numPts = 30 # How many eval points for each conditional
print('Test Limit = ', lim, 'standard deviations from mean')
print('Dimensions = ', dims, '. Conditionals = ', dims - 1)
print('Number of points to test for each conditional = ', numPts)
N = prob.N
cond = 'B'
target = 'A2'
R1 = RKHS(prob.ds, delta=None, includeVars=[target, cond], s=smoothness)
# Do some general assessment of cumulative probabilities
# Do some univariate CDF calculations. F is normal(0,1)
R0_1 = RKHS(prob.ds, includeVars=['F'], s=smoothness)
for v in [-4, -3, -2, -1, 0, 1, 2, 3, 4]:
psR = prob.P(('F', None, v))
print('cdf(', v, ') = ', R0_1.CDF(v), psR)
# Now some 2-D single conditional evals
A2std = .3
for v2 in [-1 * A2std, 0, 1 * A2std]:
for v1 in [-4, -3, -2, -1, 0, 1, 2, 3, 4]:
exp = 1 / (1 + e**(-v2 / A2std))
ps = prob.P(('A2', None, v2 + tanh(v1)), ('B', v1))
jp = R1.condCDF([v2 + tanh(v1), v1])
#ps = prob.P([('A2', None, v2+tanh(v1)), ('B', None, v1)])
#jp = R1.CDF([v2+tanh(v1),v1])
print('cdf(A2 =', v2, '| B =', v1, ')(jp, ps, exp) = ', jp, ps,
exp)
#print('A: mean, std, range, incr = ', amean, astd, arange, aincr)
evaluations = 0
start = time.time()
def run(filename):
r = getData.DataReader(filename)
dat = r.read()
ps = ProbSpace(dat, density=1, power=1)
start = time.time()
print()
print('Testing probability module.')
print()
print('Testing basic statistics for various types of distribution:')
print('stats(A) = ', ps.fieldStats('A'))
print('stats(C) = ', ps.fieldStats('C'))
a = ps.distr('A')
mean = a.mean()
std = a.stDev()
print('stats(dice1): mean, std, skew, kurtosis, median, mode = ', mean,
std, a.skew(), a.kurtosis(), ' Exp: (3.5, ?, 0, ?)')
c = ps.distr('C')
print('stats(d1 + d2): mean, std, skew, kurtosis, median, mode = ', c.E(),
c.stDev(), c.skew(), c.kurtosis(), c.median(), c.mode(),
' Exp: (7, ?, 0, ?, 7, 7)')
d = ps.distr('EXP')
print('stats(Exponential): mean, std, skew, kurtosis = ', d.E(), d.stDev(),
d.skew(), d.kurtosis(), ' Exp: (1, 1, 2, 6)')
d = ps.distr('IVB')
print('stats(Logistic): mean, std, skew, kurtosis = ', d.E(), d.stDev(),
d.skew(), d.kurtosis(), ' Exp: (0, 1.8138, 0, 1.2)')
d = ps.distr('N')
print('stats(Normal): mean, std, skew, kurtosis, median = ', d.E(),
d.stDev(), d.skew(), d.kurtosis(), d.median(), 'Exp: (0, 1, 0, 0)')
d = ps.distr('N2')
print('stats(N2: sum of normals): mean, std, skew, kurtosis = ', d.E(),
d.stDev(), d.skew(), d.kurtosis(), 'Exp: (1, 1.414, 0, 0)')
print()
print(
'Testing discrete deterministic probabilities (2-dice -- ala Craps):')
print('A is Die #1. B is Die #2. C is the total of the 2 dice.')
print('E(B) = ', ps.distr('B').E(), ' Exp: 3.5')
print('P(B=0) = ', ps.P(('B', 0)), ' Exp: 0')
print('P(B=1) = ', ps.P(('B', 1)), ' Exp: 1/6 = .166...')
print('P(B=2) = ', ps.P(('B', 2)), ' Exp: 1/6 = .166...')
print('P(B >= 0) = ', ps.P(('B', 0, None)), ' Exp: 1.0')
print('P(B < 0) = ', ps.P(('B', None, 0)), ' Exp: 0.0')
print('P(-inf <= B > inf) = ', ps.P(('B', None, None)), ' Exp: 1.0')
print('P(-1 <= B < 3) = ', ps.P(('B', -1, 3)), ' Exp: 1/3')
print('P(C = 2) =', ps.P(('C', 2)), ' Exp: 1/36 = .0277...')
print('P(C = 3) =', ps.P(('C', 3)), ' Exp: 1/18 = .055...')
print('P( 2 <= C < 4) = ', ps.P(('C', 2, 4)), ' Exp: 3/36 = .0833...')
print('P( 2 <= C < 4 | A = 1) = ', ps.P(('C', 2, 4), ('B', 1)),
' Exp: 1/3')
print('P( C = 7) = ', ps.P(('C', 7)), ' Exp: 1/6 = .166...')
