Repository: Toloka/crowd-kit

Issue:
[FEATURE] Improve ds algorithm to use worker's history error matrix info
### Problem description

The current implementation of ds algorithm doesn't take worker's history error matrix into consideration, which is a useful priori information that can help the truth inference process.

### Feature description

Improve ds algorithm to use worker's history error matrix info

### Potential alternatives

_No response_

### Papers connected with feature

_No response_

### Additional information

Hints from issue comments:

Solution patch:
diff --git a/README.md b/README.md
index 467a837..e258116 100644
--- a/README.md
+++ b/README.md
@@ -37,7 +37,8 @@ If you are interested in contributing to Crowd-Kit, use [uv](https://github.com/
 
 ```shell
 uv venv
-uv pip install -e '.[dev,docs,learning]
+uv pip install -e '.[dev,docs,learning]'
+uv tool run pre-commit install
 ```
 
 We use [pytest](https://pytest.org/) for testing and a variety of linters, including [pre-commit](https://pre-commit.com/), [Black](https://github.com/psf/black), [isort](https://github.com/pycqa/isort), [Flake8](https://github.com/pycqa/flake8), [pyupgrade](https://github.com/asottile/pyupgrade), and [nbQA](https://github.com/nbQA-dev/nbQA), to simplify code maintenance.
diff --git a/crowdkit/aggregation/classification/dawid_skene.py b/crowdkit/aggregation/classification/dawid_skene.py
index aaf4307..1fbe7e2 100644
--- a/crowdkit/aggregation/classification/dawid_skene.py
+++ b/crowdkit/aggregation/classification/dawid_skene.py
@@ -1,6 +1,6 @@
 __all__ = ["DawidSkene", "OneCoinDawidSkene"]
 
-from typing import Any, List, Optional, cast
+from typing import Any, List, Literal, Optional, cast
 
 import attr
 import numpy as np
@@ -55,6 +55,47 @@ class DawidSkene(BaseClassificationAggregator):
         >>> true_labels = gt[:1000]  # use the first 100 true labels
         >>> ds = DawidSkene(100)
         >>> result = ds.fit_predict(df, true_labels)
+
+    We can also provide the workers' initial error matrices, which come from historical performance data.
+    There two strategies to initialize the workers' error matrices: `assign` and `addition`.
+    Here we create simple error matrices with two workers:
+
+    ```
+                  0  1
+    worker label
+    w851   0      9  1
+           1      1  9
+    w6991  0      9  1
+           1      1  9
+    ```
+
+    Note:
+        1. Make sure the error matrix is indexed by `worker` and `label`
+        with columns for every `label_id` appeared in `data`.
+        You can use the `pandas.MultiIndex` to create such an index, see the example below.
+
+        2. When using `addition` strategy, the error matrix should contain the history **count**(not probability) that `worker` produces `observed_label`,
+        given that the task true label is `true_label`.
+
+    When we use the `addition` strategy, partial error matrices are acceptable,
+    which will be added to the workers' priori error matrices estimated from the given data.
+
+    Examples:
+        >>> import pandas as pd
+        >>> from crowdkit.aggregation import DawidSkene
+        >>> from crowdkit.datasets import load_dataset
+        >>> df, gt = load_dataset('relevance-2')
+        >>> error_matrix_index = pd.MultiIndex.from_arrays([['w851', 'w851', 'w6991', 'w6991'], [0, 1, 0, 1]], names=['worker', 'label'])
+        >>> initial_error = pd.DataFrame(
+        ...     data=[[9, 1], [1, 9], [9, 1], [1, 9]],
+        ...     index=error_matrix_index,
+        ...     columns=[0, 1],
+        ... )
+        >>> ds = DawidSkene(100, initial_error_strategy='addition')
+        >>> result = ds.fit_predict(df, initial_error=initial_error)
+
+    We can also use the `assign` strategy to initialize the workers' error matrices.
+    But in this case, the `initial_error` **must** contain all the workers' error matrices in the data.
     """
 
     n_iter: int = attr.ib(default=100)
@@ -64,6 +105,44 @@ class DawidSkene(BaseClassificationAggregator):
     """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."""
 
