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Embeddings

Routines for embeddings.

ClosestToAverage

Bases: BaseEmbeddingsAggregator

The Closest to Average aggregation model chooses the output with the embedding that's closest to the average embedding.

This method takes a DataFrame containing four columns: task, worker, output, and embedding. Here the embedding is a vector containing a representation of the output which might be any type of data such as text, images, NumPy arrays, etc. As a result, the method returns the output which embedding is the closest one to the average embedding of the task responses.

Source code in crowdkit/aggregation/embeddings/closest_to_average.py 
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@attr.s
class ClosestToAverage(BaseEmbeddingsAggregator):
    """The **Closest to Average** aggregation model chooses the output with the embedding that's closest to the average embedding.

    This method takes a `DataFrame` containing four columns: `task`, `worker`, `output`, and `embedding`.
    Here the `embedding` is a vector containing a representation of the `output` which might be any
    type of data such as text, images, NumPy arrays, etc. As a result, the method returns the output which
    embedding is the closest one to the average embedding of the task responses.
    """

    distance: Callable[[npt.NDArray[Any], npt.NDArray[Any]], float] = attr.ib()
    """A callable that takes two NumPy arrays (the task embedding and the aggregated embedding)
    and returns a single `float` number: the distance between these two vectors."""

    embeddings_and_outputs_: pd.DataFrame = attr.ib(init=False)
    """The task embeddings and outputs. The `pandas.DataFrame` data is indexed by `task` and has the `embedding` and `output` columns."""

    scores_: pd.DataFrame = attr.ib(init=False)
    """The task label scores. The `pandas.DataFrame` data is indexed by `task` so that `result.loc[task, label]` is a score of `label` for `task`."""

    def fit(
        self,
        data: pd.DataFrame,
        aggregated_embeddings: Optional["pd.Series[Any]"] = None,
        true_embeddings: Optional["pd.Series[Any]"] = None,
    ) -> "ClosestToAverage":
        """Fits the model to the training data.

        Args:
            data (DataFrame): The workers' outputs with their embeddings.
                The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
            aggregated_embeddings (Series): The task aggregated embeddings.
                The `pandas.Series` data is indexed by `task` and contains the corresponding aggregated embeddings.
            true_embeddings (Series): The embeddings of the true task responses.
                The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
                The multiple true embeddings are not supported for a single task.

        Returns:
            ClosestToAverage: self.
        """

        if true_embeddings is not None and not true_embeddings.index.is_unique:
            raise ValueError(
                "Incorrect data in true_embeddings: multiple true embeddings for a single task are not supported."
            )

        data = data[["task", "worker", "output", "embedding"]]
        if aggregated_embeddings is None:
            group = data.groupby("task")
            # we don't use .mean() because it does not work with np.array in older pandas versions
            avg_embeddings = group.embedding.apply(np.sum) / group.worker.count()
            avg_embeddings.update(true_embeddings)  # type: ignore
        else:
            avg_embeddings = aggregated_embeddings

        # Calculating distances (scores)
        data = data.join(avg_embeddings.rename("avg_embedding"), on="task")
        # TODO: native Python functions are slow
        data["score"] = data.apply(
            lambda row: self.distance(row.embedding, row.avg_embedding), axis=1
        )

        # Selecting best scores and outputs
        scores = data[["task", "output", "score", "embedding"]]
        # TODO: process cases when we actually have an answer in true_embeddings
        # TODO: to do that we must make true_embeddings a DataFrame with `output` column
        embeddings_and_outputs = scores[["task", "output", "embedding"]].loc[
            scores.groupby("task")["score"].idxmin()
        ]

        #
        self.scores_ = scores.set_index("task")
        self.embeddings_and_outputs_ = embeddings_and_outputs.set_index("task")

        return self

    def fit_predict_scores(
        self,
        data: pd.DataFrame,
        aggregated_embeddings: Optional["pd.Series[Any]"] = None,
    ) -> pd.DataFrame:
        """Fits the model to the training data and returns the estimated scores.

        Args:
            data (DataFrame): The workers' outputs with their embeddings.
                The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
            aggregated_embeddings (Series): The task aggregated embeddings.
                The `pandas.Series` data is indexed by `task` and contains the corresponding aggregated embeddings.

        Returns:
            DataFrame: The task label scores.
                The `pandas.DataFrame` data is indexed by `task` so that `result.loc[task, label]`
                is a score of `label` for `task`.
        """

        return self.fit(data, aggregated_embeddings).scores_

    def fit_predict(
        self,
        data: pd.DataFrame,
        aggregated_embeddings: Optional["pd.Series[Any]"] = None,
    ) -> pd.DataFrame:
        """
        Fits the model to the training data and returns the aggregated outputs.

        Args:
            data (DataFrame): The workers' outputs with their embeddings.
                The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
            aggregated_embeddings (Series): The task aggregated embeddings.
                The `pandas.Series` data is indexed by `task` and contains the corresponding aggregated embeddings.

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

        return self.fit(data, aggregated_embeddings).embeddings_and_outputs_

distance: Callable[[npt.NDArray[Any], npt.NDArray[Any]], float] = attr.ib() class-attribute instance-attribute

A callable that takes two NumPy arrays (the task embedding and the aggregated embedding) and returns a single float number: the distance between these two vectors.

embeddings_and_outputs_: pd.DataFrame = attr.ib(init=False) class-attribute instance-attribute

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

scores_: pd.DataFrame = attr.ib(init=False) class-attribute instance-attribute

The task label scores. The pandas.DataFrame data is indexed by task so that result.loc[task, label] is a score of label for task.

fit(data, aggregated_embeddings=None, true_embeddings=None)

Fits the model to the training data.

