In general, machine learning algorithms apply In general, machine learning algorithms apply some optimization algorithm to find a good some optimization algorithm to find a good hypothesis. In this case, hypothesis. In this case,

J is piecewise piecewise

constant constant, which makes this a difficult problem , which makes this a difficult problem

The maximum likelihood estimate Direct Computation. The maximum likelihood estimate

of P(x,y) can be computed from the data without search. ) can be computed from the data without search.

However, inverting the However, inverting the Σ matrix requires O(n matrix requires O(n3) time.