Iterative regularization in classification via hinge loss diagonal descent

• URL: http://arxiv.org/abs/2212.12675v2
• Date: Wed, 09 Oct 2024 09:23:34 GMT
• Title: Iterative regularization in classification via hinge loss diagonal descent
• Authors: Vassilis Apidopoulos, Tomaso Poggio, Lorenzo Rosasco, Silvia Villa,
• Abstract summary: Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. In this paper, we focus on iterative regularization in the context of classification.
• Score: 12.684351703991965
• License:
• Abstract: Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. On the one hand, it allows to design efficient algorithms controlling at the same time numerical and statistical accuracy. On the other hand it allows to shed light on the learning curves observed while training neural networks. In this paper, we focus on iterative regularization in the context of classification. After contrasting this setting with that of linear inverse problems, we develop an iterative regularization approach based on the use of the hinge loss function. More precisely we consider a diagonal approach for a family of algorithms for which we prove convergence as well as rates of convergence and stability results for a suitable classification noise model. Our approach compares favorably with other alternatives, as confirmed by numerical simulations.

Related papers

• A Mirror Descent-Based Algorithm for Corruption-Tolerant Distributed Gradient Descent [57.64826450787237]
  We show how to analyze the behavior of distributed gradient descent algorithms in the presence of adversarial corruptions. We show how to use ideas from (lazy) mirror descent to design a corruption-tolerant distributed optimization algorithm. Experiments based on linear regression, support vector classification, and softmax classification on the MNIST dataset corroborate our theoretical findings.
  arXiv  Detail & Related papers  (2024-07-19T08:29:12Z)
• Learning a Gaussian Mixture for Sparsity Regularization in Inverse Problems [2.375943263571389]
  In inverse problems, the incorporation of a sparsity prior yields a regularization effect on the solution. We propose a probabilistic sparsity prior formulated as a mixture of Gaussians, capable of modeling sparsity with respect to a generic basis. We put forth both a supervised and an unsupervised training strategy to estimate the parameters of this network.
  arXiv  Detail & Related papers  (2024-01-29T22:52:57Z)
• Intersection of Parallels as an Early Stopping Criterion [64.8387564654474]
  We propose a method to spot an early stopping point in the training iterations without the need for a validation set. For a wide range of learning rates, our method, called Cosine-Distance Criterion (CDC), leads to better generalization on average than all the methods that we compare against.
  arXiv  Detail & Related papers  (2022-08-19T19:42:41Z)
• On the generalization of learning algorithms that do not converge [54.122745736433856]
  Generalization analyses of deep learning typically assume that the training converges to a fixed point. Recent results indicate that in practice, the weights of deep neural networks optimized with gradient descent often oscillate indefinitely.
  arXiv  Detail & Related papers  (2022-08-16T21:22:34Z)
• Understanding the Generalization of Adam in Learning Neural Networks with Proper Regularization [118.50301177912381]
  We show that Adam can converge to different solutions of the objective with provably different errors, even with weight decay globalization. We show that if convex, and the weight decay regularization is employed, any optimization algorithms including Adam will converge to the same solution.
  arXiv  Detail & Related papers  (2021-08-25T17:58:21Z)
• Meta-Regularization: An Approach to Adaptive Choice of the Learning Rate in Gradient Descent [20.47598828422897]
  We propose textit-Meta-Regularization, a novel approach for the adaptive choice of the learning rate in first-order descent methods. Our approach modifies the objective function by adding a regularization term, and casts the joint process parameters.
  arXiv  Detail & Related papers  (2021-04-12T13:13:34Z)
• A Random Matrix Theory Approach to Damping in Deep Learning [0.7614628596146599]
  We conjecture that the inherent difference in generalisation between adaptive and non-adaptive gradient methods in deep learning stems from the increased estimation noise. We develop a novel random matrix theory based damping learner for second order optimiser inspired by linear shrinkage estimation.
  arXiv  Detail & Related papers  (2020-11-15T18:19:42Z)
• Analyzing the discrepancy principle for kernelized spectral filter learning algorithms [2.132096006921048]
  We study the discrepancy principle, as well as modifications based on smoothed residuals, for kernelized spectral filter learning algorithms. Our main theoretical bounds are oracle inequalities established for the empirical estimation error (fixed design), and for the prediction error (random design)
  arXiv  Detail & Related papers  (2020-04-17T20:08:44Z)
• Fiedler Regularization: Learning Neural Networks with Graph Sparsity [6.09170287691728]
  We introduce a novel regularization approach for deep learning that incorporates and respects the underlying graphical structure of the neural network. We propose to use the Fiedler value of the neural network's underlying graph as a tool for regularization.
  arXiv  Detail & Related papers  (2020-03-02T16:19:33Z)
• Optimization of Graph Total Variation via Active-Set-based Combinatorial Reconditioning [48.42916680063503]
  We propose a novel adaptive preconditioning strategy for proximal algorithms on this problem class. We show that nested-forest decomposition of the inactive edges yields a guaranteed local linear convergence rate. Our results suggest that local convergence analysis can serve as a guideline for selecting variable metrics in proximal algorithms.
  arXiv  Detail & Related papers  (2020-02-27T16:33:09Z)
• Adaptive Correlated Monte Carlo for Contextual Categorical Sequence Generation [77.7420231319632]
  We adapt contextual generation of categorical sequences to a policy gradient estimator, which evaluates a set of correlated Monte Carlo (MC) rollouts for variance control. We also demonstrate the use of correlated MC rollouts for binary-tree softmax models, which reduce the high generation cost in large vocabulary scenarios.
  arXiv  Detail & Related papers  (2019-12-31T03:01:55Z)

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.