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Drug-induced liver injury (DILI) is the most common cause of acute liver failure and a frequent reason for withdrawal of candidate drugs during preclinical and clinical testing. An important type of DILI is cholestatic liver injury, caused by buildup of bile salts within hepatocytes; it is frequently associated with inhibition of bile salt transporters, such as the bile salt export pump (BSEP). Reliable in silico models to predict BSEP inhibition directly from chemical structures would significantly reduce costs during drug discovery and could help avoid injury to patients. Unfortunately, models published to date have been insufficiently accurate to encourage wide adoption. We report our development of classification and regression models for BSEP inhibition with substantially improved performance over previously published models. Our model development leveraged the ATOM Modeling PipeLine (AMPL) developed by the ATOM Consortium, which enabled us to train and evaluate thousands of candidate models. In the course of model development, we assessed a variety of schemes for chemical featurization, dataset partitioning and class labeling, and identified those producing models that generalized best to novel chemical entities. Our best performing classification model was a neural network with ROC AUC = 0.88 on our internal test dataset and 0.89 on an independent external compound set. Our best regression model, the first ever reported for predicting BSEP IC50s, yielded a test set $R^2 = 0.56$ and mean absolute error 0.37, corresponding to a mean 2.3-fold error in predicted IC50s, comparable to experimental variation. These models will thus be useful as inputs to mechanistic predictions of DILI and as part of computational pipelines for drug discovery.