+    initial_error_strategy: Optional[Literal["assign", "addition"]] = attr.ib(
+        default=None
+    )
+    """The strategy for initializing the workers' error matrices.
+    The `assign` strategy assigns the initial error matrix to the workers' error matrices;
+    the `addition` strategy adds the initial error matrix with the workers' priori error matrices estimated
+    from the given data. If `None`, the initial error matrix is not used.
+
+    Note:
+        - `addition` strategy
+            - The initial error matrix can be partial, not all workers' error matrices need to be provided.
+            - The initial error matrix values should be the history **count** that
+              `worker` produces `observed_label`, given that the task true label is `true_label`.
+              For example(count values error matrix):
+
+                                  0  1
+                    worker label
+                    w851   0      9  1
+                           1      1  9
+                    w6991  0      9  1
+                           1      1  9
+
+        - `assign` strategy
+            - The initial error matrix must contain all the workers' error matrices in the data.
+            - The initial error matrix values could be the probability or count that
+              `worker` produces `observed_label`, given that the task true label is `true_label`.
+              When given probability error matrix, the values should sum up to 1 for each worker at each `true_label` column.
+              For example(probability values error matrix):
+
+                                  0    1
+                    worker label
+                    w851   0      0.9  0.1
+                           1      0.1  0.9
+                    w6991  0      0.9  0.1
+                           1      0.1  0.9
+                    ...
+    """
+
     probas_: Optional[pd.DataFrame] = attr.ib(init=False)
     """The probability distributions of task labels.
     The `pandas.Series` data is indexed by `task` so that `labels.loc[task]` is the most likely true label of tasks."""
@@ -83,15 +162,22 @@ class DawidSkene(BaseClassificationAggregator):
     """ A list of loss values during training."""
 
     @staticmethod
-    def _m_step(data: pd.DataFrame, probas: pd.DataFrame) -> pd.DataFrame:
+    def _m_step(
+        data: pd.DataFrame,
+        probas: pd.DataFrame,
+        initial_error: Optional[pd.DataFrame] = None,
+        initial_error_strategy: Optional[Literal["assign", "addition"]] = None,
+    ) -> pd.DataFrame:
         """Performs M-step of the Dawid-Skene algorithm.
 
         Estimates the workers' error probability matrix using the specified workers' responses and the true task label probabilities.
         """
         joined = data.join(probas, on="task")
         joined.drop(columns=["task"], inplace=True)
-
         errors = joined.groupby(["worker", "label"], sort=False).sum()
+        # Apply the initial error matrix
+        errors = initial_error_apply(errors, initial_error, initial_error_strategy)
+        # Normalize the error matrix
         errors.clip(lower=_EPS, inplace=True)
         errors /= errors.groupby("worker", sort=False).sum()
 
@@ -160,7 +246,10 @@ class DawidSkene(BaseClassificationAggregator):
         return float(joint_expectation + entropy)
 
     def fit(
-        self, data: pd.DataFrame, true_labels: Optional["pd.Series[Any]"] = None
+        self,
+        data: pd.DataFrame,
+        true_labels: Optional["pd.Series[Any]"] = None,
+        initial_error: Optional[pd.DataFrame] = None,
     ) -> "DawidSkene":
         """Fits the model to the training data with the EM algorithm.
 
@@ -171,7 +260,12 @@ class DawidSkene(BaseClassificationAggregator):
                 The `pandas.Series` data is indexed by `task`  so that `labels.loc[task]` is the task ground truth label.
                 When provided, the model will correct the probability distributions of task labels by the true labels
                 during the iterative process.
-
+            initial_error (DataFrame): The workers' initial error matrices, comes from historical performance data.
+                The `pandas.DataFrame` data is indexed by `worker` and `label` with a column
+                for every `label_id` found in `data` so that `result.loc[worker, observed_label, true_label]` is the
+                history **count** that `worker` produces `observed_label`, given that the task true label is `true_label`.
+                When the `initial_error_strategy` is `assign`, the values in the error matrix can be the probability too.
+                Check the examples in the class docstring for more details.
         Returns:
             DawidSkene: self.
         """
@@ -192,7 +286,7 @@ class DawidSkene(BaseClassificationAggregator):
         if true_labels is not None:
             probas = self._correct_probas_with_golden(probas, true_labels)
         priors = probas.mean()
-        errors = self._m_step(data, probas)
+        errors = self._m_step(data, probas, initial_error, self.initial_error_strategy)
         loss = -np.inf
         self.loss_history_ = []
 
