# 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)

The Hybrid Reliability and Representation Aware Sequence Aggregation (HRRASA) algorithm consists of four steps.

Step 1. Encode the worker answers into embeddings.

Step 2. Estimate the local workers' reliabilities that represent how well a worker responds to one particular task. The local reliability of the worker $k$ on the task $i$ is denoted by $\gamma_i^k$ and is calculated by incorporating both types of representations:

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

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

The $\gamma_{i,emb}^k$ value 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 $\gamma_{i,seq}^k$ value uses some similarity measure $sim$ on the output data, e.g. GLEU similarity on texts:

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

Step 3. Estimate the global workers' reliabilities $\beta$ by iteratively performing 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 $k$.

Step 4. Estimate the aggregated result. It is the output which embedding is the closest one to $\hat{e}_i$. If calculate_ranks is true, the method also calculates ranks for each worker 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.

In Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR '20), China (July 25–30, 2020), 1761-1764.

https://doi.org/10.1145/3397271.3401239

## Parameters description

ParametersTypeDescription
n_iterint

The maximum number of iterations.

tolfloat

The tolerance stopping criterion for iterative methods with a variable number of steps. The algorithm converges when the loss change is less than the tol parameter.

lambda_embfloat

The weight of reliability calculated on embeddings.

lambda_outfloat

The weight of reliability calculated on outputs.

alphafloat

The significance level of the chi-squared distribution quantiles in the $\beta$ parameter formula.

calculate_ranksbool

Specifies if the additional ranks_ attribute will be calculated (true) or not (false).

_output_similarity-

The similarity measure $sim$ of the output data. By default, it is equal to the GLEU similarity.

embeddings_and_outputs_-

The task embeddings and outputs. The pandas.DataFrame data is indexed by task and has the embedding and output columns.

loss_history_List[float]

A list of loss values during training.

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
fitFits the model to the training data.
fit_predictFits the model to the training data and returns the aggregated outputs.
fit_predict_scoresFits the model to the training data and returns the estimated scores.

Last updated: March 31, 2023

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