@EricHolloway/

ASC Lower Bound Violations

Python 2.7

Shows that deriving a probability lower bound from ASC does not result in violations of an a priori discount.

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  • main.py
main.py
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import math

f = math.factorial
def nCk(n,k):
    return f(n) / f(k) / f(n-k)

def binom(n,k,p):
    return nCk(n,k)*p**k*(1-p)**(n-k)

def lg2(n):
    if n == 0:
        return 0
    return math.log(n, 2)

def err_penalty(errs, bits):
    if errs == 0:
        return 2
    prefix = (lg2(errs)+1)*2 + (lg2(bits)+1)*2
    penalty = errs * bits
    return prefix + penalty

bits = 8

total = 2**bits

discount = bits

violations = 0
for cls0_cnt in range(0, total/2):
    cls1_cnt = total - cls0_cnt

    penalty = err_penalty(cls0_cnt, bits) + discount
    ASC = total - penalty
    lower_bound = 2**(-penalty/float(total))
    
    rslt_prob = 0
    for cls0_cnt2 in range(0, cls0_cnt+1):
        rslt_prob += binom(total, cls0_cnt2, 1-lower_bound)

    accidental_generation = -int(round(lg2(rslt_prob)))
        
    if accidental_generation < discount:
        violations += 1

print "Violations:", violations