I meant Lehmann's Theory of Point Estimation, but large sample theory is a good book too. The newer editions of TPE are a tad hefty in number of pages. The earlier versions would serve you fine.
The generic idea is that smaller these dimensions, easier the prediction problem. Intrinsic dimension is one that comes closest to topology. VC is very combinatorial and gives the worst of worst case bounds. For a typical sized dataset one ends up with an error probability estimate of less than 420. With PAC-Bayes the bounds are atleast less than 1.0.
I meant Lehmann's Theory of Point Estimation, but large sample theory is a good book too. The newer editions of TPE are a tad hefty in number of pages. The earlier versions would serve you fine.
The generic idea is that smaller these dimensions, easier the prediction problem. Intrinsic dimension is one that comes closest to topology. VC is very combinatorial and gives the worst of worst case bounds. For a typical sized dataset one ends up with an error probability estimate of less than 420. With PAC-Bayes the bounds are atleast less than 1.0.