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from typing import Tuple

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import numpy as np

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def generate_simple_label_matrix(

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n: int, m: int, cardinality: int, abstain_multiplier: float = 1.0

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) > Tuple[np.ndarray, np.ndarray, np.ndarray]:

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"""Generate a synthetic label matrix with true parameters and labels.

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This function generates a set of labeling function conditional probability tables,

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P(LF=l  Y=y), stored as a matrix P, and true labels Y, and then generates the

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resulting label matrix L.

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Parameters

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n

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Number of data points

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m

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Number of labeling functions

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cardinality

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Cardinality of true labels (i.e. not including abstains)

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abstain_multiplier

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Factor to multiply the probability of abstaining by

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Returns

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Tuple[np.ndarray, np.ndarray, np.ndarray]

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A tuple containing the LF conditional probabilities P,

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the true labels Y, and the output label matrix L

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"""

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# Generate the conditional probability tables for the LFs

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# The first axis is LF, second is LF output label, third is true class label

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# Note that we include abstains in the LF output space, and that we bias the

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# conditional probabilities towards being nonadversarial

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P = np.empty((m, cardinality + 1, cardinality))

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for i in range(m):

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p = np.random.rand(cardinality + 1, cardinality)

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# Bias the LFs to being nonadversarial

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p[1:, :] += (cardinality  1) * np.eye(cardinality)

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# Optionally increase the abstain probability by some multiplier; note this is

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# to simulate the common setting where LFs label very sparsely

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p[0, :] *= abstain_multiplier

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# Normalize the conditional probabilities table

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P[i] = p @ np.diag(1 / p.sum(axis=0))

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# Generate the true datapoint labels

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# Note: Assuming balanced classes to start

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Y = np.random.choice(cardinality, n)

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# Generate the label matrix L

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L = np.empty((n, m), dtype=int)

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for i in range(n):

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for j in range(m):

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L[i, j] = np.random.choice(cardinality + 1, p=P[j, :, Y[i]])  1

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return P, Y, L
