Federated learning is a machine learning paradigm that enables decentralized clients to collaboratively learn a shared model while keeping all the training data local. While considerable research has focused on federated image generation, particularly Generative Adversarial Networks, Variational Autoencoders have received less attention. In this paper, we address the challenges of non-IID (independently and identically distributed) data environments featuring multiple groups of images of different types. Specifically, heterogeneous data distributions can lead to difficulties in maintaining a consistent latent space and can also result in local generators with disparate texture features being blended during aggregation. We introduce a novel approach, FissionVAE, which decomposes the latent space and constructs decoder branches tailored to individual client groups. This method allows for customized learning that aligns with the unique data distributions of each group. Additionally, we investigate the incorporation of hierarchical VAE architectures and demonstrate the use of heterogeneous decoder architectures within our model. We also explore strategies for setting the latent prior distributions to enhance the decomposition process. To evaluate our approach, we assemble two composite datasets: the first combines MNIST and FashionMNIST; the second comprises RGB datasets of cartoon and human faces, wild animals, marine vessels, and remote sensing images of Earth. Our experiments demonstrate that FissionVAE greatly improves generation quality on these datasets compared to baseline federated VAE models.

The process of liquidity provision in financial markets can result in prolonged exposure to illiquid instruments for market makers. In this case, where a proprietary position is not desired, pro-actively targeting the right client who is likely to be interested can be an effective means to offset this position, rather than relying on commensurate interest arising through natural demand. In this paper, we consider the inference of a client profile for the purpose of corporate bond recommendation, based on typical recorded information available to the market maker. Given a historical record of corporate bond transactions and bond meta-data, we use a topic-modelling analogy to develop a probabilistic technique for compiling a curated list of client recommendations for a particular bond that needs to be traded, ranked by probability of interest. We show that a model based on Latent Dirichlet Allocation offers promising performance to deliver relevant recommendations for sales traders.