Iterative Polynomial Approximation Algorithms for Inverse Graph Filters
Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose iterative polynomial approximation algorithms to implement the inverse filter with a polynomial graph filter of commutative graph shifts in a distributed manner. The proposed algorithms exhibit exponential convergence properties, and they can be implemented on distributed networks in which agents are equipped with a data processing subsystem for limited data storage and computation power, and with a one-hop communication subsystem for direct data exchange only with their adjacent agents. Our simulations show that the proposed polynomial approximation algorithms may converge faster than the Chebyshev polynomial approximation algorithm and the conventional gradient descent algorithm do.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Wiener filters on graphs and distributed polynomial approximation algorithms
In this paper, we consider Wiener filters to reconstruct deterministic and (wide-band) stationary graph signals from their observations corrupted by random noises, and we propose distributed algorithms to implement Wiene…
DenoisingPRISM: Distribution-free Adaptive Computation of Matrix Functions for Accelerating Neural Network Training
Matrix functions such as square root, inverse roots, and orthogonalization play a central role in preconditioned gradient methods for neural network training. This has motivated the development of iterative algorithms th…
Improved algorithms for learning quantum Hamiltonians, via flat polynomials
We give an improved algorithm for learning a quantum Hamiltonian given copies of its Gibbs state, that can succeed at any temperature. Specifically, we improve over the work of Bakshi, Liu, Moitra, and Tang [BLMT24], by …
An Analytic Solution to the Inverse Ising Problem in the Tree-reweighted Approximation
Many iterative and non-iterative methods have been developed for inverse problems associated with Ising models. Aiming to derive an accurate non-iterative method for the inverse problems, we employ the tree-reweighted ap…
Belief Propagation, Bethe Approximation and Polynomials
Factor graphs are important models for succinctly representing probability distributions in machine learning, coding theory, and statistical physics. Several computational problems, such as computing marginals and partit…