Algorithm 1.

Source Accuracy Estimation for Multi-Task Weak Supervision

Input: Observed labeling rates $\widehat{\mathbb{E}}[\psi (O)]$ and covariance ${\widehat{\mathrm{\Sigma }}}_O;$ class balance $\widehat{\mathbb{E}}[\psi (\mathbf{Y})]$ and variance Σ$\mathcal{S}$; correlation sparsity structure Ω

$$\begin{gathered} \widehat{z}\leftarrow {\mathrm{argmin}}_z{\Vert {\widehat{\mathrm{\Sigma }}}_O^{-1}+z{z}^T\Vert }_{\mathrm{\Omega }} \\ \widehat{c}\leftarrow {\mathrm{\Sigma }}_{\mathcal{S}}^{-1}\left(1+{\widehat{z}}^T{\widehat{\mathrm{\Sigma }}}_O\widehat{z}\right),{\widehat{\mathrm{\Sigma }}}_{O\mathcal{S}}\leftarrow {\widehat{\mathrm{\Sigma }}}_O\widehat{z}/\sqrt{\widehat{c}} \\ {\widehat{\mu }}^{\prime }\leftarrow {\widehat{\mathrm{\Sigma }}}_{O\mathcal{S}}+\widehat{\mathbb{E}}[\psi (\mathbf{Y})]\widehat{\mathbb{E}}[\psi (O)] \end{gathered}$$

return ExpandTied $\left({\widehat{\mu }}^{\prime }\right)$