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Register a new userMulti-Facet Clustering Variational Autoencoders
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Work in deep clustering focuses on finding a single partition of data. However, high-dimensional data, such as images, typically feature multiple interesting characteristics one could cluster over. For example, images of objects against a background could be clustered over the shape of the object and separately by the colour of the background. In this paper, we introduce Multi-Facet Clustering Variational Autoencoders (MFCVAE), a novel class of variational autoencoders with a hierarchy of latent variables, each with a Mixture-of-Gaussians prior, that learns multiple clusterings simultaneously, and is trained fully unsupervised and end-to-end. MFCVAE uses a progressively-trained ladder architecture which leads to highly stable performance. We provide novel theoretical results for optimising the ELBO analytically with respect to the categorical variational posterior distribution, and corrects earlier influential theoretical work. On image benchmarks, we demonstrate that our approach separates out and clusters over different aspects of the data in a disentangled manner. We also show other advantages of our model: the compositionality of its latent space and that it provides controlled generation of samples.
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We extend variational autoencoders (VAEs) to collaborative filtering for implicit feedback. This non-linear probabilistic model enables us to go beyond the limited modeling capacity of linear factor models which still largely dominate collaborative filtering research.We introduce a generative model with multinomial likelihood and use Bayesian inference for parameter estimation. Despite widespread use in language modeling and economics, the multinomial likelihood receives less attention in the recommender systems literature. We introduce a different regularization parameter for the learning objective, which proves to be crucial for achieving competitive performance. Remarkably, there is an efficient way to tune the parameter using annealing. The resulting model and learning algorithm has information-theoretic connections to maximum entropy discrimination and the information bottleneck principle. Empirically, we show that the proposed approach significantly outperforms several state-of-the-art baselines, including two recently-proposed neural network approaches, on several real-world datasets. We also provide extended experiments comparing the multinomial likelihood with other commonly used likelihood functions in the latent factor collaborative filtering literature and show favorable results. Finally, we identify the pros and cons of employing a principled Bayesian inference approach and characterize settings where it provides the most significant improvements.
Recent advances in deep learning have shown their ability to learn strong feature representations for images. The task of image clustering naturally requires good feature representations to capture the distribution of the data and subsequently differentiate data points from one another. Often these two aspects are dealt with independently and thus traditional feature learning alone does not suffice in partitioning the data meaningfully. Variational Autoencoders (VAEs) naturally lend themselves to learning data distributions in a latent space. Since we wish to efficiently discriminate between different clusters in the data, we propose a method based on VAEs where we use a Gaussian Mixture prior to help cluster the images accurately. We jointly learn the parameters of both the prior and the posterior distributions. Our method represents a true Gaussian Mixture VAE. This way, our method simultaneously learns a prior that captures the latent distribution of the images and a posterior to help discriminate well between data points. We also propose a novel reparametrization of the latent space consisting of a mixture of discrete and continuous variables. One key takeaway is that our method generalizes better across different datasets without using any pre-training or learnt models, unlike existing methods, allowing it to be trained from scratch in an end-to-end manner. We verify our efficacy and generalizability experimentally by achieving state-of-the-art results among unsupervised methods on a variety of datasets. To the best of our knowledge, we are the first to pursue image clustering using VAEs in a purely unsupervised manner on real image datasets.
Manifold-valued data naturally arises in medical imaging. In cognitive neuroscience, for instance, brain connectomes base the analysis of coactivation patterns between different brain regions on the analysis of the correlations of their functional Magnetic Resonance Imaging (fMRI) time series - an object thus constrained by construction to belong to the manifold of symmetric positive definite matrices. One of the challenges that naturally arises consists of finding a lower-dimensional subspace for representing such manifold-valued data. Traditional techniques, like principal component analysis, are ill-adapted to tackle non-Euclidean spaces and may fail to achieve a lower-dimensional representation of the data - thus potentially pointing to the absence of lower-dimensional representation of the data. However, these techniques are restricted in that: (i) they do not leverage the assumption that the connectomes belong on a pre-specified manifold, therefore discarding information; (ii) they can only fit a linear subspace to the data. In this paper, we are interested in variants to learn potentially highly curved submanifolds of manifold-valued data. Motivated by the brain connectomes example, we investigate a latent variable generative model, which has the added benefit of providing us with uncertainty estimates - a crucial quantity in the medical applications we are considering. While latent variable models have been proposed to learn linear and nonlinear spaces for Euclidean data, or geodesic subspaces for manifold data, no intrinsic latent variable model exists to learn nongeodesic subspaces for manifold data. This paper fills this gap and formulates a Riemannian variational autoencoder with an intrinsic generative model of manifold-valued data. We evaluate its performances on synthetic and real datasets by introducing the formalism of weighted Riemannian submanifolds.
We introduce an approach for training Variational Autoencoders (VAEs) that are certifiably robust to adversarial attack. Specifically, we first derive actionable bounds on the minimal size of an input perturbation required to change a VAEs reconstruction by more than an allowed amount, with these bounds depending on certain key parameters such as the Lipschitz constants of the encoder and decoder. We then show how these parameters can be controlled, thereby providing a mechanism to ensure a priori that a VAE will attain a desired level of robustness. Moreover, we extend this to a complete practical approach for training such VAEs to ensure our criteria are met. Critically, our method allows one to specify a desired level of robustness upfront and then train a VAE that is guaranteed to achieve this robustness. We further demonstrate that these Lipschitz--constrained VAEs are more robust to attack than standard VAEs in practice.
In large studies involving multi protocol Magnetic Resonance Imaging (MRI), it can occur to miss one or more sub-modalities for a given patient owing to poor quality (e.g. imaging artifacts), failed acquisitions, or hallway interrupted imaging examinations. In some cases, certain protocols are unavailable due to limited scan time or to retrospectively harmonise the imaging protocols of two independent studies. Missing image modalities pose a challenge to segmentation frameworks as complementary information contributed by the missing scans is then lost. In this paper, we propose a novel model, Multi-modal Gaussian Process Prior Variational Autoencoder (MGP-VAE), to impute one or more missing sub-modalities for a patient scan. MGP-VAE can leverage the Gaussian Process (GP) prior on the Variational Autoencoder (VAE) to utilize the subjects/patients and sub-modalities correlations. Instead of designing one network for each possible subset of present sub-modalities or using frameworks to mix feature maps, missing data can be generated from a single model based on all the available samples. We show the applicability of MGP-VAE on brain tumor segmentation where either, two, or three of four sub-modalities may be missing. Our experiments against competitive segmentation baselines with missing sub-modality on BraTS19 dataset indicate the effectiveness of the MGP-VAE model for segmentation tasks.
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