Parameters:

Name Type Description Default
data DataFrame

The workers' outputs with their embeddings. The pandas.DataFrame data contains the task, worker, output, and embedding columns.

 required
aggregated_embeddings Series

The task aggregated embeddings. The pandas.Series data is indexed by task and contains the corresponding aggregated embeddings.

 None
true_embeddings Series

The embeddings of the true task responses. The pandas.Series data is indexed by task and contains the corresponding embeddings. The multiple true embeddings are not supported for a single task.

 None

Returns:

Name Type Description
ClosestToAverage ClosestToAverage

self.
Source code in crowdkit/aggregation/embeddings/closest_to_average.py 
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def fit(
    self,
    data: pd.DataFrame,
    aggregated_embeddings: Optional["pd.Series[Any]"] = None,
    true_embeddings: Optional["pd.Series[Any]"] = None,
) -> "ClosestToAverage":
    """Fits the model to the training data.

    Args:
        data (DataFrame): The workers' outputs with their embeddings.
            The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
        aggregated_embeddings (Series): The task aggregated embeddings.
            The `pandas.Series` data is indexed by `task` and contains the corresponding aggregated embeddings.
        true_embeddings (Series): The embeddings of the true task responses.
            The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
            The multiple true embeddings are not supported for a single task.

    Returns:
        ClosestToAverage: self.
    """

    if true_embeddings is not None and not true_embeddings.index.is_unique:
        raise ValueError(
            "Incorrect data in true_embeddings: multiple true embeddings for a single task are not supported."
        )

    data = data[["task", "worker", "output", "embedding"]]
    if aggregated_embeddings is None:
        group = data.groupby("task")
        # we don't use .mean() because it does not work with np.array in older pandas versions
        avg_embeddings = group.embedding.apply(np.sum) / group.worker.count()
        avg_embeddings.update(true_embeddings)  # type: ignore
    else:
        avg_embeddings = aggregated_embeddings

    # Calculating distances (scores)
    data = data.join(avg_embeddings.rename("avg_embedding"), on="task")
    # TODO: native Python functions are slow
    data["score"] = data.apply(
        lambda row: self.distance(row.embedding, row.avg_embedding), axis=1
    )

    # Selecting best scores and outputs
    scores = data[["task", "output", "score", "embedding"]]
    # TODO: process cases when we actually have an answer in true_embeddings
    # TODO: to do that we must make true_embeddings a DataFrame with `output` column
    embeddings_and_outputs = scores[["task", "output", "embedding"]].loc[
        scores.groupby("task")["score"].idxmin()
    ]

    #
    self.scores_ = scores.set_index("task")
    self.embeddings_and_outputs_ = embeddings_and_outputs.set_index("task")

    return self

fit_predict(data, aggregated_embeddings=None)

Fits the model to the training data and returns the aggregated outputs.

Parameters:

Name Type Description Default
data DataFrame

The workers' outputs with their embeddings. The pandas.DataFrame data contains the task, worker, output, and embedding columns.

 required
aggregated_embeddings Series

The task aggregated embeddings. The pandas.Series data is indexed by task and contains the corresponding aggregated embeddings.

 None

Returns:

Name Type Description
DataFrame DataFrame

The task embeddings and outputs. The pandas.DataFrame data is indexed by task and has the embedding and output columns.
Source code in crowdkit/aggregation/embeddings/closest_to_average.py 
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def fit_predict(
    self,
    data: pd.DataFrame,
    aggregated_embeddings: Optional["pd.Series[Any]"] = None,
) -> pd.DataFrame:
    """
    Fits the model to the training data and returns the aggregated outputs.

    Args:
        data (DataFrame): The workers' outputs with their embeddings.
            The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
        aggregated_embeddings (Series): The task aggregated embeddings.
            The `pandas.Series` data is indexed by `task` and contains the corresponding aggregated embeddings.

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

    return self.fit(data, aggregated_embeddings).embeddings_and_outputs_

fit_predict_scores(data, aggregated_embeddings=None)

Fits the model to the training data and returns the estimated scores.

Parameters:

Name Type Description Default
data DataFrame

The workers' outputs with their embeddings. The pandas.DataFrame data contains the task, worker, output, and embedding columns.

 required
aggregated_embeddings Series

The task aggregated embeddings. The pandas.Series data is indexed by task and contains the corresponding aggregated embeddings.

 None

Returns:

Name Type Description
DataFrame DataFrame

The task label scores. The pandas.DataFrame data is indexed by task so that result.loc[task, label] is a score of label for task.
Source code in crowdkit/aggregation/embeddings/closest_to_average.py 
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def fit_predict_scores(
    self,
    data: pd.DataFrame,
    aggregated_embeddings: Optional["pd.Series[Any]"] = None,
) -> pd.DataFrame:
    """Fits the model to the training data and returns the estimated scores.

    Args:
        data (DataFrame): The workers' outputs with their embeddings.
            The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
        aggregated_embeddings (Series): The task aggregated embeddings.
            The `pandas.Series` data is indexed by `task` and contains the corresponding aggregated embeddings.