@@ -225,7 +319,10 @@ class DawidSkene(BaseClassificationAggregator):
         return self
 
     def fit_predict_proba(
-        self, data: pd.DataFrame, true_labels: Optional["pd.Series[Any]"] = None
+        self,
+        data: pd.DataFrame,
+        true_labels: Optional["pd.Series[Any]"] = None,
+        initial_error: Optional[pd.DataFrame] = None,
     ) -> pd.DataFrame:
         """Fits the model to the training data and returns probability distributions of labels for each task.
 
@@ -236,6 +333,12 @@ class DawidSkene(BaseClassificationAggregator):
                 The `pandas.Series` data is indexed by `task`  so that `labels.loc[task]` is the task ground truth label.
                 When provided, the model will correct the probability distributions of task labels by the true labels
                 during the iterative process.
+            initial_error (DataFrame): The workers' initial error matrices, comes from historical performance data.
+                The `pandas.DataFrame` data is indexed by `worker` and `label` with a column
+                for every `label_id` found in `data` so that `result.loc[worker, observed_label, true_label]` is the
+                history **count** that `worker` produces `observed_label`, given that the task true label is `true_label`.
+                When the `initial_error_strategy` is `assign`, the values in the error matrix can be the probability too.
+                Check the examples in the class docstring for more details.
 
         Returns:
             DataFrame: Probability distributions of task labels.
@@ -243,12 +346,15 @@ class DawidSkene(BaseClassificationAggregator):
                 Each probability is in the range from 0 to 1, all task probabilities must sum up to 1.
         """
 
-        self.fit(data, true_labels)
+        self.fit(data, true_labels, initial_error)
         assert self.probas_ is not None, "no probas_"
         return self.probas_
 
     def fit_predict(
-        self, data: pd.DataFrame, true_labels: Optional["pd.Series[Any]"] = None
+        self,
+        data: pd.DataFrame,
+        true_labels: Optional["pd.Series[Any]"] = None,
+        initial_error: Optional[pd.DataFrame] = None,
     ) -> "pd.Series[Any]":
         """Fits the model to the training data and returns the aggregated results.
 
@@ -259,12 +365,18 @@ class DawidSkene(BaseClassificationAggregator):
                 The `pandas.Series` data is indexed by `task`  so that `labels.loc[task]` is the task ground truth label.
                 When provided, the model will correct the probability distributions of task labels by the true labels
                 during the iterative process.
+            initial_error (DataFrame): The workers' initial error matrices, comes from historical performance data.
+                The `pandas.DataFrame` data is indexed by `worker` and `label` with a column
+                for every `label_id` found in `data` so that `result.loc[worker, observed_label, true_label]` is the
+                history **count** that `worker` produces `observed_label`, given that the task true label is `true_label`.
+                When the `initial_error_strategy` is `assign`, the values in the error matrix can be the probability too.
+                Check the examples in the class docstring for more details.
 
         Returns:
             Series: Task labels. The `pandas.Series` data is indexed by `task` so that `labels.loc[task]` is the most likely true label of tasks.
         """
 
-        self.fit(data, true_labels)
+        self.fit(data, true_labels, initial_error)
         assert self.labels_ is not None, "no labels_"
         return self.labels_
 
@@ -292,6 +404,46 @@ class DawidSkene(BaseClassificationAggregator):
         return corrected_probas
 
