If you generate the subset at the beginning instead of at the end, you can simplify all the == null and != null checks:
public static int[] computeRandomSubset(int n, int k) {
Map<Integer, Integer> changed = new HashMap<>();
Random r = new Random();
int[] subset = new int[k];
for (int i = 0; i < k; i++) {
subset[i] = i;
}
for (int i = 0; i < k; i++) {
int pos = i + r.nextInt(n - i);
if (pos < subset.length) { //we are inside array, swap just those 2 elements, don't change the map
swap(subset, i, pos);
} else { //outside of the array, check if the index was changed using a map
int temp = subset[i];
subset[i] = changed.containsKey(pos) ? changed.get(pos) : pos;
changed.put(pos, temp);
}
}
return subset;
}