print('P( C = 7 | A = 1, B = 6) = ', ps.P(('C', 7), [('A', 1), ('B', 6)]),
' Exp: 1.0')
print('P( C = 7 | A >= 2, B < 5) = ',
ps.P(('C', 7), [('A', 2, None), ('B', None, 5)]), ' Exp: 1/5 = .2')
print('P(-inf <= A < inf | B >= 1) = ',
ps.P(('A', None, None), ('B', 1, None)), ' Exp: 1.0')
print('P( A >= 3, B >= 3) = ', ps.P([('A', 3, None), ('B', 3, None)]),
'Exp: 4/9 (.444...)')
print('P( C = 7, A = 5) = ', ps.P([('C', 7), ('A', 5)]),
' Exp: 1/36 (.0277...)')
print('P( C = 7, A >= 5) = ', ps.P([('C', 7), ('A', 5, None)]),
' Exp: 1/18 (.0555...)')
print('P( A = 2 | B = 5, C= 7) = ', ps.P(('A', 2), [('B', 5), ('C', 7)]),
' Exp: 1.0')
print('P( B = 5, C= 7) = ', ps.P(('B', 5), ('C', 7)),
' Exp: 1/6 (.166...)')
print('P( A = 2, B = 5) = ', ps.P([('A', 2), ('B', 5)]),
' Exp: 1/36 (.0277...)')
print('P( A = 2, B = 5 | C = 7) = ', ps.P([('A', 2), ('B', 5)], ('C', 7)),
' Exp: 1/6 (.166...)')
print('P( A = 2, B = 5, N < 0| C = 7) = ',
ps.P([('A', 2), ('B', 5), ('N', None, 0)], ('C', 7)),
' Exp: 1/12 (.08333...)')
print('E( C | A = 1, B = 6) = ',
ps.distr('C', [('A', 1), ('B', 6)]).E(), ' Exp: 7')
print('E( C | A = 1, B >= 5) = ',
ps.distr('C', [('A', 1), ('B', 5, None)]).E(), ' Exp: 6')
print()
print('Testing continuous distributions. Using N = normal(0, 1)')
n = ps.distr('N')
mu1 = n.mean()
mu2 = n.stDev()
print('stats(N): mean, std, skew, kurtosis = ', mu1, mu2, n.skew(),
n.kurtosis(), 'Exp: (0, 1, 0, 0)')
print('P( -1 >= N > 1) = ', n.P((-1, 1)), 'Exp: .682')
print('P( -2 >= N > 2) = ', n.P((-2, 2)), 'Exp: .954')
print('P( -3 >= N > 3) = ', n.P((-3, 3)), 'Exp: .997')
print('P( -inf >= N > 0) = ', n.P((None, 0)), 'Exp: .5')
print('P( 0 >= N > inf) = ', n.P((0, None)), 'Exp: .5')
print('P( -inf >= N > inf) = ', n.P((None, None)), 'Exp: 1.0')
print('E( N2 | N = 1) = ', ps.distr('N2', ('N', 1)).E(), ' Exp: 2.0')
print('E( N2 | 1 <= N < 2) = ', ps.distr('N2', ('N', 1, 2)).E())
print()
print('Dependence testing. Note: values < .5 are considered independent')
print('A _||_ B = ', ps.dependence('A', 'B'), ' Exp: < .5')
print('A _||_ C = ', ps.dependence('A', 'C'), ' Exp: > .5')
print('B _||_ C = ', ps.dependence('B', 'C'), ' Exp: > .5')
print('N _||_ N2 = ', ps.dependence('N', 'N2'), ' Exp: > .5')
print('N _||_ C = ', ps.dependence('N', 'C'), ' Exp: < .5')
print('C _||_ N = ', ps.dependence('C', 'N'), ' Exp: < .5')
print('A _||_ B | C >= 8 = ', ps.dependence('A', 'B', [('C', 8, None)]),
' Exp: > .5')
print('A _||_ B | C < 7 = ', ps.dependence('A', 'B', [('C', None, 7)]),
' Exp: > .5')
print('A _||_ B | C = 7 = ', ps.dependence('A', 'B', [('C', 7)]),
' Exp: > .5')
print('A _||_ B | C = 6 = ', ps.dependence('A', 'B', [('C', 6)]),
' Exp: > .5')
print('A _||_ B | C = 5 = ', ps.dependence('A', 'B', [('C', 5)]),
' Exp: > .5')
print('A _||_ B | C = 4 = ', ps.dependence('A', 'B', [('C', 4)]),
' Exp: > .5')
print('A _||_ B | C = 3 = ', ps.dependence('A', 'B', [('C', 3)]),
' Exp: > .5')
print('A _||_ B | C = 2 = ', ps.dependence('A', 'B', [('C', 2)]),
' Exp: < .5')
print('A _||_ B | C = 12 = ', ps.dependence('A', 'B', [('C', 12)]),
' Exp: < .5')
print('A _||_ B | C = ', ps.dependence('A', 'B', ['C']), ' Exp: > .5')
print()
print('Independence testing (values > .5 are considered independent):')
print('A _||_ B = ', ps.independence('A', 'B'), ps.isIndependent('A', 'B'),
