def grouped_workload(W, A, error_matrix, match_type='BEST'):
#
# Comment
#
def best(i, j): # partition workloads into groups assoc. with best supporting strategy
return j == np.argmin(error_matrix, axis=1)[i]
def supported(i, j): # form redundant groups based on all supporting strategies
return error_matrix[i,j] < float('inf')
def top(i, j, lim=2):
return supported(i,j) and (j in np.argsort(error_matrix, axis=1)[0:lim])
if match_type == 'BEST':
match = best
elif match_type == 'TOP':
match = top
elif match_type == 'SUPPORTED':
match = supported
else:
assert False
groups = [[] for _ in range(len(A.matrices))]
for i in range(len(W.matrices)):
for j in range(len(A.matrices)):
if match(i,j):
groups[j].append(W.matrices[i])
w_grouped = [workload.VStack(g) for g in groups if len(g) > 0]
return w_grouped
def census():
W = SF1_Persons()
workloads = []
for K in W.matrices:
w = K.matrices
Wi = workload.Kronecker([w[0], w[1], w[2], w[4]])
workloads.append(Wi)
W1 = workload.VStack(workloads)
M = workload.IdentityTotal
workloads = []
for K in W.matrices:
w = K.matrices
Wi = workload.Kronecker([w[0], w[1], w[2], w[4], M(51)])
workloads.append(Wi)
W2 = workload.VStack(workloads)
return W1, W2
def dict2workload(workload_dict: Dict[str, AbstractLinearQuery]):
""" Convert a dict of queries into HDMM Workload"""
workload_list: List[workload.Kron] = []
for query in workload_dict.values():
kron_factors = [
workload.EkteloMatrix(x) for x in query.kronFactors()
]
workload_list.append(workload.Kronecker(kron_factors))
return workload.VStack(workload_list)
def SmallKrons(blocks, size=5000):
base = [workload.Total(W.shape[1]) for W in blocks]
d = len(blocks)
concat = []
for attr in powerset(range(d)):
subs = [blocks[i] if i in attr else base[i] for i in range(d)]
tmp = reduce(lambda x, y: x * y, [blocks[i].shape[1] for i in attr], 1)
W = workload.Kronecker(subs)
if tmp <= size:
concat.append(W)
return workload.VStack(concat)
def DimKKrons(workloads, k=1):
blocks = workloads
base = [workload.Total(W.shape[1]) for W in blocks]
d = len(blocks)
concat = []
for attr in itertools.combinations(range(d), k):
subs = [blocks[i] if i in attr else base[i] for i in range(d)]
W = workload.Kronecker(subs)
concat.append(W)
return workload.VStack(concat)
def experiment3():
print('experiment3')
n = 256
"""Want to show that we can satisfy sharing incentive by running
the entire workload together, but weighting the workload of each
analyst in inverse proportion to the sensitivity of their workload """
#using experiment 1 as an example
W1 = workload.AllRange(n)
#W2 = workload.Total(n)
W2 = workload.Identity(n)
W = workload.VStack([
matrix.EkteloMatrix(np.multiply(W1.matrix, (1 / W1.sensitivity()))),
matrix.EkteloMatrix(np.multiply(W2.matrix, (1 / W2.sensitivity())))
])
#workload 1 with half the budget
pid = templates.PIdentity(max(1, n // 16), n)
pid.optimize(W1)
print("Workload 1 with half the budget")
err1 = error.expected_error(W1, pid.strategy(), eps=0.5)
print(err1)
pid = templates.PIdentity(max(1, n // 16), n)
pid.optimize(W2)
print("Workload 2 with half the budget")
err2 = error.expected_error(W2, pid.strategy(), eps=0.5)
print(err2)
#both workloads together
pid = templates.PIdentity(max(1, n // 16), n)
pid.optimize(W)
print("Both workloads with all the budgets")
err1all = error.expected_error(W1, pid.strategy(), eps=1)
err2all = error.expected_error(W2, pid.strategy(), eps=1)
print("W1")
print(err1all)
print("W2")
print(err2all)
print("Are either of the analysts violating sharing incentive")
print((err1all >= err1) or (err2all >= err2))
""" Issue when you independently scale each matrix then merge you some of the
def experiment4():
print('experiment4')
n = 256
"""Want to show that we can satisfy sharing incentive by running
the entire workload together, but weighting the workload of each
