Multimodal Prescriptive Deep Learning

Dimitris Bertsimas, Lisa Everest, Vasiliki Stoumpou

Abstract: We introduce a multimodal deep learning framework, Prescriptive Neural Networks (PNNs), that combines ideas from optimization and machine learning to perform treatment recommendation, and that, to the best of our knowledge, is among the first prescriptive approaches tested with both structured and unstructured data within a unified model. The PNN is a feedforward neural network trained on embeddings to output an outcome-optimizing prescription. In two real-world multimodal datasets, we demonstrate that PNNs prescribe treatments that are able to greatly improve estimated outcome rewards; by over 40% in transcatheter aortic valve replacement (TAVR) procedures and by 25% in liver trauma injuries. In four real-world, unimodal tabular datasets, we demonstrate that PNNs outperform or perform comparably to other well-known, state-of-the-art prescriptive models; importantly, on tabular datasets, we also recover interpretability through knowledge distillation, fitting interpretable Optimal Classification Tree models onto the PNN prescriptions as classification targets, which is critical for many real-world applications. Finally, we demonstrate that our multimodal PNN models achieve stability across randomized data splits comparable to other prescriptive methods and produce realistic prescriptions across the different datasets.

Submission Length: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=tPdIg0CK6B

Changes Since Last Submission:

Note to the editor(s)/reviewer(s) for completeness: we include our first submission URL in the previous entry (Previous TMLR Submission Url). We have followed up a second submission as a re-submission (https://openreview.net/forum?id=AwfWOCVLbJ). This current submission is our response to the review of the second submission.

We thank the editor for the acceptance and appreciate the time taken in the reply. To address the remaining reviewers’ points, we would like to emphasize, as you also kindly mentioned in your comments, that we evaluate our experiments according to the well-accepted principles of Off-Policy Evaluation. Acknowledging the limitations of evaluating prescriptive problems, we use different reward estimators on the training and test set, we perform multiple splits/bootstrap analysis, and we use different models for the reward estimation to not attribute the performance gains on only the Doubly Robust estimator. We have made this more explicit in the paper, Section 3.5.

Assigned Action Editor: ~Devendra_Singh_Dhami1

Submission Number: 5612