' Exp: > .5, True')
print('A _||_ C = ', ps.independence('A', 'C'), ps.isIndependent('A', 'C'),
' Exp: < .5, False')
print('A _||_ B | C = ', ps.independence('A', 'B', 'C'),
ps.isIndependent('A', 'B', 'C'), ' Exp: < .5, False')
print('A _||_ N = ', ps.independence('A', 'N'), ps.isIndependent('A', 'N'),
' Exp: > .5, True')
print()
print('Testing Conditionalization:')
ivaDist = ps.distr('IVA')
ivaMean = ivaDist.E()
ivaStd = ivaDist.stDev()
upper = ivaMean + .5 * ivaStd
lower = ivaMean - .5 * ivaStd
diff = upper - lower
pwr = 2
print('test interval = ', upper - lower)
ivcGupper = ps.E('IVC', ('IVA', upper), power=pwr)
print('E( IVC | IVA = upper)', ivcGupper)
ivcGlower = ps.E('IVC', ('IVA', lower), power=pwr)
print('E( IVC | IVA = upper)', ivcGupper)
print('E( IVC | IVA = lower)', ivcGlower)
ivcGupper = ps.E('IVC', [('IVA', upper), 'IVB'], power=pwr)
print('E( IVC | IVA = upper, IVB)', ivcGupper)
ivcGlower = ps.E('IVC', [('IVA', lower), 'IVB'], power=pwr)
print('E( IVC | IVA = lower, IVB)', ivcGlower)
print('ACE(A,C) = ', (ivcGupper - ivcGlower) / diff, ' Exp: ~ 0')
print()
print('Testing continuous causal dependence:')
print('IVB _||_ IVA = ', ps.dependence('IVB', 'IVA'), ' Exp: > .5')
print('IVA _||_ IVB = ', ps.dependence('IVA', 'IVB'), ' Exp: > .5')
print('IVB _||_ IVC = ', ps.dependence('IVB', 'IVC'), ' Exp: > .5')
print('IVA _||_ IVC = ', ps.dependence('IVA', 'IVC'), ' Exp: > .5')
print('IVA _||_ IVC | IVB = ', ps.dependence('IVA', 'IVC', 'IVB'),
' Exp: < .5')
print('IVA _||_ IVC | IVB, N = ',
ps.dependence('IVA', 'IVC', ['IVB', 'N']), ' Exp: < .5')
print()
print('Testing Bayesian Relationships:')
# P(C=7 | A=5) = P(A=5|C=7) * P(A=5) / P(C=7)
pA_C = ps.P(('A', 5), ('C', 7))
pA = ps.P(('A', 5))
pC = ps.P(('C', 7))
pC_A = ps.P(('C', 7), ('A', 5))
invpC_A = pA_C * pA / pC
err = abs(invpC_A - pC_A)
print(
'Inverse P(A=5 | C=7) vs measured (Bayes(P(A | C)), P(A | C), diff): ',
invpC_A, pC_A, err, ' Exp: ~ 0')
# P(0 <= IVB < 1 | 1 <= IVA < 2) = P(1 <= IVA < 2 | 0 <= IVB < 1) * P(0 <= IVB < 1) / P(1 <= IVA < 2)
pA_B = ps.P(('IVA', 1, 2), ('IVB', 0, 1))
pB = ps.P(('IVB', 0, 1))
pA = ps.P(('IVA', 1, 2))
pB_A = ps.P(('IVB', 0, 1), ('IVA', 1, 2))
invpB_A = pA_B * pB / pA
err = abs(invpB_A - pB_A)
print(
'Inverse P(0 <= IVB < 1 | 1 <= IVA < 2) vs measured (Bayes(P(IVB | IVA)), P(IVB | IVA), diff): ',
invpB_A, pB_A, err, ' Exp: ~ 0')
print()
print('Testing Prediction and Classification:')
testDat = {'A': [2, 3, 6], 'B': [5, 2, 6]}
predDat = ps.Predict('C', testDat)
for p in range(len(predDat)):
val = predDat[p]
a = testDat['A'][p]
b = testDat['B'][p]
print('Prediction(C) for A = ', a, ', B = ', b, ', = pred(C) = ', val,
' Exp:', a + b)
predDat = ps.Classify('C', testDat)
for p in range(len(predDat)):
val = predDat[p]
a = testDat['A'][p]
b = testDat['B'][p]
print('Classification(C) for A = ', a, ', B = ', b, ', = pred(C) = ',
val, ' Exp:', a + b)
testDat = {'N': [.5, 1, 1.5, 2, 2.5, 3], 'B': [1, 2, 3, 4, 5, 6]}
predDists = ps.PredictDist('N2', testDat)
for p in range(len(predDists)):
d = predDists[p]
n = testDat['N'][p]
b = testDat['B'][p]
print('Prediction(N2) for N = ', n, ', B = ', b,
', = pred(N2 (mean, std)) = ', d.E(), d.stDev(), ' Exp:', n + 1,
', 1')
print()
end = time.time()
duration = end - start
print('Test Time = ', round(duration))