import matplotlib.pyplot as plt
import sys
sys.path.append('Assignment 7')
from monte_carlo_coin_flips import probability
from monte_carlo_coin_flips import monte_carlo_probability
plt.style.use('bmh')
plt.plot([i for i in range(9)], [probability(i, 8) for i in range(9)],
linewidth=2.5)
plt.plot([i for i in range(9)],
[monte_carlo_probability(i, 8, 1000) for i in range(9)],
linewidth=0.75)
plt.plot([i for i in range(9)],
[monte_carlo_probability(i, 8, 1000) for i in range(9)],
linewidth=0.75)
plt.plot([i for i in range(9)],
[monte_carlo_probability(i, 8, 1000) for i in range(9)],
linewidth=0.75)
plt.plot([i for i in range(9)],
[monte_carlo_probability(i, 8, 1000) for i in range(9)],
linewidth=0.75)
plt.plot([i for i in range(9)],
[monte_carlo_probability(i, 8, 1000) for i in range(9)],
linewidth=0.75)
plt.legend(['True', 'MC 1', 'MC 2', 'MC 3', 'MC 4', 'MC 5'])
plt.xlabel('Number of Heads')
plt.ylabel('Probability')
plt.title('True Distribution vs Monte Carlo Simulations for 8 Coin Flips')
plt.savefig('plot.png')
import sys
from monte_carlo_coin_flips import probability
from monte_carlo_coin_flips import monte_carlo_probability
import matplotlib.pyplot as plt
plt.style.use('bmh')
plt.plot([x for x in range(0, 9)],[probability(x, 8) for x in range(0, 9)],linewidth=2.5)
plt.plot([x for x in range(0, 9)],[monte_carlo_probability(x, 8) for x in range(0, 9)],linewidth=0.75)
plt.plot([x for x in range(0, 9)],[monte_carlo_probability(x, 8) for x in range(0, 9)],linewidth=0.75)
plt.plot([x for x in range(0, 9)],[monte_carlo_probability(x, 8) for x in range(0, 9)],linewidth=0.75)
plt.plot([x for x in range(0, 9)],[monte_carlo_probability(x, 8) for x in range(0, 9)],linewidth=0.75)
plt.plot([x for x in range(0, 9)],[monte_carlo_probability(x, 8) for x in range(0, 9)],linewidth=0.75)
plt.legend(['True','MC 1','MC 2','MC 3','MC 4','MC 5'])
plt.xlabel('Number of Heads')
plt.ylabel('Probability')
plt.title('True Distribution vs Monte Carlo Simulations for 4 Coin Flips')
plt.savefig('plot.png')
def kl_divergence(p, q):
result = 0
for n in range(len(p)):
if p[n] and q[n] != 0:
result += p[n] * ln(p[n] / q[n])
return round(result, 6)
p = [0.2, 0.5, 0, 0.3]
q = [0.1, 0.8, 0.1, 0]
print(kl_divergence(p, q))
print('Computing KL Divergence for MC Simulations...')
print('100 samples --> KL Divergence =')
p = [monte_carlo_probability(n, 8, 100) for n in range(0, 8)]
q = [probability(n, 8) for n in range(0, 8)]
print(kl_divergence(p, q))
print('1000 samples --> KL Divergence =')
p = [monte_carlo_probability(n, 8, 1000) for n in range(0, 8)]
q = [probability(n, 8) for n in range(0, 8)]
print(kl_divergence(p, q))
print('10000 samples --> KL Divergence =')
p = [monte_carlo_probability(n, 8, 10000) for n in range(0, 8)]
q = [probability(n, 8) for n in range(0, 8)]
print(kl_divergence(p, q))
#As the number of samples increases, the KL divergence approaches 0. This is because as p approaches q, ln(p/q) goes to zero and D(p||q) = 0
sys.path.append('Assignment 7')
from monte_carlo_coin_flips import probability
from monte_carlo_coin_flips import monte_carlo_probability
def kl_divergence(p, q):
sum = 0
for index in range(len(p)):
if p[index] != 0 and q[index] != 0:
sum += p[index] * math.log(p[index] / q[index])
return round(sum, 11)
p = [0.2, 0.5, 0, 0.3]
q = [0.1, 0.8, 0.1, 0]
print('Testing kl_divergence...')
assert kl_divergence(p, q) == -0.09637237851
print('PASSED')
q = [probability(i, 8) for i in range(9)]
print('Computing KL Divergence for MC Simulations...')
p = [monte_carlo_probability(i, 8, 100) for i in range(9)]
print('100 samples --> KL Divergence =', kl_divergence(p, q))
p = [monte_carlo_probability(i, 8, 1000) for i in range(9)]
print('1000 samples --> KL Divergence =', kl_divergence(p, q))
p = [monte_carlo_probability(i, 8, 10000) for i in range(9)]
print('10000 samples --> KL Divergence =', kl_divergence(p, q))
# As the number of samples increases, the KL divergence approaches 0 because the approximate probability tends to approach the true distribution the more samples there are.
answer = 0
for num in range(len(p)):
if p[num] and q[num] != 0:
answer += p[num] * ln(p[num] / q[num])
return round(answer, 6)
p = [0.2, 0.5, 0, 0.3]
q = [0.1, 0.8, 0.1, 0]
if __name__ == "__main__":
print("Testing KL Divergence...")
assert kl_divergence(p, q) == -0.096372, 'failed'
print('passed')
prob = [probability(num_heads, 8) for num_heads in range(9)]
monte100 = [
monte_carlo_probability(num_heads, 8, 100) for num_heads in range(9)
]
monte1000 = [
monte_carlo_probability(num_heads, 8, 1000) for num_heads in range(9)
]
monte10000 = [
monte_carlo_probability(num_heads, 8, 10000) for num_heads in range(9)
]
if __name__ == "__main__":
print('Computing KL Divergence for MC Simulations...')
print('100 samples --> KL Divergence = {}'.format(
kl_divergence(monte100, prob)))
print('1000 samples --> KL Divergence = {}'.format(
def simple_sort(num_list):
sorted_list = []
for i in range(len(num_list)):
min_num = num_list[0]
for num in num_list:
if num < min_num:
min_num = num
sorted_list.append(min_num)
num_list.remove(min_num)
return sorted_list
true_distribution = []
for heads in range(5):
true_distribution.append(probability(heads, 4))
def count_heads(flip_sequence):
num_heads = 0
for outcome in flip_sequence:
if outcome == 'H':
num_heads += 1
return num_heads
def calculate_distribution(sample):
flip_list = [0, 0, 0, 0, 0]
flip_split = sample.split(' ')
for sample in flip_split:
for num in range(5):