Heterogeneous graph representation learning aims to learn low-dimensional vector representations of different types of entities and relations to empower downstream tasks. Existing methods either capture semantic relationships but indirectly leverage node/edge attributes in a complex way, or leverage node/edge attributes directly without taking semantic relationships into account. When involving multiple convolution operations, they also have poor scalability. To overcome these limitations, this paper proposes a flexible and efficient Graph information propagation Network (GripNet) framework. Specifically, we introduce a new supergraph data structure consisting of supervertices and superedges. A supervertex is a semantically-coherent subgraph. A superedge defines an information propagation path between two supervertices. GripNet learns new representations for the supervertex of interest by propagating information along the defined path using multiple layers. We construct multiple large-scale graphs and evaluate GripNet against competing methods to show its superiority in link prediction, node classification, and data integration.

Precise estimation of cross-correlation or similarity between two random variables lies at the heart of signal detection, hyperdimensional computing, associative memories, and neural networks. Although a vast literature exists on different methods for estimating cross-correlations, the question what is the best and simplest method to estimate cross-correlations using finite samples ? is still unclear. In this paper, we first argue that the standard empirical approach might not be the optimal method even though the estimator exhibits uniform convergence to the true cross-correlation. Instead, we show that there exists a large class of simple non-linear functions that can be used to construct cross-correlators with a higher signal-to-noise ratio (SNR). To demonstrate this, we first present a general mathematical framework using Price's Theorem that allows us to analyze cross-correlators constructed using a mixture of piece-wise linear functions. Using this framework and high-dimensional embedding, we show that some of the most promising cross-correlators are based on Huber's loss functions, margin-propagation (MP) functions, and the log-sum-exp (LSE) functions.

The population of the earth is constantly growing and therefore also the demand for food. In consequence, breeding crop plants which most efficiently make use of the available cropland is one of the greatest challenges nowadays. In particular, plants which are resilient and resistant to environmental stresses are desirable. The development of such plants relies on the investigation of the interaction between the plant's genes and the environmental stresses. In order to be able to investigate the interaction a quantitative representation of the environmental stresses is needed. Here, we consider this representation combining state-of-the-art data-driven methods with expert-driven modeling from agriculture. Briefly put, it has been reported that environmental stress such as inappropriate or extreme temperature conditions, lack of sufficient moisture, etc., can significantly impede the life cycle development of corn, thus leading to yield reductions (cf.