Out-of-Distribution Generalization in Kernel Regression

• URL: http://arxiv.org/abs/2106.02261v1
• Date: Fri, 4 Jun 2021 04:54:25 GMT
• Title: Out-of-Distribution Generalization in Kernel Regression
• Authors: Abdulkadir Canatar, Blake Bordelon, Cengiz Pehlevan
• Abstract summary: We study generalization in kernel regression when the training and test distributions are different. We identify an overlap matrix that quantifies the mismatch between distributions for a given kernel. We develop procedures for optimizing training and test distributions for a given data budget to find best and worst case generalizations under the shift.
• Score: 21.958028127426196
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In real word applications, data generating process for training a machine learning model often differs from what the model encounters in the test stage. Understanding how and whether machine learning models generalize under such distributional shifts have been a theoretical challenge. Here, we study generalization in kernel regression when the training and test distributions are different using methods from statistical physics. Using the replica method, we derive an analytical formula for the out-of-distribution generalization error applicable to any kernel and real datasets. We identify an overlap matrix that quantifies the mismatch between distributions for a given kernel as a key determinant of generalization performance under distribution shift. Using our analytical expressions we elucidate various generalization phenomena including possible improvement in generalization when there is a mismatch. We develop procedures for optimizing training and test distributions for a given data budget to find best and worst case generalizations under the shift. We present applications of our theory to real and synthetic datasets and for many kernels. We compare results of our theory applied to Neural Tangent Kernel with simulations of wide networks and show agreement. We analyze linear regression in further depth.

Related papers

• Generalizing to any diverse distribution: uniformity, gentle finetuning and rebalancing [55.791818510796645]
  We aim to develop models that generalize well to any diverse test distribution, even if the latter deviates significantly from the training data. Various approaches like domain adaptation, domain generalization, and robust optimization attempt to address the out-of-distribution challenge. We adopt a more conservative perspective by accounting for the worst-case error across all sufficiently diverse test distributions within a known domain.
  arXiv  Detail & Related papers  (2024-10-08T12:26:48Z)
• Learning Divergence Fields for Shift-Robust Graph Representations [73.11818515795761]
  In this work, we propose a geometric diffusion model with learnable divergence fields for the challenging problem with interdependent data. We derive a new learning objective through causal inference, which can guide the model to learn generalizable patterns of interdependence that are insensitive across domains.
  arXiv  Detail & Related papers  (2024-06-07T14:29:21Z)
• Gaussian Universality in Neural Network Dynamics with Generalized Structured Input Distributions [2.3020018305241337]
  We analyze the behavior of a deep learning system trained on inputs modeled as Gaussian mixtures to better simulate more general structured inputs. Under certain standardization schemes, the deep learning model converges toward Gaussian setting behavior, even when the input data follow more complex or real-world distributions.
  arXiv  Detail & Related papers  (2024-05-01T17:10:55Z)
• Amortized Inference for Causal Structure Learning [72.84105256353801]
  Learning causal structure poses a search problem that typically involves evaluating structures using a score or independence test. We train a variational inference model to predict the causal structure from observational/interventional data. Our models exhibit robust generalization capabilities under substantial distribution shift.
  arXiv  Detail & Related papers  (2022-05-25T17:37:08Z)
• More Than a Toy: Random Matrix Models Predict How Real-World Neural Representations Generalize [94.70343385404203]
  We find that most theoretical analyses fall short of capturing qualitative phenomena even for kernel regression. We prove that the classical GCV estimator converges to the generalization risk whenever a local random matrix law holds. Our findings suggest that random matrix theory may be central to understanding the properties of neural representations in practice.
  arXiv  Detail & Related papers  (2022-03-11T18:59:01Z)
• Predicting Unreliable Predictions by Shattering a Neural Network [145.3823991041987]
  Piecewise linear neural networks can be split into subfunctions. Subfunctions have their own activation pattern, domain, and empirical error. Empirical error for the full network can be written as an expectation over subfunctions.
  arXiv  Detail & Related papers  (2021-06-15T18:34:41Z)
• 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)
• Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks [17.188280334580195]
  Generalization beyond a training dataset is a main goal of machine learning. Recent observations in deep neural networks contradict conventional wisdom from classical statistics. We show that more data may impair generalization when noisy or not expressible by the kernel.
  arXiv  Detail & Related papers  (2020-06-23T17:53:11Z)
• Good Classifiers are Abundant in the Interpolating Regime [64.72044662855612]
  We develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers. We find that test errors tend to concentrate around a small typical value $varepsilon*$, which deviates substantially from the test error of worst-case interpolating model. Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice.
  arXiv  Detail & Related papers  (2020-06-22T21:12:31Z)
• Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks [17.188280334580195]
  We derive analytical expressions for the generalization performance of kernel regression as a function of the number of training samples. Our expressions apply to wide neural networks due to an equivalence between training them and kernel regression with the Neural Kernel Tangent (NTK) We verify our theory with simulations on synthetic data and MNIST dataset.
  arXiv  Detail & Related papers  (2020-02-07T00:03:40Z)

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.