    Returns:
        DataFrame: The task label scores.
            The `pandas.DataFrame` data is indexed by `task` so that `result.loc[task, label]`
            is a score of `label` for `task`.
    """

    return self.fit(data, aggregated_embeddings).scores_

HRRASA

Bases: BaseClassificationAggregator

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

Examples:

>>> 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)
Source code in crowdkit/aggregation/embeddings/hrrasa.py 
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@attr.s
class HRRASA(BaseClassificationAggregator):
    r"""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>

    Examples:
        >>> 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)
    """

    n_iter: int = attr.ib(default=100)
    """The maximum number of iterations."""

    tol: float = attr.ib(default=1e-9)
    """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_emb: float = attr.ib(default=0.5)
    """The weight of reliability calculated on embeddings."""

    lambda_out: float = attr.ib(default=0.5)
    """The weight of reliability calculated on outputs."""

    alpha: float = attr.ib(default=0.05)
    """The significance level of the chi-squared distribution quantiles in the $\beta$ parameter formula."""

    calculate_ranks: bool = attr.ib(default=False)
    """Specifies if the additional `ranks_` attribute will be calculated (true) or not (false)."""

    _output_similarity: Callable[[str, List[List[str]]], float] = attr.ib(
        default=glue_similarity
    )
    """The similarity measure $sim$ of the `output` data. By default, it is equal to the GLEU similarity."""

    embeddings_and_outputs_: pd.DataFrame = attr.ib(init=False)
    """The task embeddings and outputs.
    The `pandas.DataFrame` data is indexed by `task` and has the `embedding` and `output` columns."""

    loss_history_: List[float] = attr.ib(init=False)
    """A list of loss values during training."""

    def fit(
        self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
    ) -> "HRRASA":
        """Fits the model to the training data.

        Args:
            data (DataFrame): The workers' outputs with their embeddings.
                The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
            true_embeddings (Series): The embeddings of the true task responses.
                The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
                The multiple true embeddings are not supported for a single task.

        Returns:
            HRRASA: self.
        """

        if true_embeddings is not None and not true_embeddings.index.is_unique:
            raise ValueError(
                "Incorrect data in true_embeddings: multiple true embeddings for a single task are not supported."
            )

        data = data[["task", "worker", "embedding", "output"]]
        data, single_overlap_tasks = self._filter_single_overlap(data)
        data = self._get_local_skills(data)

        prior_skills = data.worker.value_counts().apply(
            partial(sps.chi2.isf, self.alpha / 2)
        )
        skills = pd.Series(1.0, index=data.worker.unique())
        weights = self._calc_weights(data, skills)
        aggregated_embeddings = self._aggregate_embeddings(
            data, weights, true_embeddings
        )
        self.loss_history_ = []
        last_aggregated = None

        if len(data) > 0:
            for _ in range(self.n_iter):
                aggregated_embeddings = self._aggregate_embeddings(
                    data, weights, true_embeddings
                )
                skills = self._update_skills(data, aggregated_embeddings, prior_skills)
                weights = self._calc_weights(data, skills)

                if last_aggregated is not None:
                    delta = aggregated_embeddings - last_aggregated
                    loss = (delta * delta).sum().sum() / (
                        aggregated_embeddings * aggregated_embeddings
                    ).sum().sum()
                    self.loss_history_.append(loss)
                    if loss < self.tol:
                        break
                last_aggregated = aggregated_embeddings

        self.prior_skills_ = prior_skills
        self.skills_ = skills
        self.weights_ = weights
        self.aggregated_embeddings_ = aggregated_embeddings
        if self.calculate_ranks:
            self.ranks_ = self._rank_outputs(data, skills)

        if len(single_overlap_tasks) > 0:
            self._fill_single_overlap_tasks_info(single_overlap_tasks)
        return self

    def fit_predict_scores(
        self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
    ) -> pd.DataFrame:
        """Fits the model to the training data and returns the estimated scores.

        Args:
            data (DataFrame): The workers' outputs with their embeddings.
                The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
            true_embeddings (Series): The embeddings of the true task responses.
                The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
                The multiple true embeddings are not supported for a single task.

        Returns:
            DataFrame: The task label scores.
                The `pandas.DataFrame` data is indexed by `task` so that `result.loc[task, label]`
                is a score of `label` for `task`.
        """

        return self.fit(data, true_embeddings)._apply(data, true_embeddings).scores_

    def fit_predict(  # type: ignore
        self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
    ) -> pd.DataFrame:
        """Fits the model to the training data and returns the aggregated outputs.

        Args:
            data (DataFrame): The workers' outputs with their embeddings.
                The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
            true_embeddings (Series): The embeddings of the true task responses.
                The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
                The multiple true embeddings are not supported for a single task.

