diff --git a/.readthedocs.yml b/.readthedocs.yml
index acb46ee..91913f3 100644
--- a/.readthedocs.yml
+++ b/.readthedocs.yml
@@ -2,7 +2,7 @@ version: 2
 build:
   os: ubuntu-22.04
   tools:
-    python: "3.12"
+    python: "3.13"
 
 sphinx:
    configuration: doc/conf.py
diff --git a/doc/index.rst b/doc/index.rst
index 75bd283..a65056a 100644
--- a/doc/index.rst
+++ b/doc/index.rst
@@ -19,7 +19,7 @@ API Reference
 
    FastCan
    refine
-   extend
+   minibatch
    ssc
    ols
    make_poly_ids
diff --git a/fastcan/__init__.py b/fastcan/__init__.py
index e89cf40..a1d71c1 100644
--- a/fastcan/__init__.py
+++ b/fastcan/__init__.py
@@ -2,8 +2,8 @@
 The :mod:`fastcan` module implements algorithms, including
 """
 
-from ._extend import extend
 from ._fastcan import FastCan
+from ._minibatch import minibatch
 from ._narx import (
     Narx,
     make_narx,
@@ -21,7 +21,7 @@
     "ssc",
     "ols",
     "refine",
-    "extend",
+    "minibatch",
     "make_narx",
     "print_narx",
     "Narx",
diff --git a/fastcan/_extend.py b/fastcan/_extend.py
deleted file mode 100644
index ec1465f..0000000
--- a/fastcan/_extend.py
+++ /dev/null
@@ -1,120 +0,0 @@
-"""
-Extend feature selection
-"""
-
-import math
-from copy import deepcopy
-from numbers import Integral
-
-import numpy as np
-from sklearn.utils._openmp_helpers import _openmp_effective_n_threads
-from sklearn.utils._param_validation import Interval, validate_params
-from sklearn.utils.validation import check_is_fitted
-
-from ._cancorr_fast import _forward_search  # type: ignore
-from ._fastcan import FastCan, _prepare_search
-
-
-@validate_params(
-    {
-        "selector": [FastCan],
-        "n_features_to_select": [
-            Interval(Integral, 1, None, closed="left"),
-        ],
-        "batch_size": [
-            Interval(Integral, 1, None, closed="left"),
-        ],
-    },
-    prefer_skip_nested_validation=False,
-)
-def extend(selector, n_features_to_select=1, batch_size=1):
-    """Extend FastCan with mini batches.
-
-    It is suitable for selecting a very large number of features
-    even larger than the number of samples.
-
-    Similar to the correlation filter which selects each feature without considering
-    the redundancy, the function selects features in mini-batch and the
-    redundancy between the two mini-batches will be ignored.
-
-    Parameters
-    ----------
-    selector : FastCan
-        FastCan selector.
-
-    n_features_to_select : int, default=1
-        The parameter is the absolute number of features to select.
-
-    batch_size : int, default=1
-        The number of features in a mini-batch.
-
-    Returns
-    -------
-    indices : ndarray of shape (n_features_to_select,), dtype=int
-        The indices of the selected features.
-
-    Examples
-    --------
-    >>> from fastcan import FastCan, extend
-    >>> X = [[1, 1, 0], [0.01, 0, 0], [-1, 0, 1], [0, 0, 0]]
-    >>> y = [1, 0, -1, 0]
-    >>> selector = FastCan(1, verbose=0).fit(X, y)
-    >>> print(f"Indices: {selector.indices_}")
-    Indices: [0]
-    >>> indices = extend(selector, 3, batch_size=2)
-    >>> print(f"Indices: {indices}")
-    Indices: [0 2 1]
-    """
-    check_is_fitted(selector)
-    n_inclusions = selector.indices_include_.size
-    n_features = selector.n_features_in_
-    n_to_select = n_features_to_select - selector.n_features_to_select
-    batch_size_to_select = batch_size - n_inclusions
-
-    if n_features_to_select > n_features:
-        raise ValueError(
-            f"n_features_to_select {n_features_to_select} "
-            f"must be <= n_features {n_features}."
-        )
-    if n_to_select <= 0:
-        raise ValueError(
-            f"The number of features to select ({n_to_select}) ", "is less than 0."
-        )
-    if batch_size_to_select <= 0:
-        raise ValueError(
-            "The size of mini batch without included indices ",
-            f"({batch_size_to_select}) is less than 0.",
-        )
-
-    X_transformed_ = deepcopy(selector.X_transformed_)
-
-    indices_include = selector.indices_include_
-    indices_exclude = selector.indices_exclude_
-    indices_select = selector.indices_[n_inclusions:]
-
-    n_threads = _openmp_effective_n_threads()
-
-    for i in range(math.ceil(n_to_select / batch_size_to_select)):
-        if i == 0:
-            batch_size_i = (n_to_select - 1) % batch_size_to_select + 1 + n_inclusions
-        else:
-            batch_size_i = batch_size
-        indices, scores, mask = _prepare_search(
-            n_features,
-            batch_size_i,
-            indices_include,
-            np.r_[indices_exclude, indices_select],
-        )
-        _forward_search(
-            X=X_transformed_,
-            V=selector.y_transformed_,
-            t=batch_size_i,
-            tol=selector.tol,
-            num_threads=n_threads,
-            verbose=0,
-            mask=mask,
-            indices=indices,
-            scores=scores,
-        )
-        indices_select = np.r_[indices_select, indices[n_inclusions:]]
-    return np.r_[indices_include, indices_select]
diff --git a/fastcan/_fastcan.py b/fastcan/_fastcan.py
index 5211ec0..ff5d760 100644
--- a/fastcan/_fastcan.py
+++ b/fastcan/_fastcan.py
@@ -287,7 +287,6 @@ def _get_support_mask(self):
 
