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To assess generalization, machine learning scientists typically either (i) bound the generalization gap and then (after training) plug in the empirical risk to obtain a bound on the true risk; or (ii) validate empirically on holdout data. However, (i) typically yields vacuous guarantees for overparameterized models. Furthermore, (ii) shrinks the training set and its guarantee erodes with each re-use of the holdout set. In this paper, we introduce a method that leverages unlabeled data to produce generalization bounds. After augmenting our (labeled) training set with randomly labeled fresh examples, we train in the standard fashion. Whenever classifiers achieve low error on clean data and high error on noisy data, our bound provides a tight upper bound on the true risk. We prove that our bound is valid for 0-1 empirical risk minimization and with linear classifiers trained by gradient descent. Our approach is especially useful in conjunction with deep learning due to the early learning phenomenon whereby networks fit true labels before noisy labels but requires one intuitive assumption. Empirically, on canonical computer vision and NLP tasks, our bound provides non-vacuous generalization guarantees that track actual performance closely. This work provides practitioners with an option for certifying the generalization of deep nets even when unseen labeled data is unavailable and provides theoretical insights into the relationship between random label noise and generalization.
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A growing specter in the rise of machine learning is whether the decisions made by machine learning models are fair. While research is already underway to formalize a machine-learning concept of fairness and to design frameworks for building fair models with sacrifice in accuracy, most are geared toward either supervised or unsupervised learning. Yet two observations inspired us to wonder whether semi-supervised learning might be useful to solve discrimination problems. First, previous study showed that increasing the size of the training set may lead to a better trade-off between fairness and accuracy. Second, the most powerful models today require an enormous of data to train which, in practical terms, is likely possible from a combination of labeled and unlabeled data. Hence, in this paper, we present a framework of fair semi-supervised learning in the pre-processing phase, including pseudo labeling to predict labels for unlabeled data, a re-sampling method to obtain multiple fair datasets and lastly, ensemble learning to improve accuracy and decrease discrimination. A theoretical decomposition analysis of bias, variance and noise highlights the different sources of discrimination and the impact they have on fairness in semi-supervised learning. A set of experiments on real-world and synthetic datasets show that our method is able to use unlabeled data to achieve a better trade-off between accuracy and discrimination.
In semi-supervised classification, one is given access both to labeled and unlabeled data. As unlabeled data is typically cheaper to acquire than labeled data, this setup becomes advantageous as soon as one can exploit the unlabeled data in order to produce a better classifier than with labeled data alone. However, the conditions under which such an improvement is possible are not fully understood yet. Our analysis focuses on improvements in the minimax learning rate in terms of the number of labeled examples (with the number of unlabeled examples being allowed to depend on the number of labeled ones). We argue that for such improvements to be realistic and indisputable, certain specific conditions should be satisfied and previous analyses have failed to meet those conditions. We then demonstrate examples where these conditions can be met, in particular showing rate changes from $1/sqrt{ell}$ to $e^{-cell}$ and from $1/sqrt{ell}$ to $1/ell$. These results improve our understanding of what is and isnt possible in semi-supervised learning.
An interactive image retrieval system learns which images in the database belong to a users query concept, by analyzing the example images and feedback provided by the user. The challenge is to retrieve the relevant images with minimal user interaction. In this work, we propose to solve this problem by posing it as a binary classification task of classifying all images in the database as being relevant or irrelevant to the users query concept. Our method combines active learning with graph-based semi-supervised learning (GSSL) to tackle this problem. Active learning reduces the number of user interactions by querying the labels of the most informative points and GSSL allows to use abundant unlabeled data along with the limited labeled data provided by the user. To efficiently find the most informative point, we use an uncertainty sampling based method that queries the label of the point nearest to the decision boundary of the classifier. We estimate this decision boundary using our heuristic of adaptive threshold. To utilize huge volumes of unlabeled data we use an efficient approximation based method that reduces the complexity of GSSL from $O(n^3)$ to $O(n)$, making GSSL scalable. We make the classifier robust to the diversity and noisy labels associated with images in large databases by incorporating information from multiple modalities such as visual information extracted from deep learning based models and semantic information extracted from the WordNet. High F1 scores within few relevance feedback rounds in our experiments with concepts defined on AnimalWithAttributes and Imagenet (1.2 million images) datasets indicate the effectiveness and scalability of our approach.
Data augmentation by incorporating cheap unlabeled data from multiple domains is a powerful way to improve prediction especially when there is limited labeled data. In this work, we investigate how adversarial robustness can be enhanced by leveraging out-of-domain unlabeled data. We demonstrate that for broad classes of distributions and classifiers, there exists a sample complexity gap between standard and robust classification. We quantify to what degree this gap can be bridged via leveraging unlabeled samples from a shifted domain by providing both upper and lower bounds. Moreover, we show settings where we achieve better adversarial robustness when the unlabeled data come from a shifted domain rather than the same domain as the labeled data. We also investigate how to leverage out-of-domain data when some structural information, such as sparsity, is shared between labeled and unlabeled domains. Experimentally, we augment two object recognition datasets (CIFAR-10 and SVHN) with easy to obtain and unlabeled out-of-domain data and demonstrate substantial improvement in the models robustness against $ell_infty$ adversarial attacks on the original domain.
Self-training algorithms, which train a model to fit pseudolabels predicted by another previously-learned model, have been very successful for learning with unlabeled data using neural networks. However, the current theoretical understanding of self-training only applies to linear models. This work provides a unified theoretical analysis of self-training with deep networks for semi-supervised learning, unsupervised domain adaptation, and unsupervised learning. At the core of our analysis is a simple but realistic expansion assumption, which states that a low probability subset of the data must expand to a neighborhood with large probability relative to the subset. We also assume that neighborhoods of examples in different classes have minimal overlap. We prove that under these assumptions, the minimizers of population objectives based on self-training and input-consistency regularization will achieve high accuracy with respect to ground-truth labels. By using off-the-shelf generalization bounds, we immediately convert this result to sample complexity guarantees for neural nets that are polynomial in the margin and Lipschitzness. Our results help explain the empirical successes of recently proposed self-training algorithms which use input consistency regularization.
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