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