# HRRASA

crowdkit.aggregation.embeddings.hrrasa.HRRASA | Source code

HRRASA(    self,    n_iter: int = 100,    tol: float = 1e-09,    lambda_emb: float = 0.5,    lambda_out: float = 0.5,    alpha: float = 0.05,    calculate_ranks: bool = False,    output_similarity: Callable[[str, List[List[str]]], float] = glue_similarity)

Hybrid Reliability and Representation Aware Sequence Aggregation.

At the first step, the HRRASA estimates local workers reliabilities that represent how good is a worker's answer to one particular task. The local reliability of the worker $k$ on the task $i$ is denoted by $\gamma_i^k$ and is calculated as a sum of two terms:

$\gamma_i^k = \lambda_{emb}\gamma_{i,emb}^k + \lambda_{out}\gamma_{i,out}^k, \; \lambda_{emb} + \lambda_{out} = 1$.

The $\gamma_{i,emb}^k$ is a reliability calculated on embedding and the $\gamma_{i,seq}^k$ is a reliability calculated on output.

The $\gamma_{i,emb}^k$ is calculated by the following equation:

$\gamma_{i,emb}^k = \frac{1}{|\mathcal{U}_i| - 1}\sum_{a_i^{k'} \in \mathcal{U}_i, k \neq k'}\exp\left(\frac{\|e_i^k-e_i^{k'}\|^2}{\|e_i^k\|^2\|e_i^{k'}\|^2}\right)$,

where $\mathcal{U_i}$ is a set of workers' responses on task $i$. The $\gamma_{i,out}^k$ makes use of some similarity measure $sim$ on the output data, e.g. GLUE similarity on texts:

$\gamma_{i,out}^k = \frac{1}{|\mathcal{U}_i| - 1}\sum_{a_i^{k'} \in \mathcal{U}_i, k \neq k'}sim(a_i^k, a_i^{k'})$.

The HRRASA also estimates global workers' reliabilities $\beta$ that are initialized by ones.

Next, the algorithm iteratively performs two steps:

1. For each task, estimate the aggregated embedding: $\hat{e}_i = \frac{\sum_k \gamma_i^k \beta_k e_i^k}{\sum_k \gamma_i^k \beta_k}$

2. For each worker, estimate the global reliability: $\beta_k = \frac{\chi^2_{(\alpha/2, |\mathcal{V}_k|)}}{\sum_i\left(\|e_i^k - \hat{e}_i\|^2/\gamma_i^k\right)}$, where $\mathcal{V}_k$ is a set of tasks completed by the worker $k$

Finally, the aggregated result is the output which embedding is the closest one to the $\hat{e}_i$. If calculate_ranks is true, the method also calculates ranks for each workers' response as

$s_i^k = \beta_k \exp\left(-\frac{\|e_i^k - \hat{e}_i\|^2}{\|e_i^k\|^2\|\hat{e}_i\|^2}\right) + \gamma_i^k$.

Jiyi Li. Crowdsourced Text Sequence Aggregation based on Hybrid Reliability and Representation. Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR ’20), July 25–30, 2020, Virtual Event, China. ACM, New York, NY, USA,

https://doi.org/10.1145/3397271.3401239

## Parameters Description

ParametersTypeDescription
n_iterint

A number of iterations.

lambda_embfloat

A weight of reliability calculated on embeddigs.

lambda_outfloat

A weight of reliability calculated on outputs.

alphafloat

Confidence level of chi-squared distribution quantiles in beta parameter formula.

calculate_ranksbool

If true, calculate additional attribute ranks_.

Examples:

import numpy as npimport pandas as pdfrom crowdkit.aggregation import HRRASAdf = pd.DataFrame(    [        ['t1', 'p1', 'a', np.array([1.0, 0.0])],        ['t1', 'p2', 'a', np.array([1.0, 0.0])],        ['t1', 'p3', 'b', np.array([0.0, 1.0])]    ],    columns=['task', 'worker', 'output', 'embedding'])result = HRRASA().fit_predict(df)

## Methods Summary

MethodDescription
fitFit the model.
fit_predictFit the model and return aggregated outputs.
fit_predict_scoresFit the model and return scores.
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