Distance-reducing Markov bases for sampling from a discrete sample space
Akimichi Takemura, Satoshi Aoki · Bernoulli · 2005
We study Markov bases for sampling from a discrete sample space equipped with a convenient metric. Starting from any two states in the sample space, we ask whether we can always move closer by an element of a Markov basis. We call a Markov basis distance-reducing if this is the case. The particular metric we consider in this paper is the L1-norm on the sample space. Some characterizations of L1-norm-reducing Markov bases are derived.