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

        return (
            self.fit(data, true_embeddings)
            ._apply(data, true_embeddings)
            .embeddings_and_outputs_
        )

    @staticmethod
    def _cosine_distance(
        embedding: npt.NDArray[Any], avg_embedding: npt.NDArray[Any]
    ) -> float:
        if not embedding.any() or not avg_embedding.any():
            return float("inf")
        return float(distance.cosine(embedding, avg_embedding))

    def _apply(
        self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
    ) -> "HRRASA":
        cta = ClosestToAverage(distance=self._cosine_distance)
        cta.fit(
            data,
            aggregated_embeddings=self.aggregated_embeddings_,
            true_embeddings=true_embeddings,
        )
        self.scores_ = cta.scores_
        self.embeddings_and_outputs_ = cta.embeddings_and_outputs_
        return self

    @staticmethod
    def _aggregate_embeddings(
        data: pd.DataFrame,
        weights: pd.DataFrame,
        true_embeddings: Optional["pd.Series[Any]"] = None,
    ) -> "pd.Series[Any]":
        """Calculates the weighted average of embeddings for each task."""
        data = data.join(weights, on=["task", "worker"])
        data["weighted_embedding"] = data.weight * data.embedding
        group = data.groupby("task", group_keys=False)
        aggregated_embeddings = pd.Series(
            (group.weighted_embedding.apply(np.sum) / group.weight.sum()),
            dtype=np.float64,
        )
        if true_embeddings is None:
            true_embeddings = pd.Series([], dtype=np.float64)
        aggregated_embeddings.update(true_embeddings)
        return aggregated_embeddings

    def _distance_from_aggregated(self, answers: pd.DataFrame) -> pd.DataFrame:
        """Calculates the square of Euclidian distance from the aggregated embedding for each answer."""
        with_task_aggregate = answers.set_index("task")
        with_task_aggregate["task_aggregate"] = self.aggregated_embeddings_
        with_task_aggregate["distance"] = with_task_aggregate.apply(
            lambda row: np.sum((row["embedding"] - row["task_aggregate"]) ** 2), axis=1
        )
        with_task_aggregate["distance"] = with_task_aggregate["distance"].replace(
            {0.0: 1e-5}
        )  # avoid division by zero
        return with_task_aggregate.reset_index()

    def _rank_outputs(
        self, data: pd.DataFrame, skills: "pd.Series[Any]"
    ) -> pd.DataFrame:
        """Returns the ranking score for each record in the `data` data frame."""

        if not data.size:
            return pd.DataFrame(columns=["task", "output", "rank"])

        data = self._distance_from_aggregated(data)
        data["norms_prod"] = data.apply(
            lambda row: np.sum(row["embedding"] ** 2)
            * np.sum(row["task_aggregate"] ** 2),
            axis=1,
        )
        data["rank"] = (
            skills * np.exp(-data.distance / data.norms_prod) + data.local_skill
        )
        return data[["task", "output", "rank"]]

    @staticmethod
    def _calc_weights(
        data: pd.DataFrame, worker_skills: "pd.Series[Any]"
    ) -> pd.DataFrame:
        """Calculates the weight for every embedding according to its local and global skills."""
        data = data.set_index("worker")
        data["worker_skill"] = worker_skills
        data = data.reset_index()
        data["weight"] = data["worker_skill"] * data["local_skill"]
        return data[["task", "worker", "weight"]].set_index(["task", "worker"])

    @staticmethod
    def _update_skills(
        data: pd.DataFrame,
        aggregated_embeddings: "pd.Series[Any]",
        prior_skills: "pd.Series[Any]",
    ) -> "pd.Series[Any]":
        """Estimates the global reliabilities by aggregated embeddings."""
        data = data.join(
            aggregated_embeddings.rename("aggregated_embedding"), on="task"
        )
        data["distance"] = ((data.embedding - data.aggregated_embedding) ** 2).apply(
            np.sum
        )
        data["distance"] = data["distance"] / data["local_skill"]
        total_distances = data.groupby("worker").distance.apply(np.sum)
        total_distances.clip(lower=_EPS, inplace=True)
        return prior_skills / total_distances

    def _get_local_skills(self, data: pd.DataFrame) -> pd.DataFrame:
        """Computes the local (relative) skills for each task answer."""
        index = []
        local_skills = []
        processed_pairs = set()
        for task, task_answers in data.groupby("task"):
            for worker, skill in self._local_skills_on_task(task_answers):
                if (task, worker) not in processed_pairs:
                    local_skills.append(skill)
                    index.append((task, worker))
                    processed_pairs.add((task, worker))
        data = data.set_index(["task", "worker"])
        local_skills = pd.Series(  # type: ignore
            local_skills,
            index=pd.MultiIndex.from_tuples(index, names=["task", "worker"]),
            dtype=float,
        )
        data["local_skill"] = local_skills
        return data.reset_index()

    def _local_skills_on_task(
        self, task_answers: pd.DataFrame
    ) -> Generator[Tuple[Any, float], None, None]:
        overlap = len(task_answers)

        for _, cur_row in task_answers.iterrows():
            worker = cur_row["worker"]
            emb_sum = 0.0
            seq_sum = 0.0
            emb = cur_row["embedding"]
            seq = cur_row["output"]
            emb_norm = np.sum(emb**2)
            for __, other_row in task_answers.iterrows():
                if other_row["worker"] == worker:
                    continue
                other_emb = other_row["embedding"]
                other_seq = other_row["output"]

                # embeddings similarity
                diff_norm = np.sum((emb - other_emb) ** 2)
                other_norm = np.sum(other_emb**2)
                emb_sum += np.exp(-diff_norm / (emb_norm * other_norm))

