Since, for a general artificial neural network, computing the expectation value is an exponentially costly operation in N , stochastic techniques based, for example, on the Monte Carlo method are used to estimate E ( W ) , analogously to what is done in Variational Monte Carlo, see for example for a review. More specifically, a set of M samples S ( 1 ) , S ( 2 ) … … S ( M ) , with S ( i ) = s 1 ( i ) … … s N ( i ) , is generated such that they are uniformly distributed according to the Born probability density P ( S ) ∝ ∝ | F ( s 1 … … s N ; W ) | 2 . Then it can be shown that the sample mean of the so-called "local energy" E l o c ( S ) = ⟨ ⟨ S | H ^ ^ | Ψ Ψ ⟩ ⟩ / ⟨ ⟨ S | Ψ Ψ ⟩ ⟩ is a statistical estimate of the quantum expectation value E ( W ) , i.e.