We address the problem of unsupervised disentanglement of latent representations learnt via deep generative models. In contrast to current approaches that operate on the evidence lower bound (ELBO), we argue that statistical independence in the latent space of VAEs can be enforced in a principled hierarchical Bayesian manner. To this effect, we augment the standard VAE with an inverse-Wishart (IW) prior on the covariance matrix of the latent code. By tuning the IW parameters, we are able to encourage (or discourage) independence in the learnt latent dimensions. Extensive experimental results on a range of datasets (2DShapes, 3DChairs, 3DFaces and CelebA) show our approach to outperform the @math -VAE and is competitive with the state-of-the-art FactorVAE. Our approach achieves significantly better disentanglement and reconstruction on a new dataset (CorrelatedEllipses) which introduces correlations between the factors of variation.
Early works that have demonstrated disentanglement in limited settings include @cite_15 @cite_4 @cite_18 , and several prior research has addressed the problem of disentanglement in or settings @cite_14 @cite_5 @cite_28 @cite_23 . In this work, we focus on unsupervised learning of disentangled features. Unsupervised generative models such as @cite_7 @cite_9 @cite_21 have been also shown to learn disentangled representations, although this was not the main motivation of these works. Recent work has also sought to disentangle factors of variation in sequential data in an unsupervised manner @cite_17 @cite_22 .
@cite_18 @cite_14 @cite_4 @cite_22 @cite_7 @cite_28 @cite_9 @cite_21 @cite_23 @cite_5 @cite_15 @cite_17
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The key idea behind the unsupervised learning of disentangled representations is that real-world data is generated by a few explanatory factors of variation which can be recovered by unsupervised learning algorithms. In this paper, we provide a sober look at recent progress in the field and challenge some common assumptions. We first theoretically show that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases on both the models and the data. Then, we train more than 12000 models covering most prominent methods and evaluation metrics in a reproducible large-scale experimental study on seven different data sets. We observe that while the different methods successfully enforce properties encouraged'' by the corresponding losses, well-disentangled models seemingly cannot be identified without supervision. Furthermore, increased disentanglement does not seem to lead to a decreased sample complexity of learning for downstream tasks. Our results suggest that future work on disentanglement learning should be explicit about the role of inductive biases and (implicit) supervision, investigate concrete benefits of enforcing disentanglement of the learned representations, and consider a reproducible experimental setup covering several data sets. Disentangled representations, where the higher level data generative factors are reflected in disjoint latent dimensions, offer several benefits such as ease of deriving invariant representations, transferability to other tasks, interpretability, etc. We consider the problem of unsupervised learning of disentangled representations from large pool of unlabeled observations, and propose a variational inference based approach to infer disentangled latent factors. We introduce a regularizer on the expectation of the approximate posterior over observed data that encourages the disentanglement. We evaluate the proposed approach using several quantitative metrics and empirically observe significant gains over existing methods in terms of both disentanglement and data likelihood (reconstruction quality). We introduce a conditional generative model for learning to disentangle the hidden factors of variation within a set of labeled observations, and separate them into complementary codes. One code summarizes the specified factors of variation associated with the labels. The other summarizes the remaining unspecified variability. During training, the only available source of supervision comes from our ability to distinguish among different observations belonging to the same class. Examples of such observations include images of a set of labeled objects captured at different viewpoints, or recordings of set of speakers dictating multiple phrases. In both instances, the intra-class diversity is the source of the unspecified factors of variation: each object is observed at multiple viewpoints, and each speaker dictates multiple phrases. Learning to disentangle the specified factors from the unspecified ones becomes easier when strong supervision is possible. Suppose that during training, we have access to pairs of images, where each pair shows two different objects captured from the same viewpoint. This source of alignment allows us to solve our task using existing methods. However, labels for the unspecified factors are usually unavailable in realistic scenarios where data acquisition is not strictly controlled. We address the problem of disentanglement in this more general setting by combining deep convolutional autoencoders with a form of adversarial training. Both factors of variation are implicitly captured in the organization of the learned embedding space, and can be used for solving single-image analogies. Experimental results on synthetic and real datasets show that the proposed method is capable of generalizing to unseen classes and intra-class variabilities. We present a framework for learning disentangled and interpretable jointly continuous and discrete representations in an unsupervised manner. By augmenting the continuous latent distribution of variational autoencoders with a relaxed discrete distribution and controlling the amount of information encoded in each latent unit, we show how continuous and categorical factors of variation can be discovered automatically from data. The learned model also contains an inference network which can infer quantities such as angle and width of objects from image data in a completely unsupervised manner. Our experiments show that the framework disentangles continuous and discrete generative factors on various datasets, including disentangling digit type from stroke thickness, angle and width on MNIST, chair type from azimuth and width on the Chairs dataset and age from azimuth on CelebA.