An information processing system according to an embodiment includes one or more hardware processors. The hardware processors acquire an n-dimensional vector. The hardware processors generate n coordinate arrays, where the n coordinate arrays is n pieces of n-dimensional arrays for which, with respect to each of elements of an m-th array (1≤m≤n), an element value having a same value as an index of an m-th dimensional coordinate of the elements is set. The hardware processors obtain n first probability distribution arrays including an output value of a probability density function as an element value corresponding to each of the n coordinate arrays, multiply n element values for each of elements corresponding to each of the n first probability distribution arrays, and obtain a second probability distribution array having a result of multiplication as an element value.