def learn(self, domain, data):
# Create a new model
m = Model("kDNF")
print("Data")
for row, l in data:
print(*(["{}: {:.2f}".format(v, Learner._convert(row[v])) for v in domain.variables] + [l]))
print()
# Computed constants
n_f = len(domain.variables)
n_h = (2 * self.max_hyperplanes) if self.negated_hyperplanes else self.max_hyperplanes
n_d = len(data)
k = self.k
naive_misclassification = float(Learner._get_misclassification(data))
x = [[Learner._convert(row[v]) for v in domain.variables] for row, _ in data]
# Variables
s_h = [m.addVar(vtype=GRB.BINARY, name="s_H({h})".format(h=h)) for h in range(n_h)]
s_d = [m.addVar(vtype=GRB.BINARY, name="s_D({i})".format(i=i)) for i in range(n_d)]
z_h = [
[m.addVar(vtype=GRB.BINARY, name="z_H({h}, {c})".format(h=h, c=c)) for c in range(k)]
for h in range(n_h)
]
z_d = [
[m.addVar(vtype=GRB.BINARY, name="z_D({i}, {c})".format(i=i, c=c)) for c in range(k)]
for i in range(n_d)
]
z_ih = [
[m.addVar(vtype=GRB.BINARY, name="z_IH({i}, {h})".format(i=i, h=h)) for h in range(n_h)]
for i in range(n_d)
]
z_ihc = [
[
[m.addVar(vtype=GRB.BINARY, name="z_IHC({i}, {h}, {c})".format(i=i, h=h, c=c)) for c in range(k)]
for h in range(n_h)
]
for i in range(n_d)
]
a = [
[m.addVar(vtype=GRB.CONTINUOUS, lb=-1, ub=1, name="a({h}, {j})".format(h=h, j=j)) for j in range(n_f)]
for h in range(n_h / 2 if self.negated_hyperplanes else n_h)
]
b = [m.addVar(vtype=GRB.CONTINUOUS, lb=-1, ub=1, name="b({h})".format(h=h))
for h in range(n_h / 2 if self.negated_hyperplanes else n_h)]
print()
# Set objective
misclassification = sum(1 - s_d[i] if data[i][1] else s_d[i] for i in range(n_d))
m.setObjective(misclassification / naive_misclassification + self.alpha * sum(s_h), GRB.MINIMIZE)
# Add constraint: SUM_(j = 1..n_h) a(h, j) * x(i, j) <= b(h) + M(1 - z_ih(i, h)) for all h, i
for h in range(n_h / 2 if self.negated_hyperplanes else n_h):
for i in range(n_d):
name = "SUM_(j = 1..n_H) a({h}, j) * x({i}, j) <= b({h}) + M(1 - z_IH({i}, {h}))".format(h=h, i=i)
m.addConstr(sum(a[h][j] * x[i][j] for j in range(n_f)) <= b[h] + (n_f + 1) * (1 - z_ih[i][h]), name)
print(name)
print()
for h in range(n_h / 2 if self.negated_hyperplanes else n_h):
for i in range(n_d):
name = "SUM_(j = 1..n_H) a({h}, j) * x({i}, j) >= b({h}) - mu - M * z_IH({i}, {h})".format(h=h, i=i)
m.addConstr(sum(a[h][j] * x[i][j] for j in range(n_f)) >= b[h] - self.mu - (n_f + 1) * z_ih[i][h], name)
print(name)
print()
if self.negated_hyperplanes:
for h in range(n_h / 2):
for i in range(n_d):
name = "z_IH({i}, {h}) = 1 - z_IH({i}, {hi})".format(i=i, h=h, hi=(h + n_h / 2))
m.addConstr(z_ih[i][n_h / 2 + h] == 1 - z_ih[i][h], name)
print(name)
print()
# If a hyperplane is assigned to any conjunction, it is selected (used)
for h in range(n_h):
for c in range(k):
name = "s_H({h}) >= z_H({h}, {c})".format(h=h, c=c)
m.addConstr(s_h[h] >= z_h[h][c], name)
print(name)
print()
# If a hyperplane is not assigned to any conjunction, it cannot be selected (used)
for h in range(n_h):
