diff --git a/benchmarks/bench_gap_es_score.py b/benchmarks/bench_gap_es_score.py
new file mode 100644
index 000000000..e6745896c
--- /dev/null
+++ b/benchmarks/bench_gap_es_score.py
@@ -0,0 +1,339 @@
+"""
+Benchmark hyperparameters of GapEncoder on traffic_violations dataset
+"""
+
+from utils import default_parser, find_result, monitor
+from time import perf_counter
+import numpy as np
+import pandas as pd
+from skrub.datasets import fetch_traffic_violations
+from sklearn.model_selection import train_test_split
+from sklearn.ensemble import HistGradientBoostingClassifier
+from sklearn.metrics import roc_auc_score, balanced_accuracy_score
+from skrub import GapEncoder
+from skrub._gap_encoder import (
+    GapEncoderColumn,
+    _beta_divergence,
+    batch_lookup,
+    _multiplicative_update_h,
+    _multiplicative_update_w,
+)
+import seaborn as sns
+import matplotlib.pyplot as plt
+
+
+class ModifiedGapEncoderColumn(GapEncoderColumn):
+    def __init__(self, *args, **kwargs):
+        if "max_no_improvement" in kwargs:
+            self.max_no_improvement = kwargs.pop("max_no_improvement")
+        if "verbose" in kwargs:
+            self.verbose = kwargs.pop("verbose")
+        super().__init__(*args, **kwargs)
+
+    def _minibatch_convergence(self, batch_size, batch_cost, n_samples, step, n_steps):
+        """Helper function to encapsulate the early stopping logic"""
+        # adapted from sklearn.decomposition.MiniBatchNMF
+
+        # counts steps starting from 1 for user friendly verbose mode.
+        step = step + 1
+
+        # Ignore first iteration because H is not updated yet.
+        if step == 1:
+            if self.verbose:
+                print(f"Minibatch step {step}/{n_steps}: mean batch cost: {batch_cost}")
+            return False
+
+        # Compute an Exponentially Weighted Average of the cost function to
+        # monitor the convergence while discarding minibatch-local stochastic
+        # variability: https://en.wikipedia.org/wiki/Moving_average
+        if self._ewa_cost is None:
+            self._ewa_cost = batch_cost
+        else:
+            alpha = batch_size / (n_samples + 1)
+            alpha = min(alpha, 1)
+            self._ewa_cost = self._ewa_cost * (1 - alpha) + batch_cost * alpha
+
+        # Log progress to be able to monitor convergence
+        if self.verbose:
+            print(
+                f"Minibatch step {step}/{n_steps}: mean batch cost: "
+                f"{batch_cost}, ewa cost: {self._ewa_cost}"
+            )
+
+        # Early stopping heuristic due to lack of improvement on smoothed
+        # cost function
+        if self._ewa_cost_min is None or self._ewa_cost < self._ewa_cost_min:
+            self._no_improvement = 0
+            self._ewa_cost_min = self._ewa_cost
+        else:
+            self._no_improvement += 1
+
+        if (
+            self.max_no_improvement is not None
+            and self._no_improvement >= self.max_no_improvement
+        ):
+            if self.verbose:
+                print(
+                    "Converged (lack of improvement in objective function) "
+                    f"at step {step}/{n_steps}"
+                )
+            return True
+
+        return False
+
+    def fit(self, X, y=None) -> "GapEncoderColumn":
+        """
+        Fit the GapEncoder on `X`.
+
+        Parameters
+        ----------
+        X : array-like, shape (n_samples, )
+            The string data to fit the model on.
+        y : None
+            Unused, only here for compatibility.
+
+        Returns
+        -------
+        GapEncoderColumn
+            The fitted GapEncoderColumn instance (self).
