def weighted_replicate(seq, weights, n):
"""
Return n selections from seq, with the count of each element of
seq proportional to the corresponding weight (filling in fractions
randomly).
>>> weighted_replicate('ABC', [1, 2, 1], 4)
['A', 'B', 'B', 'C']
"""
assert len(seq) == len(weights)
weights = normalize(weights)
wholes = [int(w * n) for w in weights]
fractions = [(w * n) % 1 for w in weights]
return (flatten([x] * nx for x, nx in zip(seq, wholes)) +
weighted_sample_with_replacement(n - sum(wholes), seq, fractions))
def train(dataset):
examples, target = dataset.examples, dataset.target
N = len(examples)
epsilon = 1 / (2 * N)
w = [1 / N] * N
h, z = [], []
for k in range(K):
h_k = L(dataset, w)
h.append(h_k)
error = sum(weight for example, weight in zip(examples, w)
if example[target] != h_k(example))
# Avoid divide-by-0 from either 0% or 100% error rates:
error = clip(error, epsilon, 1 - epsilon)
for j, example in enumerate(examples):
if example[target] == h_k(example):
w[j] *= error / (1 - error)
w = normalize(w)
z.append(math.log((1 - error) / error))
return WeightedMajority(h, z)
def ada_boost(dataset, L, K):
"""[Figure 18.34]"""
examples, target = dataset.examples, dataset.target
n = len(examples)
eps = 1 / (2 * n)
w = [1 / n] * n
h, z = [], []
for k in range(K):
h_k = L(dataset, w)
h.append(h_k)
error = sum(weight for example, weight in zip(examples, w)
if example[target] != h_k(example))
# avoid divide-by-0 from either 0% or 100% error rates
error = clip(error, eps, 1 - eps)
for j, example in enumerate(examples):
if example[target] == h_k(example):
w[j] *= error / (1 - error)
w = normalize(w)
z.append(math.log((1 - error) / error))
return weighted_majority(h, z)
def information_content(values):
"""Number of bits to represent the probability distribution in values."""
probabilities = normalize(removeall(0, values))
return sum(-p * math.log2(p) for p in probabilities)