def calculate_workload_error_marginals(wk, strategy, eps):
" Strategies that are a union still need special treatment " ""
expected_error = 0
table = []
weights = np.array([])
effective_queries = 0
for Wi in wk.matrices:
print(Wi)
effective_queries += Wi.weight**2 * Wi.shape[0]
err = hdmm_error.expected_error(Wi.base, strategy, eps=eps)
expected_error += Wi.weight**2 * err
rootmse = np.sqrt(err / Wi.shape[0])
res = {
'pdf': False,
'pdf_x': False,
'method': 'HDMM',
'expected_error': rootmse,
'num_query': int(Wi.shape[0]),
}
table.append(res)
rootmse = np.sqrt(expected_error / effective_queries)
graph = {
'pdf': False,
'pdf_x': False,
'message':
"Optimized strategy is marginals, doesn't support density plots.",
'method': 'HDMM',
'expected_error': rootmse,
'num_query': int(wk.shape[0]),
}
return table, graph
def experiment5():
print('experiment5')
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 = matrix.EkteloMatrix(np.random.rand(32, n))
W2 = matrix.EkteloMatrix(np.random.rand(32, n))
#W1 = workload.Prefix(n)
#W2 = workload.Total(n)
#W2 = workload.Identity(n)
W = [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 = fairtemplates.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))
"""Optimizing on egalitarian doesn't work either. it seems to be spending most of
its time optimizing the more difficult queries. In fact it seems to be getting almost
the exact same error should it have just optimized on the first one """
""" note results change if it's just total vs identity for the second workload.
def calculate_workload_error_default(wk, strategy, eps):
" Strategies that are a union still need special treatment " ""
expected_error = 0
per_query_error = np.array([])
table = []
weights = np.array([])
effective_queries = 0
for Wi in wk.matrices:
print(Wi)
effective_queries += Wi.weight**2 * Wi.shape[0]
err = hdmm_error.expected_error(Wi.base, strategy, eps=eps)
expected_error += Wi.weight**2 * err
pqe = hdmm_error.per_query_error_sampling(Wi.base,
strategy,
eps=eps,
normalize=True)
per_query_error = np.append(per_query_error, pqe)
wgt = np.ones(pqe.size) * Wi.weight**2 * Wi.shape[0]
weights = np.append(weights, wgt)
rootmse = np.sqrt(err / Wi.shape[0])
if np.var(pqe) < 1e-2:
pdf = False
pdf_x = False
else:
density = np.histogram(pqe, bins='auto', density=True)
pdf = density[0].tolist()
pdf_x = density[1][0:-1].tolist()
res = {
'pdf': pdf,
'pdf_x': pdf_x,
'method': 'HDMM',
'expected_error': rootmse,
'num_query': int(Wi.shape[0]),
}
table.append(res)
rootmse = np.sqrt(expected_error / effective_queries)
if np.var(per_query_error) < 1e-2:
pdf = False
pdf_x = False
else:
density = np.histogram(per_query_error,
bins=100,
weights=weights,
density=True)
pdf = density[0].tolist()
pdf_x = density[1][0:-1].tolist()
graph = {
'pdf': pdf,
'pdf_x': pdf_x,
'method': 'HDMM',
'expected_error': rootmse,
'num_query': int(wk.shape[0]),
}
return table, graph
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))
def compute_error_matrix(W, A):
# compute error of each subworkload Wi of W wrt to each sub-strategy Aj
# if Wi is not supported by Aj, entry (i,j) == inf
if os.path.isfile('error_matrix.pckl'):
file = open('error_matrix.pckl', 'r')
return pickle.load(file)
else:
file = open('error_matrix.pckl', 'wb')
error_matrix = np.zeros((len(W.matrices), len(A.matrices)))
for i, Wi in enumerate(W.matrices):
print(i)
for j, Aj in enumerate(A.matrices):
if error.strategy_supports_workload(W, A):
error_matrix[i, j] = error.expected_error(Wi, Aj.base)
else:
error_matrix[i, j] = float('inf')
print(error_matrix[i,:])
pickle.dump(error_matrix, file)
return error_matrix