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Statistical Learning Theory (Regressive model (Properties (Mean value of…
Statistical Learning Theory
Focus: Deviation between
target
function and
actual
function realized by network.
Regressive model
Properties
Mean value of the expectational error epsilon, given any realization x, is zero
Expectational error E is uncorrelated with the regression function f(X)
"mathematical" description of a stochastic
environment
Neural network to approximate the model
Terminology
B(w): bias of the average value of the approximating function
Inability of the neural network defined by the function
F(x, w) to accurately approximate the regression function f(x)
approximation error
V(w): variance of the approximating function F(x, w)
inadequacy of
the information contained in the training sample T about the regression function f(x)
estimation error
Empirical Risk Minimization
does not depend on the unknown distribution function
can be minimized with respect to the weight vector w in theory
Convergence
VC Dimension
measure of the capacity or expressive power of the family of classification functions realized by the learning machine
Good overall performance
B(w) & V(w) of the approximating function F(x, w) = F(x, T) would both have to be small
Bias variance dilemma
Supervised Learning components
Environment
Teacher
Learning machine (algorithm)