $\mathbf{x}$ from noisy linear measurements $\mathbf{y}=\mathbf{Ax}+\mathbf{w}$. Like the AMP proposed by Donoho, Maleki, and Montanari in 2009, VAMP is characterized by a rigorous state evolution (SE) that holds under certain large random matrices and that matches the replica prediction of optimality. But while AMP's SE holds only for large i.i.d. sub-Gaussian $\mathbf{A}$, VAMP's SE holds under the much larger class: right-rotationally invariant $\mathbf{A}$. To run VAMP, hover, one must specify the statistical parameters of the signal and noise. This work combines VAMP with Expectation-Maximization to yield an algorithm, EM-VAMP, that can jointly recover $\mathbf{x}$ while learning those statistical parameters. The fixed points of the proposed EM-VAMP algorithm are shown to be stationary points of a certain constrained free-energy, providing a variational interpretation of the algorithm. Numerical simulations show that EM-VAMP is robust to highly ill-conditioned $\mathbf{A}$ with performance nearly matching oracle-parameter VAMP.
['Alyson K. Fletcher', 'Philip Schniter']
I am writing a research paper on a idea Learning and Free Energies for Vector Approximate Message Passing
[{"from": "human", "value": "I am writing a research paper on a idea Learning and Free Energies for Vector Approximate Message Passing"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Vector approximate message passing (VAMP) is a computationally simple approach to the recovery of a signal $\\mathbf{x}$ from noisy linear measurements $\\mathbf{y}=\\mathbf{Ax}+\\mathbf{w}$. Like the AMP proposed by Donoho, Maleki, and Montanari in 2009, VAMP is characterized by a rigorous state evolution (SE) that holds under certain large random matrices and that matches the replica prediction of optimality. But while AMP's SE holds only for large i.i.d. sub-Gaussian $\\mathbf{A}$, VAMP's SE holds under the much larger class: right-rotationally invariant $\\mathbf{A}$. To run VAMP, hover, one must specify the statistical parameters of the signal and noise. This work combines VAMP with Expectation-Maximization to yield an algorithm, EM-VAMP, that can jointly recover $\\mathbf{x}$ while learning those statistical parameters. The fixed points of the proposed EM-VAMP algorithm are shown to be stationary points of a certain constrained free-energy, providing a variational interpretation of the algorithm. Numerical simulations show that EM-VAMP is robust to highly ill-conditioned $\\mathbf{A}$ with performance nearly matching oracle-parameter VAMP."}]