                # sequence similarity
                seq_sum += self._output_similarity(seq, other_seq)
            emb_sum /= overlap - 1
            seq_sum /= overlap - 1

            yield worker, self.lambda_emb * emb_sum + self.lambda_out * seq_sum

    def _filter_single_overlap(
        self, data: pd.DataFrame
    ) -> Tuple[pd.DataFrame, pd.DataFrame]:
        """Filter skills, embeddings, weights, and ranks for single overlap tasks that couldn't be processed by HRRASA."""

        single_overlap_task_ids = []
        for task, task_answers in data.groupby("task"):
            if len(task_answers) == 1:
                single_overlap_task_ids.append(task)
        data = data.set_index("task")
        return (
            data.drop(single_overlap_task_ids).reset_index(),
            data.loc[single_overlap_task_ids].reset_index(),
        )

    def _fill_single_overlap_tasks_info(
        self, single_overlap_tasks: pd.DataFrame
    ) -> None:
        """Fill skills, embeddings, weights, and ranks for single overlap tasks."""

        workers_to_append = []
        aggregated_embeddings_to_append = {}
        weights_to_append = []
        ranks_to_append = []
        for row in single_overlap_tasks.itertuples():
            if row.worker not in self.prior_skills_:
                workers_to_append.append(row.worker)
            if row.task not in self.aggregated_embeddings_:
                aggregated_embeddings_to_append[row.task] = row.embedding
                weights_to_append.append(
                    {"task": row.task, "worker": row.worker, "weight": np.nan}
                )
                ranks_to_append.append(
                    {"task": row.task, "output": row.output, "rank": np.nan}
                )

        self.prior_skills_ = pd.concat(
            [self.prior_skills_, pd.Series(np.nan, index=workers_to_append)]
        )
        self.skills_ = pd.concat(
            [self.skills_, pd.Series(np.nan, index=workers_to_append)]
        )
        self.aggregated_embeddings_ = pd.concat(
            [self.aggregated_embeddings_, pd.Series(aggregated_embeddings_to_append)]
        )
        self.weights_ = pd.concat([self.weights_, pd.DataFrame(weights_to_append)])
        if hasattr(self, "ranks_"):
            self.ranks_ = self.ranks_.append(pd.DataFrame(ranks_to_append))  # type: ignore

alpha: float = attr.ib(default=0.05) class-attribute instance-attribute

The significance level of the chi-squared distribution quantiles in the \(eta\) parameter formula.

calculate_ranks: bool = attr.ib(default=False) class-attribute instance-attribute

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

embeddings_and_outputs_: pd.DataFrame = attr.ib(init=False) class-attribute instance-attribute

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

lambda_emb: float = attr.ib(default=0.5) class-attribute instance-attribute

The weight of reliability calculated on embeddings.

lambda_out: float = attr.ib(default=0.5) class-attribute instance-attribute

The weight of reliability calculated on outputs.

loss_history_: List[float] = attr.ib(init=False) class-attribute instance-attribute

A list of loss values during training.

n_iter: int = attr.ib(default=100) class-attribute instance-attribute

The maximum number of iterations.

tol: float = attr.ib(default=1e-09) class-attribute instance-attribute

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.

fit(data, true_embeddings=None)

Fits the model to the training data.

Parameters:

Name Type Description Default
data DataFrame

The workers' outputs with their embeddings. The pandas.DataFrame data contains the task, worker, output, and embedding columns.

 required
true_embeddings Series

The embeddings of the true task responses. The pandas.Series data is indexed by task and contains the corresponding embeddings. The multiple true embeddings are not supported for a single task.

 None

Returns:

Name Type Description
HRRASA HRRASA

self.
Source code in crowdkit/aggregation/embeddings/hrrasa.py 
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def fit(
    self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
) -> "HRRASA":
    """Fits the model to the training data.

    Args:
        data (DataFrame): The workers' outputs with their embeddings.
            The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
        true_embeddings (Series): The embeddings of the true task responses.
            The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
            The multiple true embeddings are not supported for a single task.

    Returns:
        HRRASA: self.
    """

    if true_embeddings is not None and not true_embeddings.index.is_unique:
        raise ValueError(
            "Incorrect data in true_embeddings: multiple true embeddings for a single task are not supported."
        )

    data = data[["task", "worker", "embedding", "output"]]
    data, single_overlap_tasks = self._filter_single_overlap(data)
    data = self._get_local_skills(data)

    prior_skills = data.worker.value_counts().apply(
        partial(sps.chi2.isf, self.alpha / 2)
    )
    skills = pd.Series(1.0, index=data.worker.unique())
    weights = self._calc_weights(data, skills)
    aggregated_embeddings = self._aggregate_embeddings(
        data, weights, true_embeddings
    )
    self.loss_history_ = []
    last_aggregated = None

    if len(data) > 0:
        for _ in range(self.n_iter):
            aggregated_embeddings = self._aggregate_embeddings(
                data, weights, true_embeddings
            )
            skills = self._update_skills(data, aggregated_embeddings, prior_skills)
            weights = self._calc_weights(data, skills)

            if last_aggregated is not None:
                delta = aggregated_embeddings - last_aggregated
                loss = (delta * delta).sum().sum() / (
                    aggregated_embeddings * aggregated_embeddings
                ).sum().sum()
                self.loss_history_.append(loss)
                if loss < self.tol:
                    break
            last_aggregated = aggregated_embeddings

    self.prior_skills_ = prior_skills
    self.skills_ = skills
    self.weights_ = weights
    self.aggregated_embeddings_ = aggregated_embeddings
    if self.calculate_ranks:
        self.ranks_ = self._rank_outputs(data, skills)

    if len(single_overlap_tasks) > 0:
        self._fill_single_overlap_tasks_info(single_overlap_tasks)
    return self

fit_predict(data, true_embeddings=None)

Fits the model to the training data and returns the aggregated outputs.