 
+def initial_error_apply(
+    errors: pd.DataFrame,
+    initial_error: Optional[pd.DataFrame],
+    initial_error_strategy: Optional[Literal["assign", "addition"]],
+) -> pd.DataFrame:
+    if initial_error_strategy is None or initial_error is None:
+        return errors
+    # check the index names of initial_error
+    if initial_error.index.names != errors.index.names:
+        raise ValueError(
+            f"The index of initial_error must be: {errors.index.names},"
+            f"but got: {initial_error.index.names}"
+        )
+    if initial_error_strategy == "assign":
+        # check the completeness of initial_error: all the workers in data should be in initial_error
+        mask = errors.index.isin(initial_error.index)
+        if not mask.all():
+            not_found_workers = errors.index[~mask].get_level_values("worker").unique()
+            raise ValueError(
+                f"All the workers in data should be in initial_error: "
+                f"Can not find {len(not_found_workers)} workers' error matrix in initial_error"
+            )
+        # if the values in initial_error are probability, check the sum of each worker's error matrix
+        if (initial_error <= 1.0).all().all() and not np.allclose(
+            initial_error.groupby("worker", sort=False).sum(), 1.0
+        ):
+            raise ValueError(
+                "The sum of each worker's error matrix in initial_error should be 1.0"
+            )
+        errors = initial_error
+    elif initial_error_strategy == "addition":
+        errors = errors.add(initial_error, axis="index", fill_value=0.0)
+    else:
+        raise ValueError(
+            f"Invalid initial_error_strategy: {initial_error_strategy},"
+            f"should be 'assign' or 'addition'"
+        )
+    return errors
+
+
 @attr.s
 class OneCoinDawidSkene(DawidSkene):
     r"""The **one-coin Dawid-Skene** aggregation model works exactly the same as the original Dawid-Skene model


Test patch:
diff --git a/tests/aggregation/test_ds_aggregation.py b/tests/aggregation/test_ds_aggregation.py
index e6fdf5b..8fac92d 100644
--- a/tests/aggregation/test_ds_aggregation.py
+++ b/tests/aggregation/test_ds_aggregation.py
@@ -3,7 +3,7 @@ Simplest aggregation algorithms tests on toy YSDA dataset
 Testing all boundary conditions and asserts
 """
 
-from typing import Any, List, cast
+from typing import Any, List, Literal, Optional, cast
 
 import numpy as np
 import pandas as pd
@@ -13,6 +13,330 @@ from pandas.testing import assert_frame_equal, assert_series_equal
 from crowdkit.aggregation import DawidSkene, OneCoinDawidSkene
 
