Evaluating expectations on an Ising model (or Boltzmann machine) is essential for various applications, including statistical machine learning. However, in general, the evaluation computationally difficult because it involves intractable multiple summations or integrations; therefore, requires approximation. Monte Carlo integration (MCI) a well-known approximation method; more effective MCI-lik...

The adaptive multi-channel method is applied to derive probability distributions from data samples. Moreover, an explicit algorithm is introduced, for which both the channel weights and the channels themselves are adaptive, and which can be used both for data analysis and for importance sampling in Monte Carlo integration. Finally, it is pointed out how the usefulness for data analysis can be u...

A new method is proposed for Monte Carlo integration. This method is more efficient with wider coverage, including improper integrals, while the classical Monte Carlo integration can only handle bounded domain integrals. To implement this method in computer programming, you only need a random number generator. Unlike the deterministic numerical integration methods, the expected error of this me...

In this note I illustrate the program MINT, a FORTRAN program for Monte Carlo adaptive integration and generation of unweighted distributions. ∗This document has been produced using TEXmacs(see http://www.texmacs.org)

A simple procedure for decreasing the statistical error associated with Monte Carlo integration of oscillatory functions is presented. The method uses available information about the integral of a similar oscillatory function to correlate the estimates of the positive and negative components of the integral. Numerical tests show that information guided noise reduction (IGNoR) leads to substanti...