Generalization Error for Linear Regression under Distributed Learning

• URL: http://arxiv.org/abs/2004.14637v2
• Date: Mon, 4 May 2020 05:23:13 GMT
• Title: Generalization Error for Linear Regression under Distributed Learning
• Authors: Martin Hellkvist and Ay\c{c}a \"Oz\c{c}elikkale and Anders Ahl\'en
• Abstract summary: We consider the setting where the unknowns are distributed over a network of nodes. We present an analytical characterization of the dependence of the generalization error on the partitioning of the unknowns over nodes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Distributed learning facilitates the scaling-up of data processing by distributing the computational burden over several nodes. Despite the vast interest in distributed learning, generalization performance of such approaches is not well understood. We address this gap by focusing on a linear regression setting. We consider the setting where the unknowns are distributed over a network of nodes. We present an analytical characterization of the dependence of the generalization error on the partitioning of the unknowns over nodes. In particular, for the overparameterized case, our results show that while the error on training data remains in the same range as that of the centralized solution, the generalization error of the distributed solution increases dramatically compared to that of the centralized solution when the number of unknowns estimated at any node is close to the number of observations. We further provide numerical examples to verify our analytical expressions.

Related papers

• Collaborative Heterogeneous Causal Inference Beyond Meta-analysis [68.4474531911361]
  We propose a collaborative inverse propensity score estimator for causal inference with heterogeneous data. Our method shows significant improvements over the methods based on meta-analysis when heterogeneity increases.
  arXiv  Detail & Related papers  (2024-04-24T09:04:36Z)
• Distributed Bayesian Estimation in Sensor Networks: Consensus on Marginal Densities [15.038649101409804]
  We derive a distributed provably-correct algorithm in the functional space of probability distributions over continuous variables. We leverage these results to obtain new distributed estimators restricted to subsets of variables observed by individual agents. This relates to applications such as cooperative localization and federated learning, where the data collected at any agent depends on a subset of all variables of interest.
  arXiv  Detail & Related papers  (2023-12-02T21:10:06Z)
• Learning Linear Causal Representations from Interventions under General Nonlinear Mixing [52.66151568785088]
  We prove strong identifiability results given unknown single-node interventions without access to the intervention targets. This is the first instance of causal identifiability from non-paired interventions for deep neural network embeddings.
  arXiv  Detail & Related papers  (2023-06-04T02:32:12Z)
• Instance-Dependent Generalization Bounds via Optimal Transport [51.71650746285469]
  Existing generalization bounds fail to explain crucial factors that drive the generalization of modern neural networks. We derive instance-dependent generalization bounds that depend on the local Lipschitz regularity of the learned prediction function in the data space. We empirically analyze our generalization bounds for neural networks, showing that the bound values are meaningful and capture the effect of popular regularization methods during training.
  arXiv  Detail & Related papers  (2022-11-02T16:39:42Z)
• Learning Distributions by Generative Adversarial Networks: Approximation and Generalization [0.6768558752130311]
  We study how well generative adversarial networks learn from finite samples by analyzing the convergence rates of these models. Our analysis is based on a new inequality oracle that decomposes the estimation error of GAN into the discriminator and generator approximation errors. For generator approximation error, we show that neural network can approximately transform a low-dimensional source distribution to a high-dimensional target distribution.
  arXiv  Detail & Related papers  (2022-05-25T09:26:17Z)
• Robust Estimation for Nonparametric Families via Generative Adversarial Networks [92.64483100338724]
  We provide a framework for designing Generative Adversarial Networks (GANs) to solve high dimensional robust statistics problems. Our work extend these to robust mean estimation, second moment estimation, and robust linear regression. In terms of techniques, our proposed GAN losses can be viewed as a smoothed and generalized Kolmogorov-Smirnov distance.
  arXiv  Detail & Related papers  (2022-02-02T20:11:33Z)
• Decentralized Local Stochastic Extra-Gradient for Variational Inequalities [125.62877849447729]
  We consider distributed variational inequalities (VIs) on domains with the problem data that is heterogeneous (non-IID) and distributed across many devices. We make a very general assumption on the computational network that covers the settings of fully decentralized calculations. We theoretically analyze its convergence rate in the strongly-monotone, monotone, and non-monotone settings.
  arXiv  Detail & Related papers  (2021-06-15T17:45:51Z)
• Linear Regression with Distributed Learning: A Generalization Error Perspective [0.0]
  We investigate the performance of distributed learning for large-scale linear regression. We focus on the generalization error, i.e., the performance on unseen data. Our results show that the generalization error of the distributed solution can be substantially higher than that of the centralized solution.
  arXiv  Detail & Related papers  (2021-01-22T08:43:28Z)
• On the Benefits of Invariance in Neural Networks [56.362579457990094]
  We show that training with data augmentation leads to better estimates of risk and thereof gradients, and we provide a PAC-Bayes generalization bound for models trained with data augmentation. We also show that compared to data augmentation, feature averaging reduces generalization error when used with convex losses, and tightens PAC-Bayes bounds.
  arXiv  Detail & Related papers  (2020-05-01T02:08:58Z)

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.