 
+class TestWorkerInitError:
+
+    @pytest.mark.parametrize(
+        "n_iter, tol, strategy",
+        [
+            (10, 0, "addition"),
+            (10, 0, "assign"),
+            (10, 0, None),
+        ],
+    )
+    def test_without_initial_error_on_toy_ysda(
+        self,
+        n_iter: int,
+        tol: float,
+        strategy: Optional[Literal["assign", "addition"]],
+        toy_answers_df: pd.DataFrame,
+        toy_ground_truth_df: "pd.Series[Any]",
+    ) -> None:
+        """
+        Basic parameter compatibility test: None parameters
+        """
+        np.random.seed(42)
+        ds = DawidSkene(n_iter=n_iter, tol=tol, initial_error_strategy=strategy)
+        assert_series_equal(
+            ds.fit(toy_answers_df, initial_error=None).labels_.sort_index(),  # type: ignore
+            toy_ground_truth_df.sort_index(),
+        )
+
+    @pytest.mark.parametrize(
+        "n_iter, tol, strategy",
+        [
+            (10, 0, "addition"),
+            (10, 0, "assign"),
+            (100500, 1e-5, "addition"),
+            (100500, 1e-5, "assign"),
+        ],
+    )
+    def test_zero_error_addition_on_toy_ysda(
+        self,
+        n_iter: int,
+        tol: float,
+        strategy: Literal["assign", "addition"],
+        toy_answers_df: pd.DataFrame,
+        toy_ground_truth_df: "pd.Series[Any]",
+        toy_worker_init_error_zero_df: pd.DataFrame,
+    ) -> None:
+        """
+        Basic parameter compatibility test: zeros initial error matrix
+        """
+        np.random.seed(42)
+        initial_error_df = toy_worker_init_error_zero_df
+        ds = DawidSkene(n_iter=n_iter, tol=tol, initial_error_strategy=strategy)
+        if strategy == "addition":
+            assert_series_equal(
+                ds.fit(toy_answers_df, initial_error=initial_error_df).labels_.sort_index(),  # type: ignore
+                toy_ground_truth_df.sort_index(),
+            )
+        else:
+            with pytest.raises(
+                ValueError,
+                match="The sum of each worker's error matrix in initial_error should be 1.0",
+            ):
+                ds.fit(toy_answers_df, initial_error=initial_error_df)
+
+    @pytest.mark.parametrize(
+        "n_iter, tol, strategy",
+        [
+            (10, 0, "addition"),
+            (10, 0, "assign"),
+            (100500, 1e-5, "addition"),
+            (100500, 1e-5, "assign"),
+        ],
+    )
+    def test_zero_partial_error_on_toy_ysda(
+        self,
+        n_iter: int,
+        tol: float,
+        strategy: Literal["assign", "addition"],
+        toy_answers_df: pd.DataFrame,
+        toy_ground_truth_df: "pd.Series[Any]",
+        toy_worker_init_error_zero_df: pd.DataFrame,
+    ) -> None:
+        """
+        Basic parameter compatibility test: when initial_error doesn't contain all workers
+        """
+        np.random.seed(42)
+        initial_error_df = toy_worker_init_error_zero_df[:3]
+        ds = DawidSkene(n_iter=n_iter, tol=tol, initial_error_strategy=strategy)
+        if strategy == "addition":
+            assert_series_equal(
+                ds.fit(toy_answers_df, initial_error=initial_error_df).labels_.sort_index(),  # type: ignore
+                toy_ground_truth_df.sort_index(),
+            )
+        else:
+            with pytest.raises(
+                ValueError,
+            ):
+                ds.fit(toy_answers_df, initial_error=initial_error_df)
+
+    @pytest.mark.parametrize(
+        "n_iter, tol, strategy", [(10, 0, "addition"), (100500, 1e-5, "addition")]
+    )
+    def test_addition_consistency_on_toy_ysda(
+        self,
+        n_iter: int,
+        tol: float,
+        strategy: Literal["assign", "addition"],
+        toy_answers_df: pd.DataFrame,
+        toy_ground_truth_df: "pd.Series[Any]",
+        toy_worker_init_error_zero_df: "pd.Series[Any]",
+    ) -> None:
+        """
+        Behavior test: when worker's init error matrix is similar to the error matrix in these tasks,
+        the aggregation result should be the same as before(without init error)
+        """
+        np.random.seed(42)
+        # According to the ground truth data, w2's answer is always right.
+        # so when we set the initial error matrix of w2 to almost right, we should get same results
+        init_error_df = toy_worker_init_error_zero_df
