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The problem of benign overfitting asks whether it is possible for a model to perfectly fit noisy training data and still generalize well. We study benign overfitting in two- layer leaky ReLU networks trained with the hinge loss on a binary classification task. We consider input data that can be decomposed into the sum of a common signal and a random noise component, that lie on subspaces orthogonal to one another. We characterize conditions on the signal to noise ratio (SNR) of the model parameters giving rise to benign versus non-benign (or harmful) overfitting: in particular, if the SNR is high then benign overfitting occurs, conversely if the SNR is low then harmful overfitting occurs. We attribute both benign and non- benign overfitting to an approximate margin maximization property and show that leaky ReLU networks trained on hinge loss with gradient descent (GD) satisfy this property. In contrast to prior work we do not require the training data to be nearly orthogonal. Notably, for input dimension d and training sample size n, while results in prior work require d= !(n2 log n), here we require only d= ! (n).
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Predictive overfitting in immunological applications: Pitfalls and solutions
Overfitting describes the phenomenon where a highly predictive model on the training data generalizes poorly to future observations. It is a common concern when applying machine learning techniques to contemporary medical applications, such as predicting vaccination response and dis-ease status in infectious disease or cancer studies. This review examines the causes of overfitting and offers strategies to counteract it, focusing on model complexity reduction, reliable model evaluation, and harnessing data diversity. Through discussion of the underlying mathematical models and illustrative examples using both synthetic data and published real datasets, our objective is to equip analysts and bioinformaticians with the knowledge and tools necessary to detect and mitigate overfitting in their research.
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- Award ID(s):
- 2310836
- PAR ID:
- 10470206
- Publisher / Repository:
- Taylor & Francis
- Date Published:
- Journal Name:
- Human Vaccines & Immunotherapeutics
- Volume:
- 19
- Issue:
- 2
- ISSN:
- 2164-5515
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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The problem of benign overfitting asks whether it is possible for a model to perfectly fit noisy training data and still generalize well. We study benign overfitting in two- layer leaky ReLU networks trained with the hinge loss on a binary classification task. We consider input data that can be decomposed into the sum of a common signal and a random noise component, that lie on subspaces orthogonal to one another. We characterize conditions on the signal to noise ratio (SNR) of the model parameters giving rise to benign versus non-benign (or harmful) overfitting: in particular, if the SNR is high then benign overfitting occurs, conversely if the SNR is low then harmful overfitting occurs. We attribute both benign and non- benign overfitting to an approximate margin maximization property and show that leaky ReLU networks trained on hinge loss with gradient descent (GD) satisfy this property. In contrast to prior work we do not require the training data to be nearly orthogonal. Notably, for input dimension d and training sample size n, while results in prior work require d= !(n2 log n), here we require only d= ! (n).more » « less
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Detecting overfitting in generative models is an important challenge in machine learning. In this work, we formalize a form of overfitting that we call data-copying – where the gener- ative model memorizes and outputs training samples or small variations thereof. We pro- vide a three sample test for detecting data- copying that uses the training set, a separate sample from the target distribution, and a generated sample from the model, and study the performance of our test on several canon- ical models and datasets.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1080/21645515.2023.2251830
