Autoregressive Energy Machines (1904.05626v1)

Abstract: Neural density estimators are flexible families of parametric models which have seen widespread use in unsupervised machine learning in recent years. Maximum-likelihood training typically dictates that these models be constrained to specify an explicit density. However, this limitation can be overcome by instead using a neural network to specify an energy function, or unnormalized density, which can subsequently be normalized to obtain a valid distribution. The challenge with this approach lies in accurately estimating the normalizing constant of the high-dimensional energy function. We propose the Autoregressive Energy Machine, an energy-based model which simultaneously learns an unnormalized density and computes an importance-sampling estimate of the normalizing constant for each conditional in an autoregressive decomposition. The Autoregressive Energy Machine achieves state-of-the-art performance on a suite of density-estimation tasks.

• The paper introduces an energy-based autoregressive framework that models densities using unnormalized energy functions to capture complex, multi-modal distributions.
• It computes conditional energy terms autoregressively, leveraging reliable lower-dimensional normalizing constant estimates to handle sharp distribution transitions.
• Experiments show state-of-the-art performance on synthetic and tabular datasets, paving the way for future integration with generative models for latent variable tasks.

Autoregressive Energy Machines: A Summary

The paper "Autoregressive Energy Machines" introduces a novel framework for neural density estimation that leverages the expressive power of energy-based models. Traditional neural density estimators often face limitations due to the need for specifying an explicit, normalized density. The proposed approach circumvents this constraint by using an unnormalized energy function modeled via a neural network, with normalizing constants estimated using importance sampling within an autoregressive decomposition.

Key Contributions

The authors present a model referred to as the Autoregressive Energy Machine (AEM), which represents a density as a product of conditional energy terms. Such terms are computed in an autoregressive fashion, benefiting from the generally reliable estimation of normalizing constants in lower dimensions compared to high-dimensional spaces. This autoregressive setup allows for the incorporation of complex energy functions, enabling the model to capture multi-modal and discontinuous densities efficiently.

Experimental Results

The AEM achieves state-of-the-art performance across several synthetic and real-world density estimation tasks. On synthetic datasets, including challenging spirals and image-generated data, the AEM excels in accurately modeling distributions characterized by sharp transitions and high-frequency components, outperforming alternative models unable to preserve such detail. On tabular datasets, the ResMADE proposal offers a strong baseline, while AEM further enhances performance, demonstrating robust density estimation capabilities. The advantages of autoregressive energy-based modeling are evident in the improved log-likelihood scores reported in the paper.

Implications and Future Directions

The authors highlight the potential of energy-based models for greater flexibility and expressiveness in density estimation tasks. The proposed AEM framework offers enhancements in capturing complex distribution characteristics such as sharp transitions and multi-modality. Future research could explore more efficient estimation techniques for normalizing constants in high-dimensional spaces to further improve scalability and applicability.

Furthermore, the integration of this autoregressive energy-based model within variational autoencoders and other generative frameworks presents promising avenues for enhancing latent variable modeling, as evidenced by competitive results on the MNIST dataset.

Conclusion

The Autoregressive Energy Machine represents a significant advance in the domain of neural density estimation, showcasing the potential of energy-based models combined with the autoregressive decomposition technique. By leveraging the flexibility of neural networks to model unnormalized densities, the authors address longstanding challenges in the field, paving the way for more accurate and expressive density estimation methodologies.