Efficient Convex Algorithms for Universal Kernel Learning

• URL: http://arxiv.org/abs/2304.07472v3
• Date: Mon, 28 Oct 2024 20:21:35 GMT
• Title: Efficient Convex Algorithms for Universal Kernel Learning
• Authors: Aleksandr Talitckii, Brendon K. Colbert, Matthew M. Peet,
• Abstract summary: An ideal set of kernels should: admit a linear parameterization (for tractability); dense in the set of all kernels (for accuracy) Previous algorithms for optimization of kernels were limited to classification and relied on computationally complex Semidefinite Programming (SDP) algorithms. We propose a SVD-QCQPQP algorithm which dramatically reduces the computational complexity as compared with previous SDP-based approaches.
• Score: 46.573275307034336
• License:
• Abstract: The accuracy and complexity of machine learning algorithms based on kernel optimization are determined by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for tractability); be dense in the set of all kernels (for robustness); be universal (for accuracy). Recently, a framework was proposed for using positive matrices to parameterize a class of positive semi-separable kernels. Although this class can be shown to meet all three criteria, previous algorithms for optimization of such kernels were limited to classification and furthermore relied on computationally complex Semidefinite Programming (SDP) algorithms. In this paper, we pose the problem of learning semiseparable kernels as a minimax optimization problem and propose a SVD-QCQP primal-dual algorithm which dramatically reduces the computational complexity as compared with previous SDP-based approaches. Furthermore, we provide an efficient implementation of this algorithm for both classification and regression -- an implementation which enables us to solve problems with 100 features and up to 30,000 datums. Finally, when applied to benchmark data, the algorithm demonstrates the potential for significant improvement in accuracy over typical (but non-convex) approaches such as Neural Nets and Random Forest with similar or better computation time.

Related papers

• Faster Adaptive Decentralized Learning Algorithms [24.379734053137597]
  We propose a class of faster distributed non decentralized algorithms (i.e. AdaMDOS and AdaMDOF) for adaptive learning and finite-sum optimization. Some experimental results demonstrate efficiency of our algorithms.
  arXiv  Detail & Related papers  (2024-08-19T08:05:33Z)
• Stochastic Optimization for Non-convex Problem with Inexact Hessian Matrix, Gradient, and Function [99.31457740916815]
  Trust-region (TR) and adaptive regularization using cubics have proven to have some very appealing theoretical properties. We show that TR and ARC methods can simultaneously provide inexact computations of the Hessian, gradient, and function values.
  arXiv  Detail & Related papers  (2023-10-18T10:29:58Z)
• Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates [49.84541884653309]
  A current standard approach to solving convex discrete optimization problems is the use of cutting-plane algorithms. Despite the existence of a number of general-purpose cut-generating algorithms, large-scale discrete optimization problems continue to suffer from intractability. We propose a method for accelerating cutting-plane algorithms via reinforcement learning.
  arXiv  Detail & Related papers  (2023-07-17T20:11:56Z)
• Accelerated First-Order Optimization under Nonlinear Constraints [73.2273449996098]
  We exploit between first-order algorithms for constrained optimization and non-smooth systems to design a new class of accelerated first-order algorithms. An important property of these algorithms is that constraints are expressed in terms of velocities instead of sparse variables.
  arXiv  Detail & Related papers  (2023-02-01T08:50:48Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• Provably Faster Algorithms for Bilevel Optimization [54.83583213812667]
  Bilevel optimization has been widely applied in many important machine learning applications. We propose two new algorithms for bilevel optimization. We show that both algorithms achieve the complexity of $mathcalO(epsilon-1.5)$, which outperforms all existing algorithms by the order of magnitude.
  arXiv  Detail & Related papers  (2021-06-08T21:05:30Z)
• A New Algorithm for Tessellated Kernel Learning [4.264192013842097]
  An ideal set of kernels should: admit a linear parameterization (for tractability); be dense in the set of all kernels (for robustness); be universal (for accuracy) The recently proposed Tesselated Kernels (TKs) is currently the only known class which meets all three criteria. By contrast, the 2-step algorithm proposed here scales to 10,000 data points and extends to the regression problem.
  arXiv  Detail & Related papers  (2020-06-13T18:33:31Z)

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.