Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability

Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a simulator posing the need for simulation-based inference (SBI). However, the existing algorithms can yield overconfident posteriors (Hermans *et al.*, 2022) defeating the whole purpose of credibility if the uncertainty quantification is inaccurate. We propose to include a calibration term directly into the training objective of the neural model in selected amortized SBI techniques. By introducing a relaxation of the classical formulation of calibration error we enable end-to-end backpropagation. The proposed method is not tied to any particular neural model and brings moderate computational overhead compared to the profits it introduces. It is directly applicable to existing computational pipelines allowing reliable black-box posterior inference. We empirically show on six benchmark problems that the proposed method achieves competitive or better results in terms of coverage and expected posterior density than the previously existing approaches.

Incremental embedding for temporal networks

Prediction over edges and nodes in graphs requires appropriate and efficiently achieved data representation. Recent research on representation learning for dynamic networks resulted in a significant progress. However, the more precise and accurate methods, the greater computational and memory complexity. Here, we introduce ICMEN - the first-in-class incremental meta-embedding method that produces vector representations of nodes respecting temporal dependencies in the graph. ICMEN efficiently constructs nodes' embedding from historical representations by linearly convex combinations making the process less memory demanding than state-of-the-art embedding algorithms. The method is capable of constructing representation for inactive and new nodes without a need to re-embed. The results of link prediction on several real-world datasets shown that applying ICMEN incremental meta-method to any base embedding approach, we receive similar results and save memory and computational power. Taken together, our work proposes a new way of efficient online representation learning in dynamic complex networks.