Minimum-Norm Interpolation Under Covariate Shift

• URL: http://arxiv.org/abs/2404.00522v2
• Date: Wed, 17 Jul 2024 08:55:59 GMT
• Title: Minimum-Norm Interpolation Under Covariate Shift
• Authors: Neil Mallinar, Austin Zane, Spencer Frei, Bin Yu,
• Abstract summary: In-distribution research on high-dimensional linear regression has led to the identification of a phenomenon known as textitbenign overfitting We prove the first non-asymptotic excess risk bounds for benignly-overfit linear interpolators in the transfer learning setting.
• Score: 14.863831433459902
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Transfer learning is a critical part of real-world machine learning deployments and has been extensively studied in experimental works with overparameterized neural networks. However, even in the simplest setting of linear regression a notable gap still exists in the theoretical understanding of transfer learning. In-distribution research on high-dimensional linear regression has led to the identification of a phenomenon known as \textit{benign overfitting}, in which linear interpolators overfit to noisy training labels and yet still generalize well. This behavior occurs under specific conditions on the source covariance matrix and input data dimension. Therefore, it is natural to wonder how such high-dimensional linear models behave under transfer learning. We prove the first non-asymptotic excess risk bounds for benignly-overfit linear interpolators in the transfer learning setting. From our analysis, we propose a taxonomy of \textit{beneficial} and \textit{malignant} covariate shifts based on the degree of overparameterization. We follow our analysis with empirical studies that show these beneficial and malignant covariate shifts for linear interpolators on real image data, and for fully-connected neural networks in settings where the input data dimension is larger than the training sample size.

Related papers

• Cross-Entropy Is All You Need To Invert the Data Generating Process [29.94396019742267]
  Empirical phenomena suggest that supervised models can learn interpretable factors of variation in a linear fashion. Recent advances in self-supervised learning have shown that these methods can recover latent structures by inverting the data generating process. We prove that even in standard classification tasks, models learn representations of ground-truth factors of variation up to a linear transformation.
  arXiv  Detail & Related papers  (2024-10-29T09:03:57Z)
• Learning Linear Attention in Polynomial Time [115.68795790532289]
  We provide the first results on learnability of single-layer Transformers with linear attention. We show that linear attention may be viewed as a linear predictor in a suitably defined RKHS. We show how to efficiently identify training datasets for which every empirical riskr is equivalent to the linear Transformer.
  arXiv  Detail & Related papers  (2024-10-14T02:41:01Z)
• Convergence Analysis for Learning Orthonormal Deep Linear Neural Networks [27.29463801531576]
  We provide convergence analysis for training orthonormal deep linear neural networks. Our results shed light on how increasing the number of hidden layers can impact the convergence speed.
  arXiv  Detail & Related papers  (2023-11-24T18:46:54Z)
• Unsupervised Learning of Invariance Transformations [105.54048699217668]
  We develop an algorithmic framework for finding approximate graph automorphisms. We discuss how this framework can be used to find approximate automorphisms in weighted graphs in general.
  arXiv  Detail & Related papers  (2023-07-24T17:03:28Z)
• 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)
• On the ISS Property of the Gradient Flow for Single Hidden-Layer Neural Networks with Linear Activations [0.0]
  We investigate the effects of overfitting on the robustness of gradient-descent training when subject to uncertainty on the gradient estimation. We show that the general overparametrized formulation introduces a set of spurious equilibria which lay outside the set where the loss function is minimized.
  arXiv  Detail & Related papers  (2023-05-17T02:26:34Z)
• Data-driven emergence of convolutional structure in neural networks [83.4920717252233]
  We show how fully-connected neural networks solving a discrimination task can learn a convolutional structure directly from their inputs. By carefully designing data models, we show that the emergence of this pattern is triggered by the non-Gaussian, higher-order local structure of the inputs.
  arXiv  Detail & Related papers  (2022-02-01T17:11:13Z)
• Training invariances and the low-rank phenomenon: beyond linear networks [44.02161831977037]
  We show that when one trains a deep linear network with logistic or exponential loss on linearly separable data, the weights converge to rank-$1$ matrices. This is the first time a low-rank phenomenon is proven rigorously for nonlinear ReLU-activated feedforward networks. Our proof relies on a specific decomposition of the network into a multilinear function and another ReLU network whose weights are constant under a certain parameter directional convergence.
  arXiv  Detail & Related papers  (2022-01-28T07:31:19Z)
• Harmless interpolation in regression and classification with structured features [21.064512161584872]
  Overparametrized neural networks tend to perfectly fit noisy training data yet generalize well on test data. We present a general and flexible framework for upper bounding regression and classification risk in a reproducing kernel Hilbert space.
  arXiv  Detail & Related papers  (2021-11-09T15:12:26Z)
• The Interplay Between Implicit Bias and Benign Overfitting in Two-Layer Linear Networks [51.1848572349154]
  neural network models that perfectly fit noisy data can generalize well to unseen test data. We consider interpolating two-layer linear neural networks trained with gradient flow on the squared loss and derive bounds on the excess risk.
  arXiv  Detail & Related papers  (2021-08-25T22:01:01Z)
• Near-Optimal Linear Regression under Distribution Shift [63.87137348308034]
  We show that linear minimax estimators are within an absolute constant of the minimax risk even among nonlinear estimators for various source/target distributions.
  arXiv  Detail & Related papers  (2021-06-23T00:52:50Z)

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.