crowdkit.aggregation.classification.dawid_skene.OneCoinDawidSkene.md

OneCoinDawidSkene

crowdkit.aggregation.classification.dawid_skene.OneCoinDawidSkene | Source code

OneCoinDawidSkene(
    self,
    n_iter: int = 100,
    tol: float = 1e-05
)

The one-coin Dawid-Skene aggregation model works exactly the same as the original Dawid-Skene model based on the EM algorithm, except for calculating the workers' errors

at the M-step of the algorithm.

For the one-coin model, a worker confusion (error) matrix is parameterized by a single parameter $s_w$: $$ e^w_{j,z_j} = \begin{cases} s_{w} & y^w_j = z_j \ \frac{1 - s_{w}}{K - 1} & y^w_j \neq z_j \end{cases} $$ where $e^w$ is a worker confusion (error) matrix of size $K \times K$ in case of the $K$ class classification, $z_j$ be a true task label, $y^w_j$ is a worker response to the task $j$, and $s_w$ is a worker skill (accuracy).

In other words, the worker $w$ uses a single coin flip to decide their assignment. No matter what the true label is, the worker has the $s_w$ probability to assign the correct label, and has the $1 − s_w$ probability to randomly assign an incorrect label. For the one-coin model, it suffices to estimate $s_w$ for every worker $w$ and estimate $y^w_j$ for every task $j$. Because of its simplicity, the one-coin model is easier to estimate and enjoys better convergence properties.

Parameters $p$, $e^w$, and latent variables $z$ are optimized with the Expectation-Maximization algorithm:

1. E-step. Estimates the true task label probabilities using the specified workers' responses, the prior label probabilities, and the workers' error probability matrix.
2. M-step. Calculates a worker skill as their accuracy according to the label probability. Then estimates the workers' error probability matrix by assigning user skills to error matrix row by row.

Y. Zhang, X. Chen, D. Zhou, and M. I. Jordan. Spectral methods meet EM: A provably optimal algorithm for crowdsourcing. Journal of Machine Learning Research. Vol. 17, (2016), 1-44.

https://doi.org/10.48550/arXiv.1406.3824

Parameters Description

Parameters	Type	Description
n_iter	int	The maximum number of EM iterations.
tol	float	The tolerance stopping criterion for iterative methods with a variable number of steps. The algorithm converges when the loss change is less than the tol parameter.
labels_	Optional[Series]	The task labels. The pandas.Series data is indexed by task so that labels.loc[task] is the most likely true label of tasks.
probas_	Optional[DataFrame]	The probability distributions of task labels. The pandas.DataFrame data is indexed by task so that result.loc[task, label] is the probability that the task true label is equal to label. Each probability is in the range from 0 to 1, all task probabilities must sum up to 1.
priors_	Optional[Series]	The prior label distribution. The pandas.Series data is indexed by label and contains the probability of the corresponding label occurrence. Each probability is in the range from 0 to 1, all probabilities must sum up to 1.
errors_	Optional[DataFrame]	The workers' error matrices. The pandas.DataFrame data is indexed by worker and label with a column for every label_id found in data so that result.loc[worker, observed_label, true_label] is the probability that worker produces observed_label, given that the task true label is true_label.
skills_	Optional[Series]	The workers' skills. The pandas.Series data is indexed by worker and has the corresponding worker skill.
loss_history_	List[float]	A list of loss values during training.

Examples:

from crowdkit.aggregation import OneCoinDawidSkene
from crowdkit.datasets import load_dataset
df, gt = load_dataset('relevance-2')
hds = OneCoinDawidSkene(100)
result = hds.fit_predict(df)

Methods Summary

Method	Description
fit	Fits the model to the training data with the EM algorithm.