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Dropout Training as Adaptive Regularization (1307.1493v2)

Published 4 Jul 2013 in stat.ML, cs.LG, and stat.ME

Abstract: Dropout and other feature noising schemes control overfitting by artificially corrupting the training data. For generalized linear models, dropout performs a form of adaptive regularization. Using this viewpoint, we show that the dropout regularizer is first-order equivalent to an L2 regularizer applied after scaling the features by an estimate of the inverse diagonal Fisher information matrix. We also establish a connection to AdaGrad, an online learning algorithm, and find that a close relative of AdaGrad operates by repeatedly solving linear dropout-regularized problems. By casting dropout as regularization, we develop a natural semi-supervised algorithm that uses unlabeled data to create a better adaptive regularizer. We apply this idea to document classification tasks, and show that it consistently boosts the performance of dropout training, improving on state-of-the-art results on the IMDB reviews dataset.

Citations (585)

Summary

  • The paper reveals that dropout serves as an adaptive L2-regularizer by reformulating its impact using the inverse diagonal Fisher information matrix.
  • It establishes a clear connection between dropout and AdaGrad, demonstrating enhanced document classification performance, particularly for rare but valuable features.
  • Empirical results, including on IMDB reviews, validate that dropout training outperforms traditional L2 penalties by achieving a 0.73 accuracy on instances with active rare features.

Dropout Training as Adaptive Regularization

The paper investigates dropout training by framing it as an adaptive regularization approach. This paper focuses on understanding dropout not merely as a random feature omission technique but as a systematic regularization mechanism, particularly within the framework of Generalized Linear Models (GLMs).

Main Findings

The core result establishes that dropout acts as an adaptive $\LII$-regularizer, modifying the input feature space through the application of the inverse diagonal Fisher information matrix. This formulation enhances the understanding of dropout by connecting it directly to established notions of regularization and providing theoretical clarity to its functionality. The paper further reveals connections between dropout and the AdaGrad algorithm, showing that both methods facilitate learning by constantly solving linearized dropout-regularized problems.

Through this lens, dropout is interpreted as giving a natural advantage to rare but valuable features, allowing for improved model weighting and fewer penalties on these features—particularly significant for tasks like document classification.

Numerical Results

The authors validate their theoretical insights with experiments on document classification tasks, including the IMDB reviews dataset. The results consistently demonstrate that dropout augmented by unlabeled data surpasses state-of-the-art results, emphasizing dropout's strength as a regularization mechanism.

Further simulations corroborate that dropout effectively targets rare but discriminative features, offering a practical edge over traditional $\LII$-penalization. In these simulations, dropout training achieved an accuracy of 0.73 on instances with active rare features, outperforming the $\LII$ method.

Theoretical Implications

The paper's formulation of dropout as an adaptive regularizer provides valuable insight into its role in balancing the learning of features based on confidence and rarity. This understanding invites further exploration into dropout's application across other model architectures like neural networks.

The connection with AdaGrad is particularly enriching. Both dropout and AdaGrad use feature adaptation to facilitate balanced learning, suggesting potential for combining these methodologies in more complex learning environments.

Practical Implications and Future Directions

Practically, the adaptive nature of dropout, enabled by the Fisher information matrix, opens avenues for designing algorithms that target feature scaling and regularization dynamically. This work suggests fertile ground for more nuanced semi-supervised learning strategies, particularly those leveraging unlabeled data.

Future advancements could explore how dropout regularization may be fine-tuned for neural networks, providing performance gains without relying heavily on vast labeled datasets. Additionally, potential integration with other adaptive learning frameworks promises enhanced efficiency and accuracy.

By advancing dropout training within a formal regularization context, this paper lays groundwork for further theoretical refinement and application across diverse machine learning scenarios.