+        init_error_df[("w2", "yes"), "no"] = 1
+        init_error_df[("w2", "yes"), "yes"] = 99
+        init_error_df[("w2", "no"), "yes"] = 1
+        init_error_df[("w2", "no"), "no"] = 99
+
+        ds = DawidSkene(n_iter=n_iter, tol=tol, initial_error_strategy=strategy)
+        assert_series_equal(
+            ds.fit(toy_answers_df, initial_error=init_error_df).labels_.sort_index(),  # type: ignore
+            toy_ground_truth_df.sort_index(),
+        )
+
+    @pytest.mark.parametrize(
+        "n_iter, tol, strategy", [(10, 0, "assign"), (100500, 1e-5, "assign")]
+    )
+    def test_assign_consistency_on_toy_ysda(
+        self,
+        n_iter: int,
+        tol: float,
+        strategy: Literal["assign", "addition"],
+        toy_answers_df: pd.DataFrame,
+        toy_ground_truth_df: "pd.Series[Any]",
+        toy_worker_init_error_zero_df: "pd.Series[Any]",
+    ) -> None:
+        """
+        Behavior test: when worker's init error matrix is similar to the error matrix in these tasks,
+        the aggregation result should be the same as before(without init error)
+        """
+        # step1: get the original estimated error matrix
+        np.random.seed(42)
+        ds = DawidSkene(n_iter=n_iter, tol=tol, initial_error_strategy=None)
+        assert_series_equal(
+            ds.fit(toy_answers_df, initial_error=None).labels_.sort_index(),  # type: ignore
+            toy_ground_truth_df.sort_index(),
+        )
+        original_error_df = ds.errors_
+
+        # step2: use the original_error_df as initial_error to fit the model
+        init_error_df = original_error_df
+        ds = DawidSkene(n_iter=n_iter, tol=tol, initial_error_strategy=strategy)
+        # step3: check the result, which should be the same as the original one
+        assert_series_equal(
+            ds.fit(toy_answers_df, initial_error=init_error_df).labels_.sort_index(),  # type: ignore
+            toy_ground_truth_df.sort_index(),
+        )
+
+    @pytest.mark.parametrize(
+        "n_iter, tol, strategy", [(10, 0, "addition"), (100500, 1e-5, "addition")]
+    )
+    def test_addition_desired_label_on_toy_ysda(
+        self,
+        n_iter: int,
+        tol: float,
+        strategy: Literal["assign", "addition"],
+        toy_answers_df: pd.DataFrame,
+        toy_ground_truth_df: "pd.Series[Any]",
+        toy_worker_init_error_zero_df: "pd.Series[Any]",
+    ) -> None:
+        """
+        Behavior test: dedicate init error matrices should lead to desired results
+        """
+        np.random.seed(42)
+        # worker's annotation on t2: w1: yes, w2: yes, w3: yes, w4: no, w5: no
+        # ground truth: t2: yes
+
+        # When we set workers' init error matrices as fellow, we should get the desired result
+        # In these case, we want the t2's label to be no rather than yes
+        init_error_df = toy_worker_init_error_zero_df
+        item_indexes = [
+            [("w1", "yes"), "no"],
+            [("w2", "yes"), "no"],
+            [("w3", "yes"), "no"],
+            [("w4", "no"), "no"],
+            [("w5", "no"), "no"],
+        ]
+        for loc in item_indexes:
+            init_error_df.loc[loc[0], loc[1]] = 99  # type: ignore
+
+        ds = DawidSkene(n_iter=n_iter, tol=tol, initial_error_strategy=strategy)
+        ds = ds.fit(toy_answers_df, initial_error=init_error_df)  # type: ignore
+        assert ds.labels_["t2"] == "no"  # type: ignore
+
+    @pytest.mark.parametrize(
+        "n_iter, tol, strategy", [(10, 0, "assign"), (100500, 1e-5, "assign")]
+    )
+    def test_assign_desired_label_on_toy_ysda(
+        self,
+        n_iter: int,
+        tol: float,
+        strategy: Literal["assign", "addition"],
+        toy_answers_df: pd.DataFrame,
+        toy_ground_truth_df: "pd.Series[Any]",
+        toy_worker_init_error_zero_df: "pd.Series[Any]",
+    ) -> None:
+        """
+        Behavior test: dedicate init error matrices should lead to desired results
+        """
+        np.random.seed(42)
+        # worker's annotation on t2: w1: yes, w2: yes, w3: yes, w4: no, w5: no
+        # ground truth: t2: yes
+
+        # When we set workers' init error matrices as fellow, we should get the desired result
+        # In this case, we want the t2's label to be no rather than yes
+        # init all probability with 0.5
