Learning Deep-Latent Hierarchies by Stacking Wasserstein Autoencoders

Probabilistic models with hierarchical-latent-variable structures provide state-of-the-art results amongst non-autoregressive, unsupervised density-based models. However, the most common approach to training such models based on Variational Autoencoders (VAEs) often fails to leverage deep-latent hierarchies; successful approaches require complex inference and optimisation schemes. Optimal Transport is an alternative, non-likelihood-based framework for training generative models with appealing theoretical properties, in principle allowing easier training convergence between distributions. In this work we propose a novel approach to training models with deep-latent hierarchies based on Optimal Transport, without the need for highly bespoke models and inference networks. We show that our method enables the generative model to fully leverage its deep-latent hierarchy, avoiding the well known "latent variable collapse" issue of VAEs; therefore, providing qualitatively better sample generations as well as more interpretable latent representation than the original Wasserstein Autoencoder with Maximum Mean Discrepancy divergence.

Learning disentangled representations with the Wasserstein Autoencoder

Disentangled representation learning has undoubtedly benefited from objective function surgery. However, a delicate balancing act of tuning is still required in order to trade off reconstruction fidelity versus disentanglement. Building on previous successes of penalizing the total correlation in the latent variables, we propose TCWAE (Total Correlation Wasserstein Autoencoder). Working in the WAE paradigm naturally enables the separation of the total-correlation term, thus providing disentanglement control over the learned representation, while offering more flexibility in the choice of reconstruction cost. We propose two variants using different KL estimators and perform extensive quantitative comparisons on data sets with known generative factors, showing competitive results relative to state-of-the-art techniques. We further study the trade off between disentanglement and reconstruction on more-difficult data sets with unknown generative factors, where the flexibility of the WAE paradigm in the reconstruction term improves reconstructions.

Bayesian Online Meta-Learning with Laplace Approximation

Neural networks are known to suffer from catastrophic forgetting when trained on sequential datasets. While there have been numerous attempts to solve this problem for large-scale supervised classification, little has been done to overcome catastrophic forgetting for few-shot classification problems. We demonstrate that the popular gradient-based few-shot meta-learning algorithm Model-Agnostic Meta-Learning (MAML) indeed suffers from catastrophic forgetting and introduce a Bayesian online meta-learning framework that tackles this problem. Our framework incorporates MAML into a Bayesian online learning algorithm with Laplace approximation. This framework enables few-shot classification on a range of sequentially arriving datasets with a single meta-learned model. The experimental evaluations demonstrate that our framework can effectively prevent forgetting in various few-shot classification settings compared to applying MAML sequentially.

Private Machine Learning via Randomised Response

We introduce a general learning framework for private machine learning based on randomised response. Our assumption is that all actors are potentially adversarial and as such we trust only to release a single noisy version of an individual's datapoint. We discuss a general approach that forms a consistent way to estimate the true underlying machine learning model and demonstrate this in the case of logistic regression.

HiLLoC: Lossless Image Compression with Hierarchical Latent Variable Models

We make the following striking observation: fully convolutional VAE models trained on 32x32 ImageNet can generalize well, not just to 64x64 but also to far larger photographs, with no changes to the model. We use this property, applying fully convolutional models to lossless compression, demonstrating a method to scale the VAE-based 'Bits-Back with ANS' algorithm for lossless compression to large color photographs, and achieving state of the art for compression of full size ImageNet images. We release Craystack, an open source library for convenient prototyping of lossless compression using probabilistic models, along with full implementations of all of our compression results.

Variational f-divergence Minimization

Probabilistic models are often trained by maximum likelihood, which corresponds to minimizing a specific f-divergence between the model and data distribution. In light of recent successes in training Generative Adversarial Networks, alternative non-likelihood training criteria have been proposed. Whilst not necessarily statistically efficient, these alternatives may better match user requirements such as sharp image generation. A general variational method for training probabilistic latent variable models using maximum likelihood is well established; however, how to train latent variable models using other f-divergences is comparatively unknown. We discuss a variational approach that, when combined with the recently introduced Spread Divergence, can be applied to train a large class of latent variable models using any f-divergence.

Gaussian Mean Field Regularizes by Limiting Learned Information

Variational inference with a factorized Gaussian posterior estimate is a widely used approach for learning parameters and hidden variables. Empirically, a regularizing effect can be observed that is poorly understood. In this work, we show how mean field inference improves generalization by limiting mutual information between learned parameters and the data through noise. We quantify a maximum capacity when the posterior variance is either fixed or learned and connect it to generalization error, even when the KL-divergence in the objective is rescaled. Our experiments demonstrate that bounding information between parameters and data effectively regularizes neural networks on both supervised and unsupervised tasks.

Practical Lossless Compression with Latent Variables using Bits Back Coding

Deep latent variable models have seen recent success in many data domains. Lossless compression is an application of these models which, despite having the potential to be highly useful, has yet to be implemented in a practical manner. We present `Bits Back with ANS' (BB-ANS), a scheme to perform lossless compression with latent variable models at a near optimal rate. We demonstrate this scheme by using it to compress the MNIST dataset with a variational auto-encoder model (VAE), achieving compression rates superior to standard methods with only a simple VAE. Given that the scheme is highly amenable to parallelization, we conclude that with a sufficiently high quality generative model this scheme could be used to achieve substantial improvements in compression rate with acceptable running time. We make our implementation available open source at https://github.com/bits-back/bits-back .

Spread Divergences

For distributions p and q with different support, the divergence generally will not exist. We define a spread divergence on modified p and q and describe sufficient conditions for the existence of such a divergence. We give examples of using a spread divergence to train implicit generative models, including linear models (Principal Components Analysis and Independent Components Analysis) and non-linear models (Deep Generative Networks).

Modular Networks: Learning to Decompose Neural Computation

Scaling model capacity has been vital in the success of deep learning. For a typical network, necessary compute resources and training time grow dramatically with model size. Conditional computation is a promising way to increase the number of parameters with a relatively small increase in resources. We propose a training algorithm that flexibly chooses neural modules based on the data to be processed. Both the decomposition and modules are learned end-to-end. In contrast to existing approaches, training does not rely on regularization to enforce diversity in module use. We apply modular networks both to image recognition and language modeling tasks, where we achieve superior performance compared to several baselines. Introspection reveals that modules specialize in interpretable contexts.