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I have a distribution from which I can sample (namely, a Boltzmann Machine).

Which methods exists to determine frequent states (states with high probability) / the most frequent state (state with the highest probability)?

Two possibilities are, of course, computing the full distribution and taking the max (which may be computationally prohibitive for large distributions) and sampling for a long time and recording how frequent states occur (which also isn't trivial since we possibly need to keep a record for every state, this also leaves the problem of deciding when to stop).

Are there other methods capable of finding good states, i.e. when we don't require finding the most likely state but a "very likely" state is sufficient?

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