+        """
+        # Copy parameter rho
+        self.rho_ = self.rho
+        # Attributes to monitor the convergence
+        self._ewa_cost = None
+        self._ewa_cost_min = None
+        self._no_improvement = 0
+        # Check if first item has str or np.str_ type
+        assert isinstance(X[0], str), "Input data is not string. "
+        # Make n-grams counts matrix unq_V
+        unq_X, unq_V, lookup = self._init_vars(X)
+        n_batch = (len(X) - 1) // self.batch_size + 1
+        n_samples = len(X)
+        del X
+        # Get activations unq_H
+        unq_H = self._get_H(unq_X)
+
+        for n_iter_ in range(self.max_iter):
+            # Loop over batches
+            for i, (unq_idx, idx) in enumerate(batch_lookup(lookup, n=self.batch_size)):
+                # Update activations unq_H
+                unq_H[unq_idx] = _multiplicative_update_h(
+                    unq_V[unq_idx],
+                    self.W_,
+                    unq_H[unq_idx],
+                    epsilon=1e-3,
+                    max_iter=self.max_iter_e_step,
+                    rescale_W=self.rescale_W,
+                    gamma_shape_prior=self.gamma_shape_prior,
+                    gamma_scale_prior=self.gamma_scale_prior,
+                )
+                # Update the topics self.W_
+                _multiplicative_update_w(
+                    unq_V[idx],
+                    self.W_,
+                    self.A_,
+                    self.B_,
+                    unq_H[idx],
+                    self.rescale_W,
+                    self.rho_,
+                )
+                batch_cost = _beta_divergence(
+                    unq_V[idx],
+                    unq_H[idx],
+                    self.W_,
+                    "kullback-leibler",
+                    square_root=False,
+                )
+                if self._minibatch_convergence(
+                    batch_size=len(idx),
+                    batch_cost=batch_cost,
+                    n_samples=n_samples,
+                    step=n_iter_ * n_batch + i,
+                    n_steps=self.max_iter * n_batch,
+                ):
+                    break
+            else:
+                # only continue if no break occurred
+                continue
+            break
+
+        # Update self.H_dict_ with the learned encoded vectors (activations)
+        self.H_dict_.update(zip(unq_X, unq_H))
+        return self
+
+
+class ModifiedGapEncoder(GapEncoder):
+    fitted_models_: list[ModifiedGapEncoderColumn]
+
+    def _create_column_gap_encoder(self):
+        return ModifiedGapEncoderColumn(
+            ngram_range=self.ngram_range,
+            n_components=self.n_components,
+            analyzer=self.analyzer,
+            gamma_shape_prior=self.gamma_shape_prior,
+            gamma_scale_prior=self.gamma_scale_prior,
+            rho=self.rho,
+            rescale_rho=self.rescale_rho,
+            batch_size=self.batch_size,
+            tol=self.tol,
+            hashing=self.hashing,
+            hashing_n_features=self.hashing_n_features,
+            max_iter=self.max_iter,
+            init=self.init,
+            add_words=self.add_words,
+            random_state=self.random_state,
+            rescale_W=self.rescale_W,
+            max_iter_e_step=self.max_iter_e_step,
+            max_no_improvement=10,
+            verbose=True,
+        )
+
+
+###############################################################
+# Benchmarking accuracy and speed on traffic_violations dataset
+###############################################################
+
+benchmark_name = "gap_encoder_benchmark_es_score"
+
+
+@monitor(
+    memory=True,
+    time=True,
+    parametrize={
+        "high_card_feature": [
+            "seqid",
+            "description",
+            "location",
+            "search_reason_for_stop",
+            "state",
+            "charge",
+            "driver_city",
+            "driver_state",
+            "dl_state",
+        ],
