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arXiv 2020年

作者： Chen, Nutan Klushyn, Alexej Ferroni, Francesco Bayer, Justin van der Smagt, Patrick Machine Learning Research Lab Volkswagen Group Munich Germany Autonomous Intelligent Driving GmbH Munich Germany

Measuring the similarity between data points often requires domain knowledge. This can in parts be compensated by relying on unsupervised methods such as latent-variable models, where similarity/distance is estimated in a more compact latent space. Prevalent is the use of the Euclidean metric, which has the drawback of ignoring information about similarity of data stored in the decoder, as captured by the framework of Riemannian geometry. Alternatives-such as approximating the geodesic-are often computationally inefficient, rendering the methods impractical. We propose an extension to the framework of variational autoencoders allows learning flat latent manifolds, where the Euclidean metric is a proxy for the similarity between data points. This is achieved by defining the latent space as a Riemannian manifold and by regularising the metric tensor to be a scaled identity matrix. Additionally, we replace the compact prior typically used in variational auto-encoders with a recently presented, more expressive hierarchical one-and formulate the learning problem as a constrained optimisation problem. We evaluate our method on a range of data-sets, including a video-tracking benchmark, where the performance of our unsupervised approach nears that of state-of-the-art supervised approaches, while retaining the computational efficiency of straight-line-based approaches. Copyright © 2020, The Authors. All rights reserved.

关键词： Domain Knowledge

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Fast approximate geodesics for deep generative models

arXiv

引用

arXiv 2018年

作者： Chen, Nutan Ferroni, Francesco Klushyn, Alexej Paraschos, Alexandros Bayer, Justin van der Smagt, Patrick Machine Learning Research Lab Volkswagen Group Autonomous Intelligent Driving GmbH

The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the computational complexity of solving a non-convex optimisation problem. We propose finding shortest paths in a finite graph of samples from the aggregate approximate posterior, that can be solved exactly, at greatly reduced runtime, and without a notable loss in quality. Our approach, therefore, is hence applicable to high-dimensional problems, e.g., in the visual domain. We validate our approach empirically on a series of experiments using variational autoencoders applied to image data, including the Chair, FashionMNIST, and human movement data sets. Copyright © 2018, The Authors. All rights reserved.

关键词： Geodesy

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