A comment from Professor Peter Grünwald
Head, Information-theoretic Learning Group, Centrum voor Wiskunde en Informatica (CWI)
Part-time full professor at Leiden University.
This is a follow-up on Vladimir Cherkassky’s comments on Deborah’s blog. First of all let me thank Vladimir for taking the time to clarify his position. Still, there’s one issue where we disagree and which, at the same time, I think, needs clarification, so I decided to write this follow-up.[related posts 1]
The issue is about how central VC (Vapnik-Chervonenkis)-theory is to inductive inference.
I agree with Vladimir that VC-theory is one of the most important achievements in the field ever, and indeed, that it fundamentally changed our way of thinking about learning from data. Yet I also think that there are many problems of inductive inference to which it has no direct bearing. Some of these are concerned with hypothesis testing, but even when one is concerned with prediction accuracy – which Vladimir considers the basic goal – there are situations where I do not see how it plays a direct role. One of these is sequential prediction with log-loss or its generalization, Cover’s loss. This loss function plays a fundamental role in (1) language modeling, (2) on-line data compression, (3a) gambling and (3b) sequential investment on the stock market (here we need Cover’s loss). [a superquick intro to log-loss as well as some references are given below under [A]; see also my talk at the Ockham workshop (slides 16-26 about weather forecasting!) )