Iterative Amortized Inference (1807.09356v1)

Abstract: Inference models are a key component in scaling variational inference to deep latent variable models, most notably as encoder networks in variational auto-encoders (VAEs). By replacing conventional optimization-based inference with a learned model, inference is amortized over data examples and therefore more computationally efficient. However, standard inference models are restricted to direct mappings from data to approximate posterior estimates. The failure of these models to reach fully optimized approximate posterior estimates results in an amortization gap. We aim toward closing this gap by proposing iterative inference models, which learn to perform inference optimization through repeatedly encoding gradients. Our approach generalizes standard inference models in VAEs and provides insight into several empirical findings, including top-down inference techniques. We demonstrate the inference optimization capabilities of iterative inference models and show that they outperform standard inference models on several benchmark data sets of images and text.

• The paper introduces iterative inference models to address the "amortization gap" in variational auto-encoders (VAEs), where standard models yield suboptimal posterior estimates.
• Iterative inference models learn to encode gradients or errors, enabling iterative updates to approximate posterior estimates and improving inference optimization.
• Empirical results on datasets like MNIST and CIFAR-10 demonstrate that these iterative models outperform standard inference models in closing the amortization gap and improving modeling accuracy.

Iterative Amortized Inference: Towards Closing the Amortization Gap

The paper "Iterative Amortized Inference" authored by Joseph Marino, Yisong Yue, and Stephan Mandt explores the limitations of standard inference models in variational auto-encoders (VAEs) and proposes iterative inference models to address the so-called 'amortization gap'. This research provides significant insights into the optimization of inference in latent variable models and suggests methodological advancements with empirical support.

Inference models, particularly those used in conjunction with VAEs, offer computational efficiency by amortizing inference across data examples. However, the direct mapping from data to approximate posterior estimates can result in suboptimal solutions, thus constituting an amortization gap that hinders modeling performance. Recognizing this limitation, the authors introduce iterative inference models which enhance inference optimization by learning to encode gradients iteratively.

The iterative inference models presented in this paper adopt a learning-to-learn approach. They improve upon conventional optimizers by encoding gradients and iteratively updating approximate posterior estimates, akin to techniques in learning optimization such as those studied by Andrychowicz et al. (2016). A noteworthy aspect of this method is its application to latent Gaussian models, which are prevalent in deep generative frameworks. The authors propose non-recurrent models and suggest encoding errors, rather than solely gradients, to capture higher-order derivative information, leading to faster convergence.

Significantly, the paper offers theoretical justification for top-down inference, which augments hierarchical models by incorporating empirical priors effectively. The analysis in the paper substantially reformulates the understanding of optimization in these models and provides empirical evidence by demonstrating improvements in closing the amortization gap over benchmark data sets like MNIST, CIFAR-10, and RCV1. Iterative inference models are shown to outperform standard inference models in terms of optimization capability and modeling accuracy.

The implications of this research extend to enhancing the capacity of machine learning models to accommodate more complex, high-dimensional data, essentially converting the intuitive use of top-down inference techniques into theoretically grounded practices. Future developments may focus on refining these models further and exploring their application in sequential latent variable models and online inference settings, offering potential advancements in real-time data processing and model adaptability.

In conclusion, the paper "Iterative Amortized Inference" provides a rigorous analysis of inference optimization, delivering improved techniques for bridging the amortization gap in VAEs. The introduction of iterative inference models opens avenues for effectively learning fast, adaptive inference strategies, offering practical benefits and stronger theoretical foundations in the paper of complex generative models.