/// <summary>
/// Information gain for an attribute on a set of examples
/// </summary>
private static double Importance(ICollection<Example> examples, DataAttribute attr)
{
return Entropy(examples) - Remainder(examples, attr);
}
/// <summary>
/// Remaining entropy after attribute divides example set
/// </summary>
private static double Remainder(ICollection<Example> examples, DataAttribute attr)
{
var subsets = examples.ToLookup(x => x.Attributes[attr.ColNum]);
return subsets.Select(x => x.ToList())
.Select(subset => new
{
prob = (double)subset.Count / examples.Count,
entropy = Entropy(subset),
})
.Sum(x => x.prob * x.entropy);
}