Chris Wiggins gave an excellent talk at Rice this afternoon on data science at the New York Times. In the Q&A afterward, someone asked how you would set up a machine learning algorithm where you’re trying to optimize for outcomes and for information.
Here’s how I’ve approached this dilemma in the past. Information and outcomes are not directly comparable, so any objective function combining the two is going to add incommensurate things. One way around this is to put a value not on information per se but on what you’re going to do with the information.
In the context of a clinical trial, you want to treat patients in the trial effectively, and you want a high probability of picking the best treatment at the end. You can’t add patients and probabilities meaningfully. But why do you want to know which treatment is best? So you can treat future patients effectively. The value of knowing which treatment is best is the increase in the expected number of future successful treatments. This gives you a meaningful objective: maximize the expected number of effective treatments, of patients in the trial and future patients treated as a result of the trial.
The hard part is guessing what will be done with the information learned in the trial. Of course this isn’t exactly known, but it’s the key to estimating the value of the information. If nobody will be treated any differently in the future no matter how the trial turns out—and unfortunately this may be the case—then the trial should be optimized strictly for the benefit of the people in the trial. On the other hand, if a trial will determine the standard of care for thousands of future patients, then there is more value in picking the best treatment.