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Register a new userLearning Hierarchical Priors in VAEs
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We propose to learn a hierarchical prior in the context of variational autoencoders to avoid the over-regularisation resulting from a standard normal prior distribution. To incentivise an informative latent representation of the data, we formulate the learning problem as a constrained optimisation problem by extending the Taming VAEs framework to two-level hierarchical models. We introduce a graph-based interpolation method, which shows that the topology of the learned latent representation corresponds to the topology of the data manifold---and present several examples, where desired properties of latent representation such as smoothness and simple explanatory factors are learned by the prior.
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Measuring the similarity between data points often requires domain knowledge, which 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. We propose an extension to the framework of variational auto-encoders 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.
While the choice of prior is one of the most critical parts of the Bayesian inference workflow, recent Bayesian deep learning models have often fallen back on vague priors, such as standard Gaussians. In this review, we highlight the importance of prior choices for Bayesian deep learning and present an overview of different priors that have been proposed for (deep) Gaussian processes, variational autoencoders, and Bayesian neural networks. We also outline different methods of learning priors for these models from data. We hope to motivate practitioners in Bayesian deep learning to think more carefully about the prior specification for their models and to provide them with some inspiration in this regard.
We address the problem of one-to-many mappings in supervised learning, where a single instance has many different solutions of possibly equal cost. The framework of conditional variational autoencoders describes a class of methods to tackle such structured-prediction tasks by means of latent variables. We propose to incentivise informative latent representations for increasing the generalisation capacity of conditional variational autoencoders. To this end, we modify the latent variable model by defining the likelihood as a function of the latent variable only and introduce an expressive multimodal prior to enable the model for capturing semantically meaningful features of the data. To validate our approach, we train our model on the Cornell Robot Grasping dataset, and modifi
Bayesian Neural Networks (BNNs) have recently received increasing attention for their ability to provide well-calibrated posterior uncertainties. However, model selection---even choosing the number of nodes---remains an open question. Recent work has proposed the use of a horseshoe prior over node pre-activations of a Bayesian neural network, which effectively turns off nodes that do not help explain the data. In this work, we propose several modeling and inference advances that consistently improve the compactness of the model learned while maintaining predictive performance, especially in smaller-sample settings including reinforcement learning.
We place an Indian Buffet process (IBP) prior over the structure of a Bayesian Neural Network (BNN), thus allowing the complexity of the BNN to increase and decrease automatically. We further extend this model such that the prior on the structure of each hidden layer is shared globally across all layers, using a Hierarchical-IBP (H-IBP). We apply this model to the problem of resource allocation in Continual Learning (CL) where new tasks occur and the network requires extra resources. Our model uses online variational inference with reparameterisation of the Bernoulli and Beta distributions, which constitute the IBP and H-IBP priors. As we automatically learn the number of weights in each layer of the BNN, overfitting and underfitting problems are largely overcome. We show empirically that our approach offers a competitive edge over existing methods in CL.
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