csci5521/assignments/hwk01/hw1solve.py

63 lines
1.5 KiB
Python
Raw Normal View History

2023-10-02 00:24:05 +00:00
from itertools import product
2023-10-02 03:47:05 +00:00
from sympy import symbols, log, diff, exp, Product, Pow
2023-10-01 23:09:50 +00:00
2023-10-02 00:24:05 +00:00
def calc_posterior(p_c1: float, D: int, p_ij: dict[tuple[int, int], float]):
priors = {
1: p_c1,
2: 1 - p_c1,
}
2023-10-01 23:09:50 +00:00
2023-10-02 00:24:05 +00:00
def p_x_given_Ci(xs: list[int], i: int):
2023-10-02 03:47:05 +00:00
s = 1.0
2023-10-02 00:24:05 +00:00
for j in range(len(xs)):
2023-10-02 03:47:05 +00:00
s *= pow(p_ij[i, j], 1.0 - xs[j]) * pow(1.0 - p_ij[i, j], xs[j])
2023-10-02 00:24:05 +00:00
return s
2023-10-01 23:09:50 +00:00
2023-10-02 00:24:05 +00:00
posteriors = {}
for i in [1, 2]:
for xs in product([0, 1], repeat=D):
numer = p_x_given_Ci(xs, i) * priors[i]
2023-10-01 23:09:50 +00:00
2023-10-02 00:24:05 +00:00
def each_denom(k): return p_x_given_Ci(xs, k) * priors[k]
denom = sum(map(each_denom, priors.keys()))
posteriors[*xs, i] = numer / denom
print("Priors:", priors)
for xs in product([0, 1], repeat=D):
print(f"{xs = }")
for i in [1, 2]:
prob = posteriors[*xs, i]
print(f" * C{i}: {prob:0.3f}")
print()
def prob_3c():
D = 2
p_ij = {}
p_ij[1, 0] = 0.6
p_ij[1, 1] = 0.1
p_ij[2, 0] = 0.6
p_ij[2, 1] = 0.9
calc_posterior(0.2, D, p_ij)
calc_posterior(0.8, D, p_ij)
2023-10-02 03:47:05 +00:00
def prob_2a():
p, x, theta, k, n = symbols("p x theta k n")
def get_mle(expr):
likelihood_func = Product(expr, (k, 1, n))
log_likelihood_func = log(likelihood_func)
print(diff(log_likelihood_func, x).simplify())
# print(diff(expr, x))
print(get_mle(Pow(p, x) * Pow(1 - p, 1 - x)))
print(get_mle((1 / theta) * exp(-x / theta)))
prob_2a()
2023-10-02 00:24:05 +00:00
prob_3c()