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# MMSR

crowdkit.aggregation.classification.m_msr.MMSR | Source code

MMSR(
self,
n_iter: int = 10000,
tol: float = 1e-10,
random_state: Optional[int] = 0,
observation_matrix: ndarray = ...,
covariation_matrix: ndarray = ...,
n_workers: int = 0,
n_labels: int = 0,
labels_mapping: dict = ...,
workers_mapping: dict = ...,
)


Matrix Mean-Subsequence-Reduced Algorithm.

The M-MSR assumes that workers have different level of expertise and associated with a vector of "skills" $\boldsymbol{s}$ which entries $s_i$ show the probability of the worker $i$ to answer correctly to the given task. Having that, we can show that

$\mathbb{E}\left[\frac{M}{M-1}\widetilde{C}-\frac{1}{M-1}\boldsymbol{1}\boldsymbol{1}^T\right] = \boldsymbol{s}\boldsymbol{s}^T,$

where $M$ is the total number of classes, $\widetilde{C}$ is a covariation matrix between workers, and $\boldsymbol{1}\boldsymbol{1}^T$ is the all-ones matrix which has the same size as $\widetilde{C}$.

So, the problem of recovering the skills vector $\boldsymbol{s}$ becomes equivalent to the rank-one matrix completion problem. The M-MSR algorithm is an iterative algorithm for rubust rank-one matrix completion, so its result is an estimator of the vector $\boldsymbol{s}$. Then, the aggregation is the weighted majority vote with weights equal to $\log \frac{(M-1)s_i}{1-s_i}$.

Matrix Mean-Subsequence-Reduced Algorithm. Qianqian Ma and Alex Olshevsky. Adversarial Crowdsourcing Through Robust Rank-One Matrix Completion. 34th Conference on Neural Information Processing Systems (NeurIPS 2020)

https://arxiv.org/abs/2010.12181

## Parameters Description

Parameters Type Description
n_iter int

The maximum number of iterations of the M-MSR algorithm.

eps -

Convergence threshold.

random_state Optional[int]

Seed number for the random initialization.

labels_ Optional[Series]

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

skills_ Optional[Series]

workers' skills. A pandas.Series index by workers and holding corresponding worker's skill

scores_ Optional[DataFrame]

Tasks' label scores. A pandas.DataFrame indexed by task such that result.loc[task, label] is the score of label for task.

Examples:

from crowdkit.aggregation import MMSR