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"In the latest paper, Yehudayoff and his collaborators define learnability as the ability to make predictions about a large data set by sampling a small number
by placebo 8y ago
"In the latest paper, Yehudayoff and his collaborators define learnability as the ability to make predictions about a large data set by sampling a small number of data points. The link with Cantor’s problem is that there are infinitely many ways of choosing the smaller set, but the size of that infinity is unknown."
Reading this got me wondering about more philosophical aspects, such as the relation of this conclusion to to the process of human learning and prediction (which obviously works) and whether it's somehow tied in some way to the problem of induction. Could be nonsense, but I'll be putting some more thought into the meaning of this
- pas 8y agoThe problem with these papers is, that if you want to do practical ML, you can simply fix some upper bounds on various numbers that arise during the analysis of the problem, and thus make it mathematically finite, and trivial. Not easy, of course, but this frees you from the infinite regress that's the problem of induction. Sure, you can the start to ask what are the good upper bounds. How many epochs to use for training, start to quantify the training set quality, and then ask how good that must be to get a good enough model. Etc. But all of these then can be limited by estimation.
- gus_massa 8y agoDon't read too in this result. This is about perfect classifiers, if it is enough to train a perfect classifier using only a finite amount of samples of the set. People learn, but sometimes learn with mistakes. For example: * Is this mushroom edible? It's much easier to make a good enough classifier than a perfect classifier, if you allow a broad definition of good enough.