Browsing by Author "Mouton, Jacobie"

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    Integrating Bayesian network structure into normalizing flows and variational autoencoders
    (Stellenbosch : Stellenbosch University, 2023-03) Mouton, Jacobie; Kroon, Steve; Stellenbosch University. Faculty of Science. Dept. of Computer Science.
    ENGLISH ABSTRACT: Deep generative models have become more popular in recent years due to their good scalability and representation capacity. However, these models do not typically incorporate domain knowledge. In contrast, probabilistic graphical models speci_cally constrain the dependencies between the variables of interest as informed by the domain. In this work, we therefore consider integrating probabilistic graphical models and deep generative models in order to construct models that are able to learn complex distributions, while remaining interpretable by leveraging prior knowledge about variable interactions. We specifically consider the type of domain knowledge that can be represented by Bayesian networks, and restrict our study to the deep generative frameworks of normalizing flows and variational autoencoders. Normalizing flows (NFs) are an important family of deep neural networks for modelling complex distributions as transformations of simple base distributions. Graphical _ows add further structure to NFs, allowing one to encode non-trivial variable dependencies in these distributions. Previous graphical flows have focused primarily on a single _ow direction: either the normalizing direction for density estimation, or the generative direction for inference and sampling. However, to use a single _ow to perform tasks in both directions, the model must exhibit stable and efficient flow inversion. This thesis introduces graphical residual flows (GRFs)_graphical flows based on invertible residual networks_which ensure stable invertibility by spectral normalization of its weight matrices. Experiments confirm that GRFs provide performance competitive with other graphical flows for both density estimation and inference tasks. Furthermore, our model provides stable and accurate inversion that is also more time-efficient than alternative flows with similar task performance. We therefore recommend the use of GRFs over other graphical flows when the model may be required to perform reliably in both directions. Since flows employ a bijective transformation, the dimension of the base or latent distribution must have the same dimensionality as the observed data. Variational autoencoders (VAEs) address this shortcoming by allowing practitioners to specify any number of latent variables. Initial work on VAEs assumed independent latent variables with simple prior and variational distributions. Subsequent work has explored incorporating more complex distributions and dependency structures: including NFs in the encoder network allows latent variables to entangle non-linearly, creating a richer class of distributions for the approximate posterior, and stacking layers of latent variables allows more complex priors to be specified. In this vein, this thesis also explores incorporating arbitrary dependency structures_as specified by Bayesian networks_into VAEs. This is achieved by extending both the prior and inference network with the above GRF, resulting in the structured invertible residual network (SIReN) VAE. We specifically consider GRFs, since the application of the _ow in the VAE prior necessitates stable inversion. We compare our model's performance on several datasets to models that encode no special dependency structures, and show its potential to provide a more interpretable model as well as better generalization performance in data-sparse settings. We also identify posterior collapse_where some latent dimensions become inactive and are effectively ignored by the model_as an issue with SIReN-VAE, as it is linked with the encoded structure. As such, we employ various combinations of existing approaches to alleviate this phenomenon.