Sparse L0-norm based Kernel-free Quadratic Surface Support Vector Machines

• URL: http://arxiv.org/abs/2501.11268v1
• Date: Mon, 20 Jan 2025 04:26:34 GMT
• Title: Sparse L0-norm based Kernel-free Quadratic Surface Support Vector Machines
• Authors: Ahmad Mousavi, Ramin Zandvakili,
• Abstract summary: Kernel-free quadratic surface support vector machine (SVM) models have gained significant attention in machine learning. We propose sparse $ell_0$-norm based Kernel-free quadratic surface SVMs, designed to mitigate overfitting and enhance interpretability. Our analysis shows that the subproblems in this framework either admit closed-form solutions or can leverage duality theory to improve computational efficiency.
• Score: 0.0
• License:
• Abstract: Kernel-free quadratic surface support vector machine (SVM) models have gained significant attention in machine learning. However, introducing a quadratic classifier increases the model's complexity by quadratically expanding the number of parameters relative to the dimensionality of the data, exacerbating overfitting. To address this, we propose sparse $\ell_0$-norm based Kernel-free quadratic surface SVMs, designed to mitigate overfitting and enhance interpretability. Given the intractable nature of these models, we present a penalty decomposition algorithm to efficiently obtain first-order optimality points. Our analysis shows that the subproblems in this framework either admit closed-form solutions or can leverage duality theory to improve computational efficiency. Through empirical evaluations on real-world datasets, we demonstrate the efficacy and robustness of our approach, showcasing its potential to advance Kernel-free quadratic surface SVMs in practical applications while addressing overfitting concerns. All the implemented models and experiment codes are available at \url{https://github.com/raminzandvakili/L0-QSVM}.

Related papers

• Accelerated zero-order SGD under high-order smoothness and overparameterized regime [79.85163929026146]
  We present a novel gradient-free algorithm to solve convex optimization problems. Such problems are encountered in medicine, physics, and machine learning. We provide convergence guarantees for the proposed algorithm under both types of noise.
  arXiv  Detail & Related papers  (2024-11-21T10:26:17Z)
• Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inference [55.150117654242706]
  We show that model selection for computation-aware GPs trained on 1.8 million data points can be done within a few hours on a single GPU. As a result of this work, Gaussian processes can be trained on large-scale datasets without significantly compromising their ability to quantify uncertainty.
  arXiv  Detail & Related papers  (2024-11-01T21:11:48Z)
• Learning Analysis of Kernel Ridgeless Regression with Asymmetric Kernel Learning [33.34053480377887]
  This paper enhances kernel ridgeless regression with Locally-Adaptive-Bandwidths (LAB) RBF kernels. For the first time, we demonstrate that functions learned from LAB RBF kernels belong to an integral space of Reproducible Kernel Hilbert Spaces (RKHSs)
  arXiv  Detail & Related papers  (2024-06-03T15:28:12Z)
• Robust kernel-free quadratic surface twin support vector machine with capped $L_1$-norm distance metric [0.46040036610482665]
  This paper proposes a robust capped L_norm kernel-free surface twin support vector machine (CL_QTSVM) The robustness of our model is further improved by employing the capped L_norm distance metric. An iterative algorithm is developed to efficiently solve the proposed model.
  arXiv  Detail & Related papers  (2024-05-27T09:23:52Z)
• The Convex Landscape of Neural Networks: Characterizing Global Optima and Stationary Points via Lasso Models [75.33431791218302]
  Deep Neural Network Network (DNN) models are used for programming purposes. In this paper we examine the use of convex neural recovery models. We show that all the stationary non-dimensional objective objective can be characterized as the standard a global subsampled convex solvers program. We also show that all the stationary non-dimensional objective objective can be characterized as the standard a global subsampled convex solvers program.
  arXiv  Detail & Related papers  (2023-12-19T23:04:56Z)
• Learning Graphical Factor Models with Riemannian Optimization [70.13748170371889]
  This paper proposes a flexible algorithmic framework for graph learning under low-rank structural constraints. The problem is expressed as penalized maximum likelihood estimation of an elliptical distribution. We leverage geometries of positive definite matrices and positive semi-definite matrices of fixed rank that are well suited to elliptical models.
  arXiv  Detail & Related papers  (2022-10-21T13:19:45Z)
• Tensor Network Kalman Filtering for Large-Scale LS-SVMs [17.36231167296782]
  Least squares support vector machines are used for nonlinear regression and classification. A framework based on tensor networks and the Kalman filter is presented to alleviate the demanding memory and computational complexities. Results show that our method can achieve high performance and is particularly useful when alternative methods are computationally infeasible.
  arXiv  Detail & Related papers  (2021-10-26T08:54:03Z)
• Sparse Universum Quadratic Surface Support Vector Machine Models for Binary Classification [0.0]
  We design kernel-free Universum quadratic surface support vector machine models. We propose the L1 norm regularized version that is beneficial for detecting potential sparsity patterns in the Hessian of the quadratic surface. We conduct numerical experiments on both artificial and public benchmark data sets to demonstrate the feasibility and effectiveness of the proposed models.
  arXiv  Detail & Related papers  (2021-04-03T07:40:30Z)
• Efficient semidefinite-programming-based inference for binary and multi-class MRFs [83.09715052229782]
  We propose an efficient method for computing the partition function or MAP estimate in a pairwise MRF. We extend semidefinite relaxations from the typical binary MRF to the full multi-class setting, and develop a compact semidefinite relaxation that can again be solved efficiently using the solver.
  arXiv  Detail & Related papers  (2020-12-04T15:36:29Z)
• Memory and Computation-Efficient Kernel SVM via Binary Embedding and Ternary Model Coefficients [18.52747917850984]
  Kernel approximation is widely used to scale up kernel SVM training and prediction. Memory and computation costs of kernel approximation models are still too high if we want to deploy them on memory-limited devices. We propose a novel memory and computation-efficient kernel SVM model by using both binary embedding and binary model coefficients.
  arXiv  Detail & Related papers  (2020-10-06T09:41:54Z)
• Learnable Subspace Clustering [76.2352740039615]
  We develop a learnable subspace clustering paradigm to efficiently solve the large-scale subspace clustering problem. The key idea is to learn a parametric function to partition the high-dimensional subspaces into their underlying low-dimensional subspaces. To the best of our knowledge, this paper is the first work to efficiently cluster millions of data points among the subspace clustering methods.
  arXiv  Detail & Related papers  (2020-04-09T12:53:28Z)

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.