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As I can see, your goal is to predict hospital stay lengths and costs for patients at a certain hospital based on certain information about the patient. Seems like a very interesting idea. The thing that caught my eye the most was that you mentioned covering specific cases, like heart attack victims, because your model was too general. Do you have access to the condition they're coming in for? Because if you do, that would probably be worth putting in the model. I would also try different feature transformations if possible. Like since the length of stays of exponentially distributed themselves, it's very possible they have an exponential relationship with various real valued features.
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