def information_decomposition(dist, src, to=""):
rvs = src + to
P = dist.marginal(rvs)
variables = P._rvs
q_SXY = admUI.computeQUI(distSXY=P)
h_SgXY = dit.shannon.conditional_entropy(q_SXY, 'S', 'XY')
ui_SX_Y = dit.shannon.conditional_entropy(q_SXY, 'S', 'Y') - h_SgXY
ui_SY_X = dit.shannon.conditional_entropy(q_SXY, 'S', 'X') - h_SgXY
si_SXY_1 = dit.shannon.mutual_information(q_SXY, 'S', 'X') - ui_SX_Y
si_SXY_2 = dit.shannon.mutual_information(q_SXY, 'S', 'Y') - ui_SY_X
# sanity check
assert math.isclose(
si_SXY_1, si_SXY_2,
abs_tol=1e-6), "SI_S_XY: %f | %f" % (si_SXY_1, si_SXY_2)
si_SXY = si_SXY_1
ci_SXY = si_SXY - dit.multivariate.coinformation(P, rvs)
i_S_XY = dit.shannon.mutual_information(P, 'S', to)
# sanity check
assert math.isclose(i_S_XY, si_SXY + ci_SXY + ui_SX_Y + ui_SY_X, abs_tol=1e-6), \
"MI = decompose : %f | %f" % (i_S_XY, si_SXY + ci_SXY + ui_SX_Y + ui_SY_X)
uis = [ui_SX_Y, ui_SY_X]
return {
"variables": tuple(map(lambda x: rvs_to_name[x], to)),
"metrics": {
"mi": i_S_XY,
"si": si_SXY,
"ci": ci_SXY,
"ui_0": uis[variables[to[0]] - 1],
"ui_1": uis[variables[to[1]] - 1]
}
}
ltimecv = np.empty(shape=(ndist, nsmax))
for ns in range(1, nsmax):
ny = ns
nz = ns
print("--------------- ns = %s ---------------" % (ns + 1))
for i in range(0, ndist):
Pt = npy[:, i, ns]
P = Pt[Pt != 0]
Ps = P.reshape(nz + 1, ny + 1, ns + 1)
d = Distribution.from_ndarray(Ps)
d.set_rv_names('SXY')
## admUI
start_time = time.time()
Q = computeQUI(d)
UIX = dit.shannon.conditional_entropy(
Q, 'S', 'Y') + dit.shannon.conditional_entropy(
Q, 'X', 'Y') - dit.shannon.conditional_entropy(Q, 'SX', 'Y')
lapsed_time = time.time() - start_time
UIv[i, ns] = UIX
ltimev[i, ns] = lapsed_time
## dit
try:
pid = algorithms.pid_broja(d, ['X', 'Y'], 'S')
except dit.exceptions.ditException:
print(i, "ditException: P = ", P, ", ns=ny=nz=", ns + 1, ", i=", i)
dit_errorcnt = dit_errorcnt + 1
UIpv[i, ns] = 0
ltimepv[i, ns] = 0
print("Time: ",itoc_us-itic_us,"secs")
#^ if
# Prepare pdf for admUI or dit
if s != 0:
dpdf = Distribution(pdf)
dpdf.set_rv_names('SXY')
#^ if
# Compute PID using ComputeUI
if s == 1 or s == 3 or s == 5:
print("Run ComputeUI.computeQUI()")
itic_comUI = time.process_time()
Q = computeQUI(distSXY = dpdf, DEBUG = True)
UIY = dit.shannon.conditional_entropy(Q, 'S', 'Y') + dit.shannon.conditional_entropy(Q, 'X', 'Y') \
- dit.shannon.conditional_entropy(Q, 'SX', 'Y')
UIZ = dit.shannon.conditional_entropy(Q, 'S', 'X') + dit.shannon.conditional_entropy(Q, 'Y', 'X') \
- dit.shannon.conditional_entropy(Q, 'SY', 'X')
CI = dit.shannon.conditional_entropy(Q, 'S', 'XY') - dit.shannon.conditional_entropy(dpdf, 'S', 'XY')
SI = dit.shannon.entropy(Q, 'S')\
-dit.shannon.conditional_entropy(Q, 'S', 'XY') \
- dit.shannon.conditional_entropy(Q, 'S', 'Y') - dit.shannon.conditional_entropy(Q, 'X', 'Y') \
+ dit.shannon.conditional_entropy(Q, 'SX', 'Y')\
- dit.shannon.conditional_entropy(Q, 'S', 'X') - dit.shannon.conditional_entropy(Q, 'Y', 'X') \
+ dit.shannon.conditional_entropy(Q, 'SY', 'X')
itoc_comUI = time.process_time()
print("Partial information decomposition ComputeUI: ")
print("UIY_comUI: ", UIY)
print("UIZ_comUI: ", UIZ)
0.0869196091623, 0.0218631235533, 0.133963681059, 0.164924698739,
0.429533105427, 0.16279578206
])
]
# count some statistics
max_delta = 0.
total_time_admUI = 0.
total_time_dit = 0.
for d in examples:
d.set_rv_names('SXY')
print(d.to_dict())
# admUI
start_time = time.time()
Q = computeQUI(distSXY=d, DEBUG=False)
admUI_time = time.time() - start_time
total_time_admUI += admUI_time
UIX = (dit.shannon.conditional_entropy(Q, 'S', 'Y') +
dit.shannon.conditional_entropy(Q, 'X', 'Y') -
dit.shannon.conditional_entropy(Q, 'SX', 'Y'))
# UIX2 = (dit.shannon.entropy(Q, 'SY') + dit.shannon.entropy(Q, 'XY')
# - dit.shannon.entropy(Q, 'SXY') - dit.shannon.entropy(Q, 'Y'))
# print(abs(UIX - UIX2) < 1e-10)
UIY = (dit.shannon.conditional_entropy(Q, 'S', 'X') +
dit.shannon.conditional_entropy(Q, 'Y', 'X') -
dit.shannon.conditional_entropy(Q, 'SY', 'X'))
SI = dit.shannon.mutual_information(Q, 'S', 'X') - UIX
# SI2 = (dit.shannon.entropy(Q, 'S') + dit.shannon.entropy(Q, 'X')
# - dit.shannon.entropy(Q, 'SX') - UIX)
# SI3 = (dit.shannon.entropy(Q, 'S') + dit.shannon.entropy(Q, 'X')
for ns in range(1, nsmax):
ny = ns
nz = ns
print("--------------- ns= %s ---------------" % (ns + 1))
for i in range(0, ndist):
Pt = npy[:, i, ns]
P = Pt[Pt != 0]
Ps = P.reshape(nz + 1, ny + 1, ns + 1)
d = dit.Distribution.from_ndarray(Ps)
d.set_rv_names('SXY')
print(i)
# admUI
start_time = time.time()
Q = computeQUI(distSXY=d) # , DEBUG=True)
UIX = (dit.shannon.conditional_entropy(Q, 'S', 'Y') +
dit.shannon.conditional_entropy(Q, 'X', 'Y') -
dit.shannon.conditional_entropy(Q, 'SX', 'Y'))
lapsed_time = time.time() - start_time
UIv[i, ns] = UIX
ltimev[i, ns] = lapsed_time
if logging:
cvsfile.write("{}, ".format(ns + 1))
cvsfile.write("{:.15f}, {:.15f}, ".format(UIX, lapsed_time))
else:
print("admUI = %.15f" % UIX, " time = %.15f" % lapsed_time)
# cvxopt
pdf = dict(zip(d.outcomes, d.pmf))
start_timec = time.time()