analyst in inverse proportion to the sensitivity of their workload """
""" This time we try scaling the big workload matrix"""
#using experiment 1 as an example
W1 = workload.AllRange(n)
#W2 = workload.Total(n)
W2 = workload.Identity(n)
W = workload.VStack([W1, W2])
W = matrix.EkteloMatrix((np.multiply(W.matrix, (1 / W.sensitivity()))))
#workload 1 with half the budget
pid = templates.PIdentity(max(1, n // 16), n)
pid.optimize(W1)
print("Workload 1 with half the budget")
err1 = error.expected_error(W1, pid.strategy(), eps=0.5)
print(err1)
pid = templates.PIdentity(max(1, n // 16), n)
pid.optimize(W2)
print("Workload 2 with half the budget")
err2 = error.expected_error(W2, pid.strategy(), eps=0.5)
print(err2)
#both workloads together
pid = templates.PIdentity(max(1, n // 16), n)
pid.optimize(W)
print("Both workloads with all the budgets")
err1all = error.expected_error(W1, pid.strategy(), eps=1)
err2all = error.expected_error(W2, pid.strategy(), eps=1)
print("W1")
print(err1all)
print("W2")
print(err2all)
print("Are either of the analysts violating sharing incentive")
print((err1all >= err1) or (err2all >= err2))
"""Doesn't work either. May work when the number of analysts scales too high.
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 experiment1():
print('Experiment1')
n = 256
""" We want an example to show that naively running HDMM on the
entire workload ignoring identities of individual analysts does not
satisfy sharing incentive. Intuitively, this should happen when one
analyst has a much smaller/easier workload than the other analysts,
such that their errors dominate the optimization """
W1 = workload.AllRange(n)
W2 = workload.Total(n)
#W2 = workload.IdentityTotal(n)
W = workload.VStack([W1, W2])
#workload 1 with half the budget
pid = templates.PIdentity(max(1, n // 16), n)
pid.optimize(W1)
print("Workload 1 with half the budget")
err1 = error.expected_error(W1, pid.strategy(), eps=0.5)
print(err1)
pid = templates.PIdentity(max(1, n // 16), n)
pid.optimize(W2)
print("Workload 2 with half the budget")
err2 = error.expected_error(W2, pid.strategy(), eps=0.5)
print(err2)
#both workloads together
pid = templates.PIdentity(max(1, n // 16), n)
pid.optimize(W)
print("Both workloads with all the budgets")
err1all = error.expected_error(W1, pid.strategy(), eps=1)
err2all = error.expected_error(W2, pid.strategy(), eps=1)
print("W1")
print(err1all)
print("W2")
print(err2all)
print("Are either of the analysts violating sharing incentive")
print((err1all >= err1) or (err2all >= err2))
def experiment2():
print("experiment2")
n = 256
""" We want to show that fixing this problem by partitioning the
privacy budget and running each workload independently can make
all of the agents worse off in terms of error (should be easy to
see when the analysts have similar workloads)."""
W1 = workload.Total(n)
W1 = np.multiply(W1, 1.1)
W2 = workload.Total(n)
W = workload.VStack([W1, W2])
#workload 1 with half the budget
pid = templates.PIdentity(max(1, n // 16), n)
pid.optimize(W1)
print("Workload 1 with half the budget")
err1 = error.expected_error(W1, pid.strategy(), eps=0.5)
print(err1)
pid = templates.PIdentity(max(1, n // 16), n)
pid.optimize(W2)
print("Workload 2 with half the budget")
err2 = error.expected_error(W2, pid.strategy(), eps=0.5)
print(err2)
#both workloads together
pid = templates.PIdentity(max(1, n // 16), n)
pid.optimize(W)
print("Both workloads with all the budgets")
err1all = error.expected_error(W1, pid.strategy(), eps=1)
err2all = error.expected_error(W2, pid.strategy(), eps=1)
print("W1")
print(err1all)
print("W2")
print(err2all)
print("Are both agents worse off by seperating their strategy")
print((err1all < err1) and (err1all < err2))
# 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
