Double Descent and Overfitting under Noisy Inputs and Distribution Shift for Linear Denoisers
- URL: http://arxiv.org/abs/2305.17297v3
- Date: Thu, 14 Mar 2024 23:02:53 GMT
- Title: Double Descent and Overfitting under Noisy Inputs and Distribution Shift for Linear Denoisers
- Authors: Chinmaya Kausik, Kashvi Srivastava, Rishi Sonthalia,
- Abstract summary: A concern about studying supervised denoising is that one might not always have noiseless training data from the test distribution.
Motivated by this, we study supervised denoising and noisy-input regression under distribution shift.
- Score: 3.481985817302898
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Despite the importance of denoising in modern machine learning and ample empirical work on supervised denoising, its theoretical understanding is still relatively scarce. One concern about studying supervised denoising is that one might not always have noiseless training data from the test distribution. It is more reasonable to have access to noiseless training data from a different dataset than the test dataset. Motivated by this, we study supervised denoising and noisy-input regression under distribution shift. We add three considerations to increase the applicability of our theoretical insights to real-life data and modern machine learning. First, while most past theoretical work assumes that the data covariance matrix is full-rank and well-conditioned, empirical studies have shown that real-life data is approximately low-rank. Thus, we assume that our data matrices are low-rank. Second, we drop independence assumptions on our data. Third, the rise in computational power and dimensionality of data have made it important to study non-classical regimes of learning. Thus, we work in the non-classical proportional regime, where data dimension $d$ and number of samples $N$ grow as $d/N = c + o(1)$. For this setting, we derive data-dependent, instance specific expressions for the test error for both denoising and noisy-input regression, and study when overfitting the noise is benign, tempered or catastrophic. We show that the test error exhibits double descent under general distribution shift, providing insights for data augmentation and the role of noise as an implicit regularizer. We also perform experiments using real-life data, where we match the theoretical predictions with under 1\% MSE error for low-rank data.
Related papers
- DiffImpute: Tabular Data Imputation With Denoising Diffusion Probabilistic Model [9.908561639396273]
We propose DiffImpute, a novel Denoising Diffusion Probabilistic Model (DDPM)
It produces credible imputations for missing entries without undermining the authenticity of the existing data.
It can be applied to various settings of Missing Completely At Random (MCAR) and Missing At Random (MAR)
arXiv Detail & Related papers (2024-03-20T08:45:31Z) - Learning with Noisy Foundation Models [95.50968225050012]
This paper is the first work to comprehensively understand and analyze the nature of noise in pre-training datasets.
We propose a tuning method (NMTune) to affine the feature space to mitigate the malignant effect of noise and improve generalization.
arXiv Detail & Related papers (2024-03-11T16:22:41Z) - Understanding and Mitigating the Label Noise in Pre-training on
Downstream Tasks [91.15120211190519]
This paper aims to understand the nature of noise in pre-training datasets and to mitigate its impact on downstream tasks.
We propose a light-weight black-box tuning method (NMTune) to affine the feature space to mitigate the malignant effect of noise.
arXiv Detail & Related papers (2023-09-29T06:18:15Z) - Learning to Abstain From Uninformative Data [20.132146513548843]
We study the problem of learning and acting under a general noisy generative process.
In this problem, the data distribution has a significant proportion of uninformative samples with high noise in the label.
We propose a novel approach to learning under these conditions via a loss inspired by the selective learning theory.
arXiv Detail & Related papers (2023-09-25T15:55:55Z) - On-the-fly Denoising for Data Augmentation in Natural Language
Understanding [101.46848743193358]
We propose an on-the-fly denoising technique for data augmentation that learns from soft augmented labels provided by an organic teacher model trained on the cleaner original data.
Our method can be applied to general augmentation techniques and consistently improve the performance on both text classification and question-answering tasks.
arXiv Detail & Related papers (2022-12-20T18:58:33Z) - The Optimal Noise in Noise-Contrastive Learning Is Not What You Think [80.07065346699005]
We show that deviating from this assumption can actually lead to better statistical estimators.
In particular, the optimal noise distribution is different from the data's and even from a different family.
arXiv Detail & Related papers (2022-03-02T13:59:20Z) - Provably Efficient Causal Reinforcement Learning with Confounded
Observational Data [135.64775986546505]
We study how to incorporate the dataset (observational data) collected offline, which is often abundantly available in practice, to improve the sample efficiency in the online setting.
We propose the deconfounded optimistic value iteration (DOVI) algorithm, which incorporates the confounded observational data in a provably efficient manner.
arXiv Detail & Related papers (2020-06-22T14:49:33Z) - Learning from Noisy Similar and Dissimilar Data [84.76686918337134]
We show how to learn a classifier from noisy S and D labeled data.
We also show important connections between learning from such pairwise supervision data and learning from ordinary class-labeled data.
arXiv Detail & Related papers (2020-02-03T19:59:16Z)
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.