name = "s_H({h}) <= SUM_(c = 1..k) z_H({h}, c)".format(h=h)
m.addConstr(s_h[h] <= sum(z_h[h][c] for c in range(k)), name)
print(name)
print()
# If an example i is not assigned to c, then it cannot be assigned to every h that is assigned to c
# for c in range(k):
# for i in range(n_d):
# # TODO name
# name = "z_IH({i}, {h}) + z_H({h}, {c}) >= 2 - 2 * (1 - z_D({i}, {c}))".format(h=h, c=c, i=i)
# m.addConstr(sum(z_h[h][c] for h in range(n_h)) - sum(z_ihc[i][h][c] for h in range(n_h)) <= n_h * (1 - z_d[i][c]))
# m.addConstr(sum(z_h[h][c] for h in range(n_h)) - sum(z_ihc[i][h][c] for h in range(n_h)) >= n_h * (1 - z_d[i][c]))
# print(name)
# print()
# If (h, c) then (i, c) can only be selected if every (i, h, c) is selected
for c in range(k):
for h in range(n_h):
for i in range(n_d):
name = "z_D({i}, {c}) <= z_IHC({i}, {h}, {c}) + (1 - z_H({h}, {c}))".format(c=c, h=h, i=i)
m.addConstr(z_d[i][c] <= z_ihc[i][h][c] + (1 - z_h[h][c]), name)
print(name)
print()
# If (h, c) then (i, c) can only not be selected if some (i, h, c) is not selected
# for c in range(k):
# for h in range(n_h):
# for i in range(n_d):
# name = "z_D({i}, {c}) <= z_IHC({i}, {h}, {c}) + (1 - z_H({h}, {c}))".format(c=c, h=h, i=i)
# m.addConstr(z_d[i][c] <= z_ihc[i][h][c] + (1 - z_h[h][c]), name)
# print(name)
# print()
# If (i, c) is not selected, then there must exist an h such that: (h, c) and not (i, h, c)
for c in range(k):
for i in range(n_d):
name = "..." # TODO name
m.addConstr(sum(z_h[h][c] for h in range(n_h)) - sum(z_ihc[i][h][c] for h in range(n_h)) >= 1 - z_d[i][c], name)
print(name)
print()
# If (i, c) is selected, then there must be at least one selected tuple (h, c)
for c in range(k):
for i in range(n_d):
name = "SUM_(h = 1..n_H) z_H(h, {c}) >= 1 - (1 - z_D({i}, {c}))".format(c=c, i=i)
m.addConstr(sum(z_h[h][c] for h in range(n_h)) >= 1 - (1 - z_d[i][c]))
print(name)
print()
# If the triple (i, h, c) is selected, then both (i, h) and (h, c) must be true
for h in range(n_h):
for c in range(k):
for i in range(n_d):
name = "z_IH({i}, {h}) + z_H({h}, {c}) >= 2 - 2 * (1 - z_IHC({i}, {h}, {c}))".format(h=h, c=c, i=i)
m.addConstr(z_ih[i][h] + z_h[h][c] >= 2 - 2 * (1 - z_ihc[i][h][c]), name)
print(name)
print()
# If the triple (i, h, c) is not selected, then either (i, h) or (h, c) must be false
for h in range(n_h):
for c in range(k):
for i in range(n_d):
name = "z_IH({i}, {h}) + z_H({h}, {c}) <= 2 * z_IHC({i}, {h}, {c}) + 1".format(h=h, c=c, i=i)
m.addConstr(z_ih[i][h] + z_h[h][c] <= 2 * z_ihc[i][h][c] + 1, name)
print(name)
print()
# If an example is assigned to any conjunction, it is selected (covered)
for i in range(n_d):
for c in range(k):
name = "s_D({i}) >= z_D({i}, {c})".format(i=i, c=c)
m.addConstr(s_d[i] >= z_d[i][c], name)
print(name)
print()
# If an example is not assigned to any conjunction, it cannot be selected (covered)
for i in range(n_d):
name = "s_D({i}) <= SUM_(c = 1..k) z_D({i}, c)".format(i=i)
m.addConstr(s_d[i] <= sum(z_d[i][c] for c in range(k)), name)