+        "max_rows": [5_000, 20_000, 50_000],
+        "modif": [True, False],
+    },
+    save_as=benchmark_name,
+    repeat=2,
+)
+def benchmark(
+    high_card_feature: str,
+    max_rows: int,
+    modif: bool,
+):
+    ds = fetch_traffic_violations()
+    X = np.array(ds.X[high_card_feature]).reshape(-1, 1).astype(str)
+    y = ds.y
+    # only keep the first max_rows rows
+    # split the data into train and test
+    X_train, X_test, y_train, y_test = train_test_split(
+        X[:max_rows],
+        y[:max_rows],
+        test_size=0.2,
+    )
+    if not modif:
+        gap = GapEncoder(batch_size=512)
+    else:
+        gap = ModifiedGapEncoder(verbose=False, batch_size=512)
+    start_time = perf_counter()
+    gap.fit(X_train)
+    end_time = perf_counter()
+    score_train = gap.score(X_train)
+    score_test = gap.score(X_test)
+
+    # evaluate the accuracy using the encoding
+    X_train_encoded = gap.transform(X_train)
+    X_test_encoded = gap.transform(X_test)
+
+    clf = HistGradientBoostingClassifier()
+    clf.fit(X_train_encoded, y_train)
+    roc_auc_hgb_train = roc_auc_score(
+        y_train, clf.predict_proba(X_train_encoded), multi_class="ovr"
+    )
+    roc_auc_hgb_test = roc_auc_score(
+        y_test, clf.predict_proba(X_test_encoded), multi_class="ovr"
+    )
+    balanced_accuracy_hgb_train = balanced_accuracy_score(
+        y_train, clf.predict(X_train_encoded)
+    )
+    balanced_accuracy_hgb_test = balanced_accuracy_score(
+        y_test, clf.predict(X_test_encoded)
+    )
+
+    res_dic = {
+        "time_fit": end_time - start_time,
+        "score_train": score_train,
+        "score_test": score_test,
+        "roc_auc_hgb_train": roc_auc_hgb_train,
+        "roc_auc_hgb_test": roc_auc_hgb_test,
+        "balanced_accuracy_hgb_train": balanced_accuracy_hgb_train,
+        "balanced_accuracy_hgb_test": balanced_accuracy_hgb_test,
+        "train_size": X_train.shape[0],
+        "test_size": X_test.shape[0],
+    }
+
+    return res_dic
+
+
+def plot(df: pd.DataFrame):
+    sns.lineplot(
+        x="train_size", y="time_fit", data=df, hue="high_card_feature", style="modif"
+    )
+    plt.yscale("log")
+    # put the legend out of the figure
+    plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.0)
+    plt.ylabel("Time (s)")
+    plt.xlabel("Train size")
+    plt.title("Time to fit the encoder")
+    # make sure the plot is not cut
+    plt.tight_layout()
+    plt.show()
+
+    sns.lineplot(
+        x="train_size", y="score_train", data=df, hue="high_card_feature", style="modif"
+    )
+    plt.yscale("log")
+    # put the legend out of the figure
+    plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.0)
+    plt.ylabel("Score")
+    plt.xlabel("Train size")
+    plt.title("Score on train set")
+    # make sure the plot is not cut
+    plt.tight_layout()
+    plt.show()
+
+    sns.lineplot(
+        x="train_size",
+        y="balanced_accuracy_hgb_test",
+        data=df,
+        hue="high_card_feature",
+        style="modif",
+    )
+    plt.yscale("log")
+    # put the legend out of the figure
+    plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.0)
+    plt.ylabel("Balanced accuracy")
+    plt.xlabel("Train size")
+    plt.title("Balanced accuracy on test set")
+    # make sure the plot is not cut
+    plt.tight_layout()
+    plt.show()
+
+
+if __name__ == "__main__":
+    from argparse import ArgumentParser
+
+    _args = ArgumentParser(
+        description="Benchmark for the batch feature of the MinHashEncoder.",
+        parents=[default_parser],
+    ).parse_args()
+
+    if _args.run:
+        df = benchmark()
+    else:
+        result_file = find_result(benchmark_name)
+        df = pd.read_parquet(result_file)
+
+    if _args.plot:
+        plot(df)
diff --git a/benchmarks/results/gap_encoder_benchmark_es_score-20230731.parquet b/benchmarks/results/gap_encoder_benchmark_es_score-20230731.parquet
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