eXact-Prior Variational Autoencoder (X-VAE): Learning Data-Adaptive Gaussian Mixture Priors for Latent Distributions

Collection of 12 recent arXiv submissions (2026-07-03) in statistics and machine learning. Key contributions include: X-VAE — a data-adaptive Gaussian-mixture-like prior for VAEs to improve reconstruction and controllability; LF-IBIS — a likelihood-free algorithm for full Bayesian reinforcement learning enabling online posterior updates when likelihoods are intractable; theoretical results for k-means with data missing completely at random; auto-relevance and Shapley-based lag-importance measures for univariate time series; a continuum variational formulation for shallow neural networks with ℓ