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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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----------
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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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-------
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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 non-adversarial
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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 non-adversarial
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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
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vincentschen