Comment by 3eb7988a1663
10 days ago
Instead of a naive dense matrix, you can use some implementation that allows sparsity. If element does not exist, gets a non-zero value which can still be sampled. Which theoretically enables all outputs.
10 days ago
Instead of a naive dense matrix, you can use some implementation that allows sparsity. If element does not exist, gets a non-zero value which can still be sampled. Which theoretically enables all outputs.
You're describing "temperature". That is usually done using the softmax function which cannot output zero for any element. In fact zero temperature is special cased, or they do exactly what you just said (add a teeny tiny epsilon to everything) in order to avoid having to treat zero temperature as a special case.
i think at that point it's definitionally not a markov chain anymore. how do you sample an open set of unknown values?
Yes it is, there's no rule saying you can't manually mess with the state transition function while designing and building the chain. It's still a fixed function at runtime. It's just that you don't need to do so in the first place, because this is done already after the markov chain has been evaluated, if temperature is set to nonzero (and some systems don't even really allow you to use zero temperature, they only allow you to make it really small)