Graph Neural Networks (GNNs) have revolutionized the domain of graph representation learning by utilizing neighborhood aggregation schemes in many popular architectures, such as message passing graph neural networks (MPGNNs). This scheme involves iteratively calculating a node's representation vector by aggregating and transforming the representation vectors of its adjacent nodes. Despite their effectiveness, MPGNNs face significant issues, such as oversquashing, oversmoothing, and underreaching, which hamper their effectiveness. Additionally, the reliance of MPGNNs on the homophily assumption, where edges typically connect nodes with similar labels and features, limits their performance in heterophilic contexts, where connected nodes often have significant differences. This necessitates the development of models that can operate effectively in both homophilic and heterophilic settings. In this paper, we propose a novel approach, ClassContrast, grounded in Energy Landscape Theory from Chemical Physics, to overcome these limitations. ClassContrast combines spatial and contextual information, leveraging a physics-inspired energy landscape to model node embeddings that are both discriminative and robust across homophilic and heterophilic settings. Our approach introduces contrast-based homophily matrices to enhance the understanding of class interactions and tendencies. Through extensive experiments, we demonstrate that ClassContrast outperforms traditional GNNs in node classification and link prediction tasks, proving its effectiveness and versatility in diverse real-world scenarios.

We introduce OpportunityFinder, a code-less framework for performing a variety of causal inference studies with panel data for non-expert users. In its current state, OpportunityFinder only requires users to provide raw observational data and a configuration file. A pipeline is then triggered that inspects/processes data, chooses the suitable algorithm(s) to execute the causal study. It returns the causal impact of the treatment on the configured outcome, together with sensitivity and robustness results. Causal inference is widely studied and used to estimate the downstream impact of individual's interactions with products and features. It is common that these causal studies are performed by scientists and/or economists periodically. Business stakeholders are often bottle-necked on scientist or economist bandwidth to conduct causal studies. We offer OpportunityFinder as a solution for commonly performed causal studies with four key features: (1) easy to use for both Business Analysts and Scientists, (2) abstraction of multiple algorithms under a single I/O interface, (3) support for causal impact analysis under binary treatment with panel data and (4) dynamic selection of algorithm based on scale of data.

We propose $\textit{weighted inner product similarity}$ (WIPS) for neural-network based graph embedding, where we optimize the weights of the inner product in addition to the parameters of neural networks. Despite its simplicity, WIPS can approximate arbitrary general similarities including positive definite, conditionally positive definite, and indefinite kernels. WIPS is free from similarity model selection, yet it can learn any similarity models such as cosine similarity, negative Poincar\'e distance and negative Wasserstein distance. Our extensive experiments show that the proposed method can learn high-quality distributed representations of nodes from real datasets, leading to an accurate approximation of similarities as well as high performance in inductive tasks.