Parameters:

Name Type Description Default
data DataFrame

The workers' outputs with their embeddings. The pandas.DataFrame data contains the task, worker, output, and embedding columns.

 required
true_embeddings Series

The embeddings of the true task responses. The pandas.Series data is indexed by task and contains the corresponding embeddings. The multiple true embeddings are not supported for a single task.

 None

Returns:

Name Type Description
DataFrame DataFrame

The task embeddings and outputs. The pandas.DataFrame data is indexed by task and has the embedding and output columns.
Source code in crowdkit/aggregation/embeddings/hrrasa.py 
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def fit_predict(  # type: ignore
    self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
) -> pd.DataFrame:
    """Fits the model to the training data and returns the aggregated outputs.

    Args:
        data (DataFrame): The workers' outputs with their embeddings.
            The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
        true_embeddings (Series): The embeddings of the true task responses.
            The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
            The multiple true embeddings are not supported for a single task.

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

    return (
        self.fit(data, true_embeddings)
        ._apply(data, true_embeddings)
        .embeddings_and_outputs_
    )

fit_predict_scores(data, true_embeddings=None)

Fits the model to the training data and returns the estimated scores.

Parameters:

Name Type Description Default
data DataFrame

The workers' outputs with their embeddings. The pandas.DataFrame data contains the task, worker, output, and embedding columns.

 required
true_embeddings Series

The embeddings of the true task responses. The pandas.Series data is indexed by task and contains the corresponding embeddings. The multiple true embeddings are not supported for a single task.

 None

Returns:

Name Type Description
DataFrame DataFrame

The task label scores. The pandas.DataFrame data is indexed by task so that result.loc[task, label] is a score of label for task.
Source code in crowdkit/aggregation/embeddings/hrrasa.py 
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def fit_predict_scores(
    self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
) -> pd.DataFrame:
    """Fits the model to the training data and returns the estimated scores.

    Args:
        data (DataFrame): The workers' outputs with their embeddings.
            The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
        true_embeddings (Series): The embeddings of the true task responses.
            The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
            The multiple true embeddings are not supported for a single task.

    Returns:
        DataFrame: The task label scores.
            The `pandas.DataFrame` data is indexed by `task` so that `result.loc[task, label]`
            is a score of `label` for `task`.
    """

    return self.fit(data, true_embeddings)._apply(data, true_embeddings).scores_

RASA

Bases: BaseEmbeddingsAggregator

The Reliability Aware Sequence Aggregation (RASA) algorithm consists of three steps.

Step 1. Encode the worker answers into embeddings.

Step 2. Estimate the global workers' reliabilities \(\beta\) by iteratively performing two steps: 1. For each task, estimate the aggregated embedding: \(\hat{e}_i = \frac{\sum_k \beta_k e_i^k}{\sum_k \beta_k}\) 2. For each worker, estimate the global reliability: \(\beta_k = \frac{\chi^2_{(\alpha/2, |\mathcal{V}_k|)}}{\sum_i\left(\|e_i^k - \hat{e}_i\|^2\right)}\), where \(\mathcal{V}_k\) is a set of tasks completed by the worker \(k\).

Step 3. Estimate the aggregated result. It is the output which embedding is the closest one to \(\hat{e}_i\).

Jiyi Li, Fumiyo Fukumoto. A Dataset of Crowdsourced Word Sequences: Collections and Answer Aggregation for Ground Truth Creation. In Proceedings of the First Workshop on Aggregating and Analysing Crowdsourced Annotations for NLP, Hong Kong, China (November 3, 2019), 24–28. https://doi.org/10.18653/v1/D19-5904

Examples:

>>> import numpy as np
>>> import pandas as pd
>>> from crowdkit.aggregation import RASA
>>> 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 = RASA().fit_predict(df)
Source code in crowdkit/aggregation/embeddings/rasa.py 
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@attr.s
class RASA(BaseEmbeddingsAggregator):
    r"""The **Reliability Aware Sequence Aggregation** (RASA) algorithm consists of three steps.

    **Step 1**. Encode the worker answers into embeddings.

    **Step 2**. Estimate the *global* workers' reliabilities $\beta$ by iteratively performing two steps:
    1. For each task, estimate the aggregated embedding: $\hat{e}_i = \frac{\sum_k
    \beta_k e_i^k}{\sum_k \beta_k}$
    2. For each worker, estimate the global reliability: $\beta_k = \frac{\chi^2_{(\alpha/2,
    |\mathcal{V}_k|)}}{\sum_i\left(\|e_i^k - \hat{e}_i\|^2\right)}$, where $\mathcal{V}_k$
    is a set of tasks completed by the worker $k$.

