def test_marginals(self):
# full rank case
W = workload.Range2D(4)
temp = templates.Marginals((4, 4))
temp._set_workload(W)
x0 = self.prng.rand(4)
func = lambda p: temp._loss_and_grad(p)[0]
grad = lambda p: temp._loss_and_grad(p)[1]
err = check_grad(func, grad, x0)
print(err)
#self.assertTrue(err <= 1e-5)
# low rank case
P = workload.Prefix(4)
T = workload.Total(4)
W1 = workload.Kronecker([P, T])
W2 = workload.Kronecker([T, P])
W = workload.VStack([W1, W2])
temp = templates.Marginals((4, 4))
temp._set_workload(W)
x0 = np.array([1, 1, 1, 0.0])
func = lambda p: temp._loss_and_grad(p)[0]
grad = lambda p: temp._loss_and_grad(p)[1]
f, g = func(x0), grad(x0)
g2 = np.zeros(4)
for i in range(4):
x0[i] -= 0.00001
f1 = func(x0)
x0[i] += 0.00002
f2 = func(x0)
x0[i] -= 0.00001
g2[i] = (f2 - f1) / 0.00002
print(g)
print(g2)
np.testing.assert_allclose(g, g2, atol=1e-5)
def example3():
""" Optimize Union-of-Kronecker product workload using kronecker parameterization
and marginals parameterization """
print('Example 3')
sub_workloads1 = [workload.Prefix(64) for _ in range(4)]
sub_workloads2 = [workload.AllRange(64) for _ in range(4)]
W1 = workload.Kronecker(sub_workloads1)
W2 = workload.Kronecker(sub_workloads2)
W = workload.VStack([W1, W2])
K = templates.KronPIdentity([4]*4, [64]*4)
K.optimize(W)
print(error.expected_error(W, K.strategy()))
M = templates.Marginals([64]*4)
M.optimize(W)
print(error.expected_error(W, M.strategy()))
identity = workload.Kronecker([workload.Identity(64) for _ in range(4)])
print(error.expected_error(W, identity))
def setUp(self):
self.prng = np.random.RandomState(0)
self.domain = (2,3,4)
I = lambda n: workload.Identity(n)
T = lambda n: workload.Total(n)
P = lambda n: workload.Prefix(n)
R = lambda n: matrix.EkteloMatrix(self.prng.rand(n,n))
W1 = workload.Kronecker([I(2), T(3), P(4)])
W2 = workload.Kronecker([T(2), T(3), I(4)])
W3 = workload.Kronecker([I(2), I(3), T(4)])
self.W = workload.VStack([W1, W2, W3])
# three representations of Identity matrix
self.A1 = I(2*3*4)
self.A2 = workload.Kronecker([I(2),I(3),I(4)])
self.A3 = workload.Marginals.fromtuples(self.domain, {(0,1,2) : 1.0 })
self.A4 = workload.Marginals(self.domain, self.prng.rand(8))
self.A5 = workload.Kronecker([R(2), R(3), R(4)])
# this is a 2d example: domain = (10, 25) # densely represented sub-workloads in each of the dimensions identity1 = workload.EkteloMatrix(np.eye(10)) identity2 = workload.EkteloMatrix(np.eye(25)) total = workload.EkteloMatrix(np.ones((1, 10))) prefix = workload.EkteloMatrix(np.tril(np.ones((25, 25)))) # form the kron products in each dimension W1 = workload.Kronecker([identity1, identity2]) W2 = workload.Kronecker([total, prefix]) # form the union of krons W = workload.VStack([W1, W2]) # find a Kronecker product strategy by optimizing the workload ps = [2, 2] # parameter for P-Identity strategies template = templates.KronPIdentity(ps, domain) # run optimization template.optimize(W) # get the sparse, explicit representation of the optimized strategy A = template.strategy().sparse_matrix().tocsr() # Round for Geometric Mechanism (skip this if using Laplace Mechanism) A = np.round(A * 1000) / 1000.0 # Extract diagonal and non-diagonal portion of strategy