Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials

• URL: http://arxiv.org/abs/2302.00596v1
• Date: Fri, 30 Dec 2022 17:07:26 GMT
• Title: Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials
• Abstract summary: We propose a new algorithm for the computation of Racahs called Improved Stabilization (ImSt) ImSt works for wider range of parameters until higher degree than the current algorithms.
• Score: 0.6445605125467573
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: One of the most effective orthogonal moments, discrete Racah polynomials (DRPs) and their moments are used in many disciplines of sciences, including image processing, and computer vision. Moments are the projections of a signal on the polynomial basis functions. Racah polynomials were introduced by Wilson and modified by Zhu for image processing and they are orthogonal on a discrete set of samples. However, when the moment order is high, they experience the issue of numerical instability. In this paper, we propose a new algorithm for the computation of DRPs coefficients called Improved Stabilization (ImSt). In the proposed algorithm, {the DRP plane is partitioned into four parts, which are asymmetric because they rely on the values of the polynomial size and the DRP parameters.} The logarithmic gamma function is utilized to compute the initial values, which empower the computation of the initial value for a wide range of DRP parameter values as well as large size of the polynomials. In addition, a new formula is used to compute the values of the initial sets based on the initial value. Moreover, we optimized the use of the stabilizing condition in specific parts of the algorithm. ImSt works for wider range of parameters until higher degree than the current algorithms. We compare it with the other methods in a number of experiments.

Related papers

• A Polynomial-time Algorithm for Online Sparse Linear Regression with Improved Regret Bound under Weaker Conditions [75.69959433669244]
  We study the problem of online sparse linear regression (OSLR) where the algorithms are restricted to accessing only $k$ out of $d$ per instance for prediction.<n>We introduce a new extend-time algorithm, which significantly improves previous regret bounds.
  arXiv  Detail & Related papers  (2025-10-31T05:02:33Z)
• Differentially Private Optimization with Sparse Gradients [60.853074897282625]
  We study differentially private (DP) optimization problems under sparsity of individual gradients. Building on this, we obtain pure- and approximate-DP algorithms with almost optimal rates for convex optimization with sparse gradients.
  arXiv  Detail & Related papers  (2024-04-16T20:01:10Z)
• GINN-LP: A Growing Interpretable Neural Network for Discovering Multivariate Laurent Polynomial Equations [1.1142444517901018]
  We propose GINN-LP, an interpretable neural network, to discover the form of a Laurent Polynomial equation. To the best of our knowledge, this is the first neural network that can discover arbitrary terms without any prior information on the order. We show that GINN-LP outperforms the state-of-theart symbolic regression methods on datasets.
  arXiv  Detail & Related papers  (2023-12-18T03:44:29Z)
• Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applications [8.438718130535296]
  We prove upper bounds on the covering number of sets in Euclidean space. We show that bounds improve the best known general bound by Yomdin-Comte. We illustrate the power of the result on three computational applications.
  arXiv  Detail & Related papers  (2023-11-09T03:06:59Z)
• Numerical Methods for Convex Multistage Stochastic Optimization [86.45244607927732]
  We focus on optimisation programming (SP), Optimal Control (SOC) and Decision Processes (MDP) Recent progress in solving convex multistage Markov problems is based on cutting planes approximations of the cost-to-go functions of dynamic programming equations. Cutting plane type methods can handle multistage problems with a large number of stages, but a relatively smaller number of state (decision) variables.
  arXiv  Detail & Related papers  (2023-03-28T01:30:40Z)
• Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm [62.997667081978825]
  We propose a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are used through the use of plug-in empirical Bayes estimates. The proposed approach is implemented in the R package probe.
  arXiv  Detail & Related papers  (2022-09-16T19:15:50Z)
• Alternating Mahalanobis Distance Minimization for Stable and Accurate CP Decomposition [4.847980206213335]
  We introduce a new formulation for deriving singular values and vectors of a tensor by considering the critical points of a function different from what is used in the previous work. We show that a subsweep of this algorithm can achieve a superlinear convergence rate for exact CPD with known rank. We then view the algorithm as optimizing a Mahalanobis distance with respect to each factor with ground metric dependent on the other factors.
  arXiv  Detail & Related papers  (2022-04-14T19:56:36Z)
• Computational-Statistical Gaps in Reinforcement Learning [23.517741855454044]
  We show a reduction from Unique-Sat, where we convert a CNF formula into an MDP Hypothesis with deterministic transitions, constant number of actions and low dimensional linear optimal value functions. This result also exhibits the first computational-statistical gap in reinforcement learning with linear function approximation.
  arXiv  Detail & Related papers  (2022-02-11T04:48:35Z)
• Fast Computation of Hahn Polynomials for High Order Moments [2.022925087410209]
  This paper developed a new mathematical model for computing the initial value of the DHP and for different values of DHP parameters ($alpha$ and $beta$) It is compared with state-of-the-art algorithms in terms of computational cost and the maximum size that can be correctly generated.
  arXiv  Detail & Related papers  (2021-11-10T22:28:21Z)
• Numerical Solution of Stiff Ordinary Differential Equations with Random Projection Neural Networks [0.0]
  We propose a numerical scheme based on Random Projection Neural Networks (RPNN) for the solution of Ordinary Differential Equations (ODEs) We show that our proposed scheme yields good numerical approximation accuracy without being affected by the stiffness, thus outperforming in same cases the textttode45 and textttode15s functions.
  arXiv  Detail & Related papers  (2021-08-03T15:49:17Z)
• Average-Reward Off-Policy Policy Evaluation with Function Approximation [66.67075551933438]
  We consider off-policy policy evaluation with function approximation in average-reward MDPs. bootstrapping is necessary and, along with off-policy learning and FA, results in the deadly triad. We propose two novel algorithms, reproducing the celebrated success of Gradient TD algorithms in the average-reward setting.
  arXiv  Detail & Related papers  (2021-01-08T00:43:04Z)
• Determinantal Point Processes in Randomized Numerical Linear Algebra [80.27102478796613]
  Numerical Linear Algebra (RandNLA) uses randomness to develop improved algorithms for matrix problems that arise in scientific computing, data science, machine learning, etc. Recent work has uncovered deep and fruitful connections between DPPs and RandNLA which lead to new guarantees and improved algorithms.
  arXiv  Detail & Related papers  (2020-05-07T00:39:52Z)
• Optimal Randomized First-Order Methods for Least-Squares Problems [56.05635751529922]
  This class of algorithms encompasses several randomized methods among the fastest solvers for least-squares problems. We focus on two classical embeddings, namely, Gaussian projections and subsampled Hadamard transforms. Our resulting algorithm yields the best complexity known for solving least-squares problems with no condition number dependence.
  arXiv  Detail & Related papers  (2020-02-21T17:45:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.