GLAD

crowdkit.aggregation.classification.glad.GLAD | Source code

GLAD(
    self,
    n_iter: int = 100,
    tol: float = 1e-05,
    silent: bool = True,
    labels_priors: Optional[Series] = None,
    alphas_priors_mean: Optional[Series] = None,
    betas_priors_mean: Optional[Series] = None,
    m_step_max_iter: int = 25,
    m_step_tol: float = 0.01
)

Generative model of Labels, Abilities, and Difficulties.

A probabilistic model that parametrizes workers' abilities and tasks' dificulties. Let's consider a case of $K$ class classification. Let $p$ be a vector of prior class probabilities, $\alpha_i \in (-\infty, +\infty)$ be a worker's ability parameter, $\beta_j \in (0, +\infty)$ be an inverse task's difficulty, $z_j$ be a latent variable representing the true task's label, and $y^i_j$ be a worker's response that we observe. The relationships between this variables and parameters according to GLAD are represented by the following latent label model:

The prior probability of $z_j$ being equal to $c$ is

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

the probability distribution of the worker's responses conditioned by the true label value $c$ follows the single coin Dawid-Skene model where the true label probability is a sigmoid function of the product of worker's ability and inverse task's difficulty:

$$\operatorname{Pr}(y^i_j = k | z_j = c) = \begin{cases}a(i, j), & k = c \\ \frac{1 - a(i,j)}{K-1}, & k \neq c\end{cases},$$

where

$$a(i,j) = \frac{1}{1 + \exp(-\alpha_i\beta_j)}.$$

Parameters $p$, $\alpha$, $\beta$ and latent variables $z$ are optimized through the Expectation-Minimization algorithm.

J. Whitehill, P. Ruvolo, T. Wu, J. Bergsma, and J. Movellan. Whose Vote Should Count More: Optimal Integration of Labels from Labelers of Unknown Expertise. Proceedings of the 22nd International Conference on Neural Information Processing Systems, 2009

https://proceedings.neurips.cc/paper/2009/file/f899139df5e1059396431415e770c6dd-Paper.pdf

Parameters Description

Examples:

from crowdkit.aggregation import GLAD
from crowdkit.datasets import load_dataset
df, gt = load_dataset('relevance-2')
glad = GLAD()
result = glad.fit_predict(df)

Methods Summary