Algorithm 1. TreeShap.

1: function TS(x, tree)

2:   ϕ = array of len(x) zeroes

3:   function RECURSE(j, m, pz, po, pi)

4:    m = EXTEND(m, pz, po, pi)

5:    if vj == leaf then

6:     for $i\leftarrow 2$ to len(m) do

7:      w = sum(UNWIND(m, i).w)

8:       ${\varphi }_{m_i.d}={\varphi }_{m_i.d}+w(m_i.o-m_i.z)v_j$

9:    else

10:      $h,c=x_{d_j}\le t_j?(a_j,b_j):(b_j,a_j)$

11:     iz = io = 1

12:     k = FINDFIRST(m.d, dj)

13:     if k ≠ nothing then

14:      iz, io = (mk.z, mk.o)

15:      m = UNWIND(m, k)

16:    RECURSE(h, m, izrh/rj, io, dj)

17:    RECURSE(c, m, izrc/rj, 0, dj)

18:   function EXTEND(m, pz, po, pi)

19:    l = len(m)

20:    m = copy(m) {m is copied so recursions down other branches are not affected.}

21:    ml+1.(d, z, o, w) = (pi, pz, po, l = 0 ? 1 : 0)

22:    for $i\leftarrow l$ to 1 do

23:     mi+1.w = mi+1.w + po ⋅ mi.w ⋅ i/(l + 1)

24:     mi.w = pz ⋅ mi.w ⋅ (l + 1 − i)/(l + 1)

25:    return m

26:   function UNWIND(m, i)

27:    l = len(m)

28:    n = ml.w

29:    m = copy(m1⋯l−1)

30:    for $j\leftarrow l-1$ to 1 do

31:     if mi.o ≠ 0 then

32:      t = mj.w

33:      mj.w = n ⋅ l/(j ⋅ mi.o)

34:      n = t − mj.w ⋅ mi.z ⋅ (l − j)/l

35:    else

36:     mj.w = (mj.w ⋅ l)/(mi.z ⋅ (l − j))

37:    for $j\leftarrow i$ to l − 1 do

38:     mj.(d, z, o) = mj+1.(d, z, o)

39:    return m

40:   RECURSE(1, [], 1, 1, 0)

41:   return ϕ