print(name)
print()
# Examples can only be assigned to active hyperplanes
# z_ih <= s_h for all i, h
# for h in range(n_h):
# for i in range(n_d):
# name = "z_ih({i}, {h}) <= s_h({h})".format(i=i, h=h)
# m.addConstr(z_ih[i][h] <= s_h[h], name)
# print(name)
# print()
# Hack example
# m.addConstr(a[0][0] == 1)
# m.addConstr(a[0][1] == 0)
# m.addConstr(b[0] == 0.5)
#
# m.addConstr(a[1][0] == 0)
# m.addConstr(a[1][1] == 1)
# m.addConstr(b[1] == 0.5)
#
# m.addConstr(a[2][0] == -1)
# m.addConstr(a[2][1] == 0)
# m.addConstr(b[2] == -0.5)
#
# m.addConstr(a[3][0] == 0)
# m.addConstr(a[3][1] == -1)
# m.addConstr(b[3] == -0.5)
#
# m.addConstr(s_h[0] == 1)
# m.addConstr(s_h[1] == 1)
# m.addConstr(s_h[2] == 1)
# m.addConstr(s_h[3] == 1)
# m.addConstr(z_h[0][0] == 1)
# m.addConstr(z_h[1][0] == 1)
# m.addConstr(z_h[2][0] == 0)
# m.addConstr(z_h[3][0] == 0)
# m.addConstr(z_h[0][1] == 0)
# m.addConstr(z_h[1][1] == 0)
# m.addConstr(z_h[2][1] == 1)
# m.addConstr(z_h[3][1] == 1)
# m.addConstr(z_ih[0][0] == 1)
# m.addConstr(z_ih[1][0] == 0)
# m.addConstr(z_ih[2][0] == 1)
# m.addConstr(z_ih[3][0] == 0)
# m.addConstr(z_ih[0][1] == 1)
# m.addConstr(z_ih[1][1] == 0)
# m.addConstr(z_ih[2][1] == 0)
# m.addConstr(z_ih[3][1] == 1)
# m.addConstr(z_ih[0][2] == 0)
# m.addConstr(z_ih[1][2] == 1)
# m.addConstr(z_ih[2][2] == 0)
# m.addConstr(z_ih[3][2] == 1)
# m.addConstr(z_ih[0][3] == 0)
# m.addConstr(z_ih[1][3] == 1)
# m.addConstr(z_ih[2][3] == 1)
# m.addConstr(z_ih[3][3] == 0)
# m.addConstr(z_d[0][0] == 1)
# m.addConstr(z_d[1][0] == 0)
# m.addConstr(z_d[2][0] == 0)
# m.addConstr(z_d[3][0] == 0)
# m.addConstr(z_d[0][1] == 0)
# m.addConstr(z_d[1][1] == 0)
# m.addConstr(z_d[2][1] == 1)
# m.addConstr(z_d[3][1] == 0)
# Wrong solution
# m.addConstr(a[0][0] == 1)
# m.addConstr(a[0][1] == 0)
# m.addConstr(b[0] == 0.5)
#
# m.addConstr(a[1][0] == 0)
# m.addConstr(a[1][1] == 1)
# m.addConstr(b[1] == 0.5)
#
# m.addConstr(a[2][0] == -1)
# m.addConstr(a[2][1] == 0)
# m.addConstr(b[2] == -0.6)
#
# m.addConstr(a[3][0] == 0)
# m.addConstr(a[3][1] == -1)
# m.addConstr(b[3] == -0.6)
#
# m.addConstr(s_h[0] == 1)
# m.addConstr(s_h[1] == 1)
# m.addConstr(s_h[2] == 1)
# m.addConstr(s_h[3] == 1)
m.optimize()
for v in m.getVars():
print(v.varName, v.x)
print('Obj:', m.objVal)
print()
# Lets extract the kDNF formulation
print("Hyperplanes")
conjunctions = []
from pysmt.shortcuts import And, Or, Real, LE, Plus, Times, Symbol
for conj in range(k):
conjunction = []
for h in range(n_h):
if int(z_h[h][conj].x) == 1:
if h < n_h / 2 or not self.negated_hyperplanes:
coefficients = [Real(float(a[h][j].x)) for j in range(n_f)]
constant = Real(float(b[h].x))
else:
coefficients = [Real(-float(a[h - n_h / 2][j].x)) for j in range(n_f)]
constant = Real(-float(b[h - n_h / 2].x))
linear_sum = Plus([Times(c, domain.get_symbol(v)) for c, v in zip(coefficients, domain.variables)])
conjunction.append(LE(linear_sum, constant))
conjunctions.append(conjunction)
return conjunctions
