 Strong minimax lower bounds for learningAndras Antos and Gabor Lugosi Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra Abstract: Minimax lower bounds for concept learning state, for example, that for each sample size $n$ and learning rule $g_n$, there exists a distribution of the observation $X$ and a concept $C$ to be learnt such that the expected error of $g_n$ is at least a constant times $V/n$, where $V$ is the VC dimension of the concept class. However, these bounds do not tell anything about the rate of decrease of the error for a {\sl fixed} distribution--concept pair.\\ In this paper we investigate minimax lower bounds in such a--stronger--sense. We show that for several natural $k$--parameter concept classes, including the class of linear halfspaces, the class of balls, the class of polyhedra with a certain number of faces, and a class of neural networks, for any {\sl sequence} of learning rules $\{g_n\}$, there exists a fixed distribution of $X$ and a fixed concept $C$ such that the expected error is larger than a constant times $k/n$ for {\sl infinitely many n}. We also obtain such strong minimax lower bounds for the tail distribution of the probability of error, which extend the corresponding minimax lower bounds. Keywords: Estimation; hypothesis testing; statistical decision theory: operations research (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:upf:upfgen:197 Access Statistics for this paper More papers in Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.