# HRRASA
`crowdkit.aggregation.embeddings.hrrasa.HRRASA` | [Source code](https://github.com/Toloka/crowd-kit/blob/v1.0.0/crowdkit/aggregation/embeddings/hrrasa.py#L34)

```python
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=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

| Parameters | Type | Description |
| :----------| :----| :-----------|
`n_iter`|**int**|<p>A number of iterations.</p>
`lambda_emb`|**float**|<p>A weight of reliability calculated on embeddigs.</p>
`lambda_out`|**float**|<p>A weight of reliability calculated on outputs.</p>
`alpha`|**float**|<p>Confidence level of chi-squared distribution quantiles in beta parameter formula.</p>
`calculate_ranks`|**bool**|<p>If true, calculate additional attribute `ranks_`.</p>

**Examples:**

```python
import numpy as np
import pandas as pd
from crowdkit.aggregation import HRRASA
df = 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

| Method | Description |
| :------| :-----------|
[fit](crowdkit.aggregation.embeddings.hrrasa.HRRASA.fit.md)| Fit the model.
[fit_predict](crowdkit.aggregation.embeddings.hrrasa.HRRASA.fit_predict.md)| Fit the model and return aggregated outputs.
[fit_predict_scores](crowdkit.aggregation.embeddings.hrrasa.HRRASA.fit_predict_scores.md)| Fit the model and return scores.
