Friedman's "Prediction vs. Explanation"

Eliezer Yudkowsky

We do ten experiments. A scientist observes the results, constructs a theory consistent with them, and uses it to predict the results of the next ten. We do them and the results fit his predictions. A second scientist now constructs a theory consistent with the results of all twenty experiments.

The two theories give different predictions for the next experiment. Which do we believe? Why?

One of the commenters links to Overcoming Bias, but as of 11PM on Sep 28th, David's blog's time, no one has given the exact answer that I would have given. It's interesting that a question so basic has received so many answers.

David D. Friedman asks:

We do ten experiments. A scientist observes the results, constructs a theory consistent with them, and uses it to predict the results of the next ten. We do them and the results fit his predictions. A second scientist now constructs a theory consistent with the results of all twenty experiments.

The two theories give different predictions for the next experiment. Which do we believe? Why?

As a machine-learning problem, it would be straightforward: The second learning algorithm (scientist) did it wrong. He's supposed to train on half the data and test on the other half. Instead he trained on all of it and skipped validation. We'd also be able to measure how relatively complex the theories were, but the problem statement doesn't give us that information.

As a human learning problem, it's foggier. The second guy could still have honestly validated his theory against the data, or not. And it's not straightforward to show that one human-readable theory is more complex than another.

But with the information we're given, we don't know anything about that. So ISTM the problem statement has abstracted away those elements, leaving us with learning algorithms done right and done wrong.

9

Friedman's "Prediction vs. Explanation"

9

9

9

Friedman's "Prediction vs. Explanation"

9

9