Unsupervised and Semi-supervised Learning with Categorical Generative Adversarial Networks (1511.06390v2)

Abstract: In this paper we present a method for learning a discriminative classifier from unlabeled or partially labeled data. Our approach is based on an objective function that trades-off mutual information between observed examples and their predicted categorical class distribution, against robustness of the classifier to an adversarial generative model. The resulting algorithm can either be interpreted as a natural generalization of the generative adversarial networks (GAN) framework or as an extension of the regularized information maximization (RIM) framework to robust classification against an optimal adversary. We empirically evaluate our method - which we dub categorical generative adversarial networks (or CatGAN) - on synthetic data as well as on challenging image classification tasks, demonstrating the robustness of the learned classifiers. We further qualitatively assess the fidelity of samples generated by the adversarial generator that is learned alongside the discriminative classifier, and identify links between the CatGAN objective and discriminative clustering algorithms (such as RIM).

Unsupervised and Semi-supervised Learning with Categorical Generative Adversarial Networks

The paper presents Categorical Generative Adversarial Networks (CatGANs), a novel approach to learning discriminative classifiers from unlabeled or partially labeled data. The methodology entails balancing the trade-off between mutual information of observed examples and their predicted categorical class distribution, against adversarial robustness. This leads to a natural generalization of the GAN framework or can be seen as an extension to the regularized information maximization (RIM) framework, tailored for robust classification against an optimal adversary.

Introduction

Extracting meaningful classifications from unlabeled or partially labeled data remains a pivotal challenge in machine learning. The underlying assumption in unsupervised learning is that the distribution of the input data holds intrinsic information valuable for inferring labels. Traditional clustering methods, such as Gaussian mixture models and k-means, aim to model the data distribution directly, while discriminative clustering methods (e.g., MMC, RIM) focus on grouping data into distinct categories. However, discriminative clustering often leads to overfitting, especially when combined with powerful non-linear classifiers.

Recent progress in neural networks has demonstrated promise in unsupervised and semi-supervised learning by either training generative models or using reconstruction-based techniques like autoencoders. However, these methods generally seek perfect reconstruction, which may conflict with the goal of class label prediction.

CatGAN introduces a hybrid approach to leverage both generative and discriminative perspectives. Classifiers are designed to maximize mutual information between inputs and predicted class distributions while remaining robust against examples produced by adversarial generative models.

Generative Adversarial Networks (GANs)

GANs involve a two-player zero-sum game where a generator produces examples aimed at fooling a discriminator tasked with distinguishing between real and generated input data. The aim is for the generator to improve at creating realistic data while the discriminator enhances its ability to classify data correctly.

CatGAN Objective

CatGANs extend the GAN framework for multi-class classification. The discriminator is adjusted to assign each example to one of $K$ categories. The optimization problem for CatGANs involves:

1. Ensuring the discriminator is confident about its predictions for real data.
2. Retaining uncertainty for generated data.
3. Ensuring equal utilization of all classes.

The generator, in turn, aims to produce samples leading to confident class assignments and a balanced distribution across all classes. This is formally captured through an information-theoretic lens, maximizing mutual information between the data distribution and the predicted class distribution.

Extension to Semi-supervised Learning

CatGANs can seamlessly accommodate semi-supervised learning by incorporating a cross-entropy term for the additional labeled data, weighted appropriately to balance between labeled and unlabeled data contributions.

Empirical Evaluation

CatGANs display impressive performance across a range of benchmarks:

• Outperforming k-means and RIM in synthetic clustering tasks, particularly those with complex decision boundaries.
• Achieving competitive results in semi-supervised learning on PI-MNIST, approaching state-of-the-art and excelling even with minimal labeled examples.
• Excelling in unsupervised learning, underlining robust clustering capabilities with effective task generalization from unlabeled data.

The performance on image classification benchmarks such as MNIST and CIFAR-10, using both fully connected and convolutional networks, underscores the utility of CatGANs. The semi-supervised CatGAN model delivers results that rival top-performing methods such as Ladder Networks.

Generative Model Evaluation

The generative model within CatGANs is capable of producing high-fidelity samples. Qualitative evaluations on MNIST, LFW, and CIFAR-10 datasets confirm the visual plausibility and diversity of generated images. Quantitatively, CatGAN achieves competitive log-likelihood scores, indicative of its generative robustness.

Theoretical and Practical Implications

Theoretically, CatGANs bridge discriminative and generative learning paradigms, enhancing classifier robustness and information extraction from unlabeled data. Practically, they provide a versatile framework suitable for a diverse set of classification and clustering tasks, particularly beneficial in domains with limited labeled data.

Future Developments

Future directions might involve combining CatGANs with more advanced generator architectures, enhancing stability through architectural innovations, and exploring CatGAN applicability to other domains (e.g., text or audio). Additionally, refining the approach for more complex priors on empirical class distribution could further broaden the framework's utility.

CatGAN thus emerges as a robust, versatile approach for unsupervised and semi-supervised learning, demonstrating outstanding capability in clustering, classification, and generative modeling.