+        init_error_df = toy_worker_init_error_zero_df
+        init_error_df.loc[:, :] = 0.5
+        # set dedicated probability
+        item_indexes = [
+            [("w1", "yes"), ("w1", "no")],
+            [("w2", "yes"), ("w2", "no")],
+            [("w3", "yes"), ("w3", "no")],
+            [("w4", "no"), ("w4", "yes")],
+            [("w5", "no"), ("w5", "yes")],
+        ]
+        for loc in item_indexes:
+            init_error_df.loc[loc[0], "no"] = 0.99
+            init_error_df.loc[loc[1], "no"] = 0.01
+
+        ds = DawidSkene(n_iter=n_iter, tol=tol, initial_error_strategy=strategy)
+        ds = ds.fit(toy_answers_df, initial_error=init_error_df)  # type: ignore
+        assert ds.labels_["t2"] == "no"  # type: ignore
+
+    def test_addition_inner_state_on_toy_ysda(
+        self,
+        toy_answers_df: pd.DataFrame,
+        toy_ground_truth_df: "pd.Series[Any]",
+        toy_worker_init_error_zero_df: "pd.Series[Any]",
+    ) -> None:
+        """
+        Inner state test.
+
+        Without init error, w2's error matrix(without avg) in iter 0 is as fellows:
+
+                no  yes
+        label
+        yes    0.9  2.1
+        no     1.4  0.6
+
+        After fitting with init error, w2's error matrix(without avg) in iter 0 should be:
+
+                no  yes
+        label
+        yes    2  3
+        no     2  1
+
+        After the avg of error matrix:
+                no  yes
+        label
+        yes    0.5  0.75
+        no     0.5  0.25
+        """
+        np.random.seed(42)
+        init_error_df = toy_worker_init_error_zero_df
+        init_error_df.loc[("w2", "yes"), "no"] = 1.1  # 1.1 + 0.9 = 2
+        init_error_df.loc[("w2", "yes"), "yes"] = 0.9  # 0.9 + 2.1 = 3
+        init_error_df.loc[("w2", "no"), "yes"] = 0.4  # 0.4 + 0.6 = 1
+        init_error_df.loc[("w2", "no"), "no"] = 0.6  # 0.6 + 1.4 = 2
+
+        # fit with init error
+        with_init_errors = DawidSkene(
+            n_iter=0,
+            tol=0.0,
+            initial_error_strategy="addition",
+        ).fit(
+            toy_answers_df, initial_error=init_error_df  # type: ignore
+        )
+
+        # check w2 error matrix
+        item_probs = [
+            ("yes", "no", 0.5),
+            ("yes", "yes", 0.75),
+            ("no", "yes", 0.25),
+            ("no", "no", 0.5),
+        ]
+        for observed, label, prob in item_probs:
+            assert np.isclose(with_init_errors.errors_.loc["w2"].loc[observed, label], prob)  # type: ignore
+
+    def test_assign_inner_state_on_toy_ysda(
+        self,
+        toy_answers_df: pd.DataFrame,
+        toy_ground_truth_df: "pd.Series[Any]",
+        toy_worker_init_error_zero_df: "pd.Series[Any]",
+    ) -> None:
+        """
+        Inner state test.
+        """
+        np.random.seed(42)
+        # generate random init error matrix
+        init_error_df = toy_worker_init_error_zero_df
+        init_error_df.loc[:, :] = np.random.randint(1, 100, size=init_error_df.shape)
+        init_error_df = (
+            init_error_df / init_error_df.groupby("worker", sort=False).sum()
+        )
+        # fit with init error
+        ds = DawidSkene(
+            n_iter=0,
+            tol=0.0,
+            initial_error_strategy="assign",
+        ).fit(
+            toy_answers_df, initial_error=init_error_df  # type: ignore
+        )
+
+        # check w2 error matrix
+        assert_frame_equal(init_error_df, ds.errors_)  # type: ignore
+
+
 @pytest.mark.parametrize("n_iter, tol", [(10, 0), (100500, 1e-5)])
 def test_aggregate_ds_gold_on_toy_ysda(
     n_iter: int,
diff --git a/tests/conftest.py b/tests/conftest.py
index 898c3bf..6fc7bbf 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -67,6 +67,23 @@ def toy_gold_df() -> "pd.Series[Any]":
     )
 
 
+@pytest.fixture
+def toy_worker_init_error_zero_df() -> pd.DataFrame:
+    """
+    The initial error matrix for toy dataset, which is filled with zeros.
+    """
+    worker_labels = [["w1", "w2", "w3", "w4", "w5"], ["yes", "no"]]
+    worker_label_index = pd.MultiIndex.from_product(
+        worker_labels, names=["worker", "label"]
+    )
+    init_error_df = pd.DataFrame(
+        np.zeros((len(worker_label_index), 2)),
+        index=worker_label_index,
+        columns=["no", "yes"],
+    )
+    return init_error_df
+
+
 # Simple dataset that imitates real toloka answers