powerlaw {OptHoldoutSize}

Power law function

Description

Power law function for modelling learning curve (taken to mean change in expected loss per sample with training set size)

Recommended in review of learning curve forms

If theta=c(a,b,c) then models as ⁠a n^(-b) + c⁠. Note b is negated.

Note that powerlaw(n,c(a,b,c)) has limit c as n tends to infinity, if ⁠a,b > 0⁠

Usage

powerlaw(n, theta)

Arguments

n

Set of training set sizes to evaluate

theta

Parameter of values

Value

Vector of values of same length as n

Examples

ncheck=seq(1000,10000)
plot(ncheck, powerlaw(ncheck, c(5e3,1.2,0.3)),type="l",xlab="n",ylab="powerlaw(n)")