Many real-world data can be modeled as 3D graphs, but learning representations that incorporates 3D information completely and efficiently is challenging. Existing methods either use partial 3D information, or suffer from excessive computational cost. To incorporate 3D information completely and efficiently, we propose a novel message passing scheme that operates within 1-hop neighborhood.

Impactful applications such as materials discovery, hardware design, neural architecture search, or portfolio optimization require optimizing high-dimensional black-box functions with mixed and combinatorial input spaces. While Bayesian optimization has recently made significant progress in solving such problems, an in-depth analysis reveals that the current state-of-the-art methods are not reliable. Their performances degrade substantially when the unknown optima of the function do not have a certain structure. To fill the need for a reliable algorithm for combinatorial and mixed spaces, this paper proposes Bounce that relies on a novel map of various variable types into nested embeddings of increasing dimensionality. Comprehensive experiments show that Bounce reliably achieves and often even improves upon state-of-the-art performance on a variety of high-dimensional problems.

In partial multi-label learning (PML), each training example is associated with a set of candidate labels, among which only some labels are valid. As a common strategy to tackle PML problem, disambiguation aims to recover the ground-truth labeling information from such inaccurate annotations. However, existing approaches mainly rely on heuristics or ad-hoc rules to disambiguate candidate labels, which may not be universal enough in complicated real-world scenarios. To provide a principled way for disambiguation, we make a first attempt to explore the probabilistic graphical model for PML problem, where a directed graph is tailored to infer latent ground-truth labeling information from the generative process of partial multi-label data. Under the framework of stochastic gradient variational Bayes, a unified variational lower bound is derived for this graphical model, which is further relaxed probabilistically so that the desired prediction model can be induced with simultaneously identified ground-truth labeling information. Comprehensive experiments on multiple synthetic and real-world data sets show that our approach outperforms the state-of-the-art counterparts.