# DawidSkene

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

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

Dawid-Skene aggregation model.

Probabilistic model that parametrizes workers' level of expertise through confusion matrices.

Let $e^w$ be a worker's confusion (error) matrix of size $K \times K$ in case of $K$ class classification,

$p$ be a vector of prior classes probabilities, $z_j$ be a true task's label, and $y^w_j$ be a worker's answer for the task $j$. The relationships between these parameters are represented by the following latent label model.

Here the prior true label probability is

$\operatorname{Pr}(z_j = c) = p[c]$,

and the distribution on the worker's responses given the true label $c$ is represented by the corresponding column of the error matrix:

$\operatorname{Pr}(y_j^w = k | z_j = c) = e^w[k, c]$

Parameters $p$ and $e^w$ and latent variables $z$ are optimized through the Expectation-Maximization algorithm.

A. Philip Dawid and Allan M. Skene. Maximum Likelihood Estimation of Observer Error-Rates Using the EM Algorithm. Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 28, 1 (1979), 20–28.

https://doi.org/10.2307/2346806

## Parameters Description

ParametersTypeDescription
n_iterint

The number of EM iterations.

labels_Optional[Series]

Tasks' labels. A pandas.Series indexed by task such that labels.loc[task] is the tasks's most likely true label.

probas_Optional[DataFrame]

Tasks' label probability distributions. A pandas.DataFrame indexed by task such that result.loc[task, label] is the probability of task's true label to be equal to label. Each probability is between 0 and 1, all task's probabilities should sum up to 1

priors_Optional[Series]

A prior label distribution. A pandas.Series indexed by labels and holding corresponding label's probability of occurrence. Each probability is between 0 and 1, all probabilities should sum up to 1

errors_Optional[DataFrame]

Workers' error matrices. A pandas.DataFrame indexed by worker and label with a column for every label_id found in data such that result.loc[worker, observed_label, true_label] is the probability of worker producing an observed_label given that a task's true label is true_label

Examples:

from crowdkit.aggregation import DawidSkenefrom crowdkit.datasets import load_datasetdf, gt = load_dataset('relevance-2')ds = DawidSkene(100)result = ds.fit_predict(df)

## Methods Summary

MethodDescription
fitFit the model through the EM-algorithm.
fit_predictFit the model and return aggregated results.
fit_predict_probaFit the model and return probability distributions on labels for each task.
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