As machine learning algorithms start to get integrated into the decision-making process of companies and organizations, insurance products are being developed to protect their owners from liability risk. Algorithmic liability differs from human liability since it is based on a single model compared to multiple heterogeneous decision-makers and its performance is known a priori for a given set of data. Traditional actuarial tools for human liability do not take these properties into consideration, primarily focusing on the distribution of historical claims. We propose, for the first time, a quantitative framework to estimate the risk exposure of insurance contracts for machine-driven liability, introducing the concept of algorithmic insurance. Specifically, we present an optimization formulation to estimate the risk exposure of a binary classification model given a pre-defined range of premiums. We adjust the formulation to account for uncertainty in the resulting losses using robust optimization. Our approach outlines how properties of the model, such as accuracy, interpretability, and generalizability, can influence the insurance contract evaluation. To showcase a practical implementation of the proposed framework, we present a case study of medical malpractice in the context of breast cancer detection. Our analysis focuses on measuring the effect of the model parameters on the expected financial loss and identifying the aspects of algorithmic performance that predominantly affect the risk of the contract.

Artificial intelligence methods including deep neural networks (DNN) can provide rapid molecular classification of tumors from routine histology with accuracy that matches or exceeds human pathologists. Discerning how neural networks make their predictions remains a significant challenge, but explainability tools help provide insights into what models have learned when corresponding histologic features are poorly defined. Here, we present a method for improving explainability of DNN models using synthetic histology generated by a conditional generative adversarial network (cGAN). We show that cGANs generate high-quality synthetic histology images that can be leveraged for explaining DNN models trained to classify molecularly-subtyped tumors, exposing histologic features associated with molecular state. Fine-tuning synthetic histology through class and layer blending illustrates nuanced morphologic differences between tumor subtypes. Finally, we demonstrate the use of synthetic histology for augmenting pathologist-in-training education, showing that these intuitive visualizations can reinforce and improve understanding of histologic manifestations of tumor biology.