Eout

Eout (often written E_out) is a term used in multiple disciplines, most prominently in statistical learning theory to denote the out-of-sample or generalization error of a hypothesis. In this context, E_out is defined as the expected loss of a model h on the true data distribution, typically expressed as E_out = E_{(X,Y)~P}[L(h(X), Y)]. For classification with 0-1 loss, E_out is the probability that h makes a wrong prediction; for regression with squared loss, it is the expected squared error. E_out is contrasted with E_in, the error on the training sample, and with empirical risk as estimated from data.

In learning theory, E_out provides a target measure of performance on unseen data and is central to generalization. The gap between E_in and E_out depends on sample size and the complexity of the hypothesis class, with bounds derived from VC dimension, Rademacher complexity, and related concepts. These bounds guide model selection and learning guarantees.

In engineering and signal processing, Eout may appear as a symbol for an output error term or external output in a system model; however, its interpretation is not standardized and varies by author. Across disciplines, the concept of an out-of-sample or external output error remains a common thread.