    **Step 3**. Estimate the aggregated result. It is the output which embedding is
    the closest one to $\hat{e}_i$.

    Jiyi Li, Fumiyo Fukumoto. A Dataset of Crowdsourced Word Sequences: Collections and Answer Aggregation for Ground Truth Creation.
    In *Proceedings of the First Workshop on Aggregating and Analysing Crowdsourced Annotations for NLP*,
    Hong Kong, China (November 3, 2019), 24–28.
    <https://doi.org/10.18653/v1/D19-5904>

    Examples:
        >>> import numpy as np
        >>> import pandas as pd
        >>> from crowdkit.aggregation import RASA
        >>> 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 = RASA().fit_predict(df)
    """

    n_iter: int = attr.ib(default=100)
    """The maximum number of iterations."""

    tol: float = attr.ib(default=1e-9)
    """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."""

    alpha: float = attr.ib(default=0.05)
    """The significance level of the chi-squared distribution quantiles in the $\beta$ parameter formula."""

    loss_history_: List[float] = attr.ib(init=False)
    """A list of loss values during training."""

    @staticmethod
    def _aggregate_embeddings(
        data: pd.DataFrame,
        skills: "pd.Series[Any]",
        true_embeddings: Optional["pd.Series[Any]"] = None,
    ) -> "pd.Series[Any]":
        """Calculates the weighted average of embeddings for each task."""
        data = data.join(skills.rename("skill"), on="worker")
        data["weighted_embedding"] = data.skill * data.embedding
        group = data.groupby("task")
        aggregated_embeddings = (
            group.weighted_embedding.apply(np.sum) / group.skill.sum()
        )
        if true_embeddings is None:
            true_embeddings = pd.Series([], dtype=np.float64)
        aggregated_embeddings.update(true_embeddings)
        return aggregated_embeddings

    @staticmethod
    def _update_skills(
        data: pd.DataFrame,
        aggregated_embeddings: "pd.Series[Any]",
        prior_skills: "pd.Series[Any]",
    ) -> "pd.Series[Any]":
        """Estimates the global reliabilities by aggregated embeddings."""
        data = data.join(
            aggregated_embeddings.rename("aggregated_embedding"), on="task"
        )
        data["distance"] = ((data.embedding - data.aggregated_embedding) ** 2).apply(
            np.sum
        )
        total_distances = data.groupby("worker").distance.apply(np.sum)
        total_distances.clip(lower=_EPS, inplace=True)
        return prior_skills / total_distances

    @staticmethod
    def _cosine_distance(
        embedding: npt.NDArray[Any], avg_embedding: npt.NDArray[Any]
    ) -> float:
        if not embedding.any() or not avg_embedding.any():
            return float("inf")
        return float(distance.cosine(embedding, avg_embedding))

    def _apply(
        self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
    ) -> "RASA":
        cta = ClosestToAverage(distance=self._cosine_distance)
        cta.fit(
            data,
            aggregated_embeddings=self.aggregated_embeddings_,
            true_embeddings=true_embeddings,
        )
        self.scores_ = cta.scores_
        self.embeddings_and_outputs_ = cta.embeddings_and_outputs_
        return self

    def fit(
        self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
    ) -> "RASA":
        """Fits the model to the training data.

        Args:
            data (DataFrame): The workers' outputs with their embeddings.
                The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
            true_embeddings (Series): The embeddings of the true task responses.
                The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
                The multiple true embeddings are not supported for a single task.

        Returns:
            RASA: self.
        """

        data = data[["task", "worker", "embedding"]]

        if true_embeddings is not None and not true_embeddings.index.is_unique:
            raise ValueError(
                "Incorrect data in true_embeddings: multiple true embeddings for a single task are not supported."
            )

        # What we call skills here is called reliabilities in the paper
        prior_skills = data.worker.value_counts().apply(
            partial(sps.chi2.isf, self.alpha / 2)
        )
        skills = pd.Series(1.0, index=data.worker.unique())
        aggregated_embeddings = None
        last_aggregated = None

        for _ in range(self.n_iter):
            aggregated_embeddings = self._aggregate_embeddings(
                data, skills, true_embeddings
            )
            skills = self._update_skills(data, aggregated_embeddings, prior_skills)

            if last_aggregated is not None:
                delta = aggregated_embeddings - last_aggregated
                loss = (delta * delta).sum().sum() / (
                    aggregated_embeddings * aggregated_embeddings
                ).sum().sum()
                if loss < self.tol:
                    break
            last_aggregated = aggregated_embeddings

        self.prior_skills_ = prior_skills
        self.skills_ = skills
        self.aggregated_embeddings_ = aggregated_embeddings
        return self

    def fit_predict_scores(
        self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
    ) -> pd.DataFrame:
        """Fits the model to the training data and returns the estimated scores.

        Args:
            data (DataFrame): The workers' outputs with their embeddings.
                The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
            true_embeddings (Series): The embeddings of the true task responses.
                The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
                The multiple true embeddings are not supported for a single task.

        Returns:
            DataFrame: The task label scores.
                The `pandas.DataFrame` data is indexed by `task` so that `result.loc[task, label]`
                is a score of `label` for `task`.
        """

        return self.fit(data, true_embeddings)._apply(data, true_embeddings).scores_

    def fit_predict(
        self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
    ) -> pd.DataFrame:
        """Fits the model to the training data and returns the aggregated outputs.

        Args:
            data (DataFrame): The workers' outputs with their embeddings.
                The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
            true_embeddings (Series): The embeddings of the true task responses.
                The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
                The multiple true embeddings are not supported for a single task.

