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We introduce a simple and effective method for learning VAEs with controllable inductive biases by using an intermediary set of latent variables. This allows us to overcome the limitations of the standard Gaussian prior assumption. In particular, it allows us to impose desired properties like sparsity or clustering on learned representations, and incorporate prior information into the learned model. Our approach, which we refer to as the Intermediary Latent Space VAE (InteL-VAE), is based around controlling the stochasticity of the encoding process with the intermediary latent variables, before deterministically mapping them forward to our target latent representation, from which reconstruction is performed. This allows us to maintain all the advantages of the traditional VAE framework, while incorporating desired prior information, inductive biases, and even topological information through the latent mapping. We show that this, in turn, allows InteL-VAEs to learn both better generative models and representations.
The variational auto-encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. However, traditional VAEs map data in a Euclidean latent space which cannot efficient
We present a method for learning latent stochastic differential equations (SDEs) from high dimensional time series data. Given a time series generated from a lower dimensional It^{o} process, the proposed method uncovers the relevant parameters of th
We propose the Wasserstein Auto-Encoder (WAE)---a new algorithm for building a generative model of the data distribution. WAE minimizes a penalized form of the Wasserstein distance between the model distribution and the target distribution, which lea
It has been conjectured that the Fisher divergence is more robust to model uncertainty than the conventional Kullback-Leibler (KL) divergence. This motivates the design of a new class of robust generative auto-encoders (AE) referred to as Fisher auto
We investigate how to exploit structural similarities of an individuals potential outcomes (POs) under different treatments to obtain better estimates of conditional average treatment effects in finite samples. Especially when it is unknown whether a