Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics ofobservedsequence data.

We exemplify our result in two tasks of interest in statistical learning: a) classification for a mixture with sparse means, wherewestudytheefficiencyof `1penaltywithrespectto `2;b)max-marginmulticlass classification, where we characterise the phase transition on the existence ofthemulti-class logistic maximum likelihood estimator forK >2.

Federated Learning (FL) [1]provides acommunication-efficient andprivacypreserving means to learn from data distributed across clients such as cell phones, autonomous vehicles, and hospitals. FL aims for each client to benefit from collaborating in the learning process without sacrificing data privacy or paying a substantial communication cost. Federated Averaging (FedAvg) [1] is the predominant FL algorithm.

Most work, however, focuses on either node-or graph-level supervised learning, such as node, link or graph classification or node-level unsupervised learning (e.g., node clustering). Despite its wide range of possible applications, graph-level unsupervised representation learning has not received much attention yet. This might be mainly attributed to the high representation complexity ofgraphs, which can berepresented byn!equivalent adjacencymatrices, where n is the number of nodes. In this work we address this issue by proposing a permutation-invariant variational autoencoder for graph structured data.