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

        return (
            self.fit(data, true_embeddings)
            ._apply(data, true_embeddings)
            .embeddings_and_outputs_
        )

alpha: float = attr.ib(default=0.05) class-attribute instance-attribute

The significance level of the chi-squared distribution quantiles in the \(eta\) parameter formula.

loss_history_: List[float] = attr.ib(init=False) class-attribute instance-attribute

A list of loss values during training.

n_iter: int = attr.ib(default=100) class-attribute instance-attribute

The maximum number of iterations.

tol: float = attr.ib(default=1e-09) class-attribute instance-attribute

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.

fit(data, true_embeddings=None)

Fits the model to the training data.

Parameters:

Name Type Description Default
data DataFrame

The workers' outputs with their embeddings. The pandas.DataFrame data contains the task, worker, output, and embedding columns.

 required
true_embeddings Series

The embeddings of the true task responses. The pandas.Series data is indexed by task and contains the corresponding embeddings. The multiple true embeddings are not supported for a single task.

 None

Returns:

Name Type Description
RASA RASA

self.
Source code in crowdkit/aggregation/embeddings/rasa.py 
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def fit(
    self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
) -> "RASA":
    """Fits the model to the training data.

    Args:
        data (DataFrame): The workers' outputs with their embeddings.
            The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
        true_embeddings (Series): The embeddings of the true task responses.
            The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
            The multiple true embeddings are not supported for a single task.

    Returns:
        RASA: self.
    """

    data = data[["task", "worker", "embedding"]]

    if true_embeddings is not None and not true_embeddings.index.is_unique:
        raise ValueError(
            "Incorrect data in true_embeddings: multiple true embeddings for a single task are not supported."
        )

    # What we call skills here is called reliabilities in the paper
    prior_skills = data.worker.value_counts().apply(
        partial(sps.chi2.isf, self.alpha / 2)
    )
    skills = pd.Series(1.0, index=data.worker.unique())
    aggregated_embeddings = None
    last_aggregated = None

    for _ in range(self.n_iter):
        aggregated_embeddings = self._aggregate_embeddings(
            data, skills, true_embeddings
        )
        skills = self._update_skills(data, aggregated_embeddings, prior_skills)

        if last_aggregated is not None:
            delta = aggregated_embeddings - last_aggregated
            loss = (delta * delta).sum().sum() / (
                aggregated_embeddings * aggregated_embeddings
            ).sum().sum()
            if loss < self.tol:
                break
        last_aggregated = aggregated_embeddings

    self.prior_skills_ = prior_skills
    self.skills_ = skills
    self.aggregated_embeddings_ = aggregated_embeddings
    return self

fit_predict(data, true_embeddings=None)

Fits the model to the training data and returns the aggregated outputs.

Parameters:

Name Type Description Default
data DataFrame

The workers' outputs with their embeddings. The pandas.DataFrame data contains the task, worker, output, and embedding columns.

 required
true_embeddings Series

The embeddings of the true task responses. The pandas.Series data is indexed by task and contains the corresponding embeddings. The multiple true embeddings are not supported for a single task.

 None

Returns:

Name Type Description
DataFrame DataFrame

The task embeddings and outputs. The pandas.DataFrame data is indexed by task and has the embedding and output columns.
Source code in crowdkit/aggregation/embeddings/rasa.py 
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def fit_predict(
    self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
) -> pd.DataFrame:
    """Fits the model to the training data and returns the aggregated outputs.

    Args:
        data (DataFrame): The workers' outputs with their embeddings.
            The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
        true_embeddings (Series): The embeddings of the true task responses.
            The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
            The multiple true embeddings are not supported for a single task.

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

    return (
        self.fit(data, true_embeddings)
        ._apply(data, true_embeddings)
        .embeddings_and_outputs_
    )

fit_predict_scores(data, true_embeddings=None)

Fits the model to the training data and returns the estimated scores.

Parameters:

Name Type Description Default
data DataFrame

The workers' outputs with their embeddings. The pandas.DataFrame data contains the task, worker, output, and embedding columns.

 required
true_embeddings Series

The embeddings of the true task responses. The pandas.Series data is indexed by task and contains the corresponding embeddings. The multiple true embeddings are not supported for a single task.

 None

Returns:

Name Type Description
DataFrame DataFrame

The task label scores. The pandas.DataFrame data is indexed by task so that result.loc[task, label] is a score of label for task.
Source code in crowdkit/aggregation/embeddings/rasa.py 
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def fit_predict_scores(
    self, data: pd.DataFrame, true_embeddings: Optional["pd.Series[Any]"] = None
) -> pd.DataFrame:
    """Fits the model to the training data and returns the estimated scores.

    Args:
        data (DataFrame): The workers' outputs with their embeddings.
            The `pandas.DataFrame` data contains the `task`, `worker`, `output`, and `embedding` columns.
        true_embeddings (Series): The embeddings of the true task responses.
            The `pandas.Series` data is indexed by `task` and contains the corresponding embeddings.
            The multiple true embeddings are not supported for a single task.

    Returns:
        DataFrame: The task label scores.
            The `pandas.DataFrame` data is indexed by `task` so that `result.loc[task, label]`
            is a score of `label` for `task`.
    """

    return self.fit(data, true_embeddings)._apply(data, true_embeddings).scores_