epsilon

const epsilon: 0.0001 = 0.0001

Defined in: src/epsilon.js:35

We use ε, epsilon, as a stopping criterion when we want to iterate until we’re “close enough”. Epsilon is a very small number: for simple statistics, that number is 0.0001

This is used in calculations like the binomialDistribution, in which the process of finding a value is iterative: it progresses until it is close enough.

Below is an example of using epsilon in gradient descent, where we’re trying to find a local minimum of a function’s derivative, given by the fDerivative method.

Example

// From calculation, we expect that the local minimum occurs at x=9/4
var x_old = 0;
// The algorithm starts at x=6
var x_new = 6;
var stepSize = 0.01;

function fDerivative(x) {
  return 4 * Math.pow(x, 3) - 9 * Math.pow(x, 2);
}

// The loop runs until the difference between the previous
// value and the current value is smaller than epsilon - a rough
// meaure of 'close enough'
while (Math.abs(x_new - x_old) > ss.epsilon) {
  x_old = x_new;
  x_new = x_old - stepSize * fDerivative(x_old);
}

console.log('Local minimum occurs at', x_new);