We introduce @math , an extreme case of semi-supervised learning with ultra-sparse categorisation where some classes have no labels in the training set. That is, in the training data some classes are sparsely labelled and other classes appear only as unlabelled data. Many real-world datasets are conceivably of this type. We demonstrate that effective learning in this regime is only possible when a model is capable of capturing both semi-supervised and unsupervised learning. We develop two deep generative models for classification in this regime that extend previous deep generative models designed for semi-supervised learning. By changing their probabilistic structure to contain a mixture of Gaussians in their continuous latent space, these new models can learn in both unsupervised and semi-unsupervised paradigms. We demonstrate their performance both for semi-unsupervised and unsupervised learning on various standard datasets. We show that our models can learn in an semi-unsupervised manner on Fashion-MNIST. Here we artificially mask out all labels for half of the classes of data and keep @math of labels for the remaining classes. Our model is able to learn effectively, obtaining a trained classifier with @math test set accuracy. We also can train on Fashion-MNIST unsupervised, obtaining @math test set accuracy. Additionally, doing the same for MNIST unsupervised we get @math test set accuracy, which is state-of-the art for fully probabilistic deep generative models.
For clustering, both VaDE @cite_4 and GM-VAE @cite_37 extend VAEs with some form of mixture model in their learnt, continuous latent space. VaDE has the same forward model as the first model we will propose, but it uses Bayes' rule to define its classifier variational posterior over labels, rather than having a separate network parameterising it. The GM-VAE has a mixture of Gaussians in one of its stochastic layers, where this mixture is conditioned on another stochastic variable. The Cluster-aware Generative Model (CaGeM) @cite_7 can, like our models, learn in both unsupervised and semi-supervised regimes. However, the model's performance at clustering data into components corresponding to ground-truth classes is not given.
@cite_37 @cite_4 @cite_7
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Clustering is among the most fundamental tasks in computer vision and machine learning. In this paper, we propose Variational Deep Embedding (VaDE), a novel unsupervised generative clustering approach within the framework of Variational Auto-Encoder (VAE). Specifically, VaDE models the data generative procedure with a Gaussian Mixture Model (GMM) and a deep neural network (DNN): 1) the GMM picks a cluster; 2) from which a latent embedding is generated; 3) then the DNN decodes the latent embedding into observables. Inference in VaDE is done in a variational way: a different DNN is used to encode observables to latent embeddings, so that the evidence lower bound (ELBO) can be optimized using Stochastic Gradient Variational Bayes (SGVB) estimator and the reparameterization trick. Quantitative comparisons with strong baselines are included in this paper, and experimental results show that VaDE significantly outperforms the state-of-the-art clustering methods on 4 benchmarks from various modalities. Moreover, by VaDE's generative nature, we show its capability of generating highly realistic samples for any specified cluster, without using supervised information during training. Lastly, VaDE is a flexible and extensible framework for unsupervised generative clustering, more general mixture models than GMM can be easily plugged in. We study a variant of the variational autoencoder model (VAE) with a Gaussian mixture as a prior distribution, with the goal of performing unsupervised clustering through deep generative models. We observe that the known problem of over-regularisation that has been shown to arise in regular VAEs also manifests itself in our model and leads to cluster degeneracy. We show that a heuristic called minimum information constraint that has been shown to mitigate this effect in VAEs can also be applied to improve unsupervised clustering performance with our model. Furthermore we analyse the effect of this heuristic and provide an intuition of the various processes with the help of visualizations. Finally, we demonstrate the performance of our model on synthetic data, MNIST and SVHN, showing that the obtained clusters are distinct, interpretable and result in achieving competitive performance on unsupervised clustering to the state-of-the-art results. This paper proposes a generative model-based speaker clustering algorithm in the maximum a posteriori adapted Gaussian mixture model (GMM) mean supervector space. The algorithm can be viewed as an extension of the standard expectation maximization algorithm for fitting a mixture model to the data, which iterates between two steps - a sample re-assignment step (E-step) and a model re-estimation step (M-step) - until it converges. The directional scattering patterns of GMM mean supervectors suggest that we employ a mixture of von Mises-Fisher distributions in the model re-estimation step. In the sample re-assignment step, four sample-to-mixture assignment strategies, namely soft, hard, stochastic, and deterministic annealing assignments, are used. Our experiments on the GALE Mandarin dataset show that the use of a mixture of von Mises-Fisher distributions as the underlying model yields significantly higher speaker clustering accuracies than the use of a mixture of Gaussian distributions. It is further shown that deterministic annealing assignment outperforms soft assignment, that soft assignment is comparable to stochastic assignment, and that both soft and stochastic assignments outperform hard assignment. Many different methods to train deep generative models have been introduced in the past. In this paper, we propose to extend the variational auto-encoder (VAE) framework with a new type of prior which we call "Variational Mixture of Posteriors" prior, or VampPrior for short. The VampPrior consists of a mixture distribution (e.g., a mixture of Gaussians) with components given by variational posteriors conditioned on learnable pseudo-inputs. We further extend this prior to a two layer hierarchical model and show that this architecture with a coupled prior and posterior, learns significantly better models. The model also avoids the usual local optima issues related to useless latent dimensions that plague VAEs. We provide empirical studies on six datasets, namely, static and binary MNIST, OMNIGLOT, Caltech 101 Silhouettes, Frey Faces and Histopathology patches, and show that applying the hierarchical VampPrior delivers state-of-the-art results on all datasets in the unsupervised permutation invariant setting and the best results or comparable to SOTA methods for the approach with convolutional networks.