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Title: Elastic-InfoGAN: Unsupervised Disentangled Representation Learning in Imbalanced Data

Paper content:
We propose a novel unsupervised generative model, Elastic-InfoGAN, that learns to disentangle object identity from other low-level aspects in class-imbalanced datasets.
We first investigate the issues surrounding the assumptions about uniformity made by InfoGAN, and demonstrate its ineffectiveness to properly disentangle object identity in imbalanced data.
Our key idea is to make the discovery of the discrete latent factor of variation invariant to identity-preserving transformations in real images, and use that as the signal to learn the latent distribution's parameters.
Experiments on both artificial (MNIST) and real-world (YouTube-Faces) datasets demonstrate the effectiveness of our approach in imbalanced data by:
(i) better disentanglement of object identity as a latent factor of variation; and
(ii) better approximation of class imbalance in the data, as reflected in the learned parameters of the latent distribution.
Generative models aim to model the true data distribution, so that fake samples that seemingly belong to the modeled distribution can be generated (Ackley et al. (1985) ; Rabiner (1989) ; Blei et al. (2003) ).
Recent deep neural network based models such as Generative Adversarial Networks (Goodfellow et al. (2014) ; Salimans et al. (2016) ; ) and Variational Autoencoders (Kingma & Welling (2014) ; Higgins et al. (2017) ) have led to promising results in generating realistic samples for high-dimensional and complex data such as images.
More advanced models show how to discover disentangled representations ; Chen et al. (2016) ; Tran et al. (2017) ; Hu et al. (2018) ; Singh et al. (2019) ), in which different latent dimensions can be made to represent independent factors of variation (e.g., pose, identity) in the data (e.g., human faces).
InfoGAN ) in particular, tries to learn an unsupervised disentangled representation by maximizing the mutual information between the discrete or continuous latent variables and the corresponding generated samples.
For discrete latent factors (e.g., digit identities), it assumes that they are uniformly distributed in the data, and approximates them accordingly using a fixed uniform categorical distribution.
Although this assumption holds true for many existing benchmark datasets (e.g., MNIST LeCun (1998)), real-word data often follows a long-tailed distribution and rarely exhibits perfect balance between the categories.
Indeed, applying InfoGAN on imbalanced data can result in incoherent groupings, since it is forced to discover potentially non-existent factors that are uniformly distributed in the data; see Fig. 1 .
In this work, we augment InfoGAN to discover disentangled categorical representations from imbalanced data.
Our model, Elastic-InfoGAN, makes two modifications to InfoGAN which are simple and intuitive.
First, we remodel the way the latent distribution is used to fetch the latent variables; we lift the assumption of any knowledge about class imbalance, where instead of deciding and fixing them beforehand, we treat the class probabilities as learnable parameters of the optimization process.
To enable the flow of gradients back to the class probabilities, we employ the Gumbel-Softmax distribution (Jang et al. (2017) ; Maddison et al. (2017) ), which acts as a proxy for the categorical distribution, generating differentiable samples having properties similar to that of categorical samples.
Second, we enforce our network to assign the same latent category for an image I and its transformed image I , which induces the discovered latent factors to be invariant to identity-preserving transformations like illumination, translation, rotation, and scale changes.
Although there are multiple meaningful ways to partition unlabeled data-e.g., with digits, one partitioning could be based Samples generated with an InfoGAN model learned with a fixed uniform categorical distribution Cat(K = 10, p = 0.1) on balanced and imbalanced data, respectively.
Each row corresponds to a different learned latent category.
(Right): Samples generated with Elastic-InfoGAN using its automatically learned latent categorical distribution.
Although InfoGAN discovers digit identities in the balanced data, it produces redundant/incoherent groupings in the imbalanced data.
In contrast, our model is able to discover digit identities in the imbalanced data.
on identity, whereas another could be based on stroke width-we aim to discover the partitioning that groups objects according to a high-level factor like identity while being invariant to low-level "nuisance" factors like lighting, pose, and scale changes.
Such partitionings focusing on object identity are more likely to be useful for downstream visual recognition applications (e.g., semi-supervised object recognition).
In sum, our modifications to InfoGAN lead to better disentanglement and categorical grouping of the data (Fig. 1) , while at the same time enabling the discovery of the original imbalance through the learned probability parameters of the Gumbel softmax distribution.
Importantly, these modifications do not impede InfoGAN's ability to jointly model both continuous and discrete factors in either balanced or imbalanced data scenarios.
Our contributions can be summarized as follows: (1) To our knowledge, our work is the first to tackle the problem of unsupervised generative modeling of categorical disentangled representations in imbalanced data.
We show qualitatively and quantitatively our superiority in comparison to Info-GAN and other relevant baselines.
(2) Our work takes a step forward in the direction of modeling real data distributions, by not only explaining what modes of a factor of variation are present in the data, but also discovering their respective proportions.
In this work, we proposed a new unsupervised generative model that learns categorical disentanglement in imbalanced data.
Our model learns the class distribution of the imbalanced data and enforces invariance to be learned in the discrete latent variables.
Our results demonstrate superior performance over alternative baselines.
We hope this work will motivate other researchers to pursue this interesting research direction in generative modeling of imbalanced data.

assistant: text: Elastic-InfoGAN is a modification of InfoGAN that learns, without any supervision, disentangled representations in class imbalanced data