 
 def _prepare_search(n_features, n_features_to_select, indices_include, indices_exclude):
-    """ """
     # initiated with -1
     indices = np.full(n_features_to_select, -1, dtype=np.intc, order="F")
     indices[: indices_include.size] = indices_include
diff --git a/fastcan/_minibatch.py b/fastcan/_minibatch.py
new file mode 100644
index 0000000..148dfab
--- /dev/null
+++ b/fastcan/_minibatch.py
@@ -0,0 +1,134 @@
+"""
+Feature selection with mini-batch
+"""
+
+from copy import deepcopy
+from numbers import Integral
+
+import numpy as np
+from sklearn.utils._openmp_helpers import _openmp_effective_n_threads
+from sklearn.utils._param_validation import Interval, validate_params
+from sklearn.utils.validation import check_X_y
+
+from ._cancorr_fast import _forward_search  # type: ignore
+from ._fastcan import FastCan, _prepare_search
+
+
+@validate_params(
+    {
+        "X": ["array-like"],
+        "y": ["array-like"],
+        "n_features_to_select": [
+            Interval(Integral, 1, None, closed="left"),
+        ],
+        "batch_size": [
+            Interval(Integral, 1, None, closed="left"),
+        ],
+        "verbose": ["verbose"],
+    },
+    prefer_skip_nested_validation=False,
+)
+def minibatch(X, y, n_features_to_select=1, batch_size=1, verbose=1):
+    """FastCan selection with mini batches.
+
+    It is suitable for selecting a very large number of features
+    even larger than the number of samples.
+
+    Similar to the correlation filter which selects each feature without considering
+    the redundancy, the function selects features in mini-batch and the
+    redundancy between the two mini-batches will be ignored.
+
+    Parameters
+    ----------
+    X : array-like of shape (n_samples, n_features)
+        Feature matrix.
+
+    y : array-like of shape (n_samples, n_outputs)
+        Target matrix.
+
+    n_features_to_select : int, default=1
+        The parameter is the absolute number of features to select.
+
+    batch_size : int, default=1
+        The number of features in a mini-batch.
+        It is recommended that batch_size be less than n_samples.
+
+    verbose : int, default=1
+        The verbosity level.
+
+    Returns
+    -------
+    indices : ndarray of shape (n_features_to_select,), dtype=int
+        The indices of the selected features.
+
+    Examples
+    --------
+    >>> from fastcan import minibatch
+    >>> X = [[1, 1, 0], [0.01, 0, 0], [-1, 0, 1], [0, 0, 0]]
+    >>> y = [1, 0, -1, 0]
+    >>> indices = minibatch(X, y, 3, batch_size=2, verbose=0)
+    >>> print(f"Indices: {indices}")
+    Indices: [0 1 2]
+    """
+    X, y = check_X_y(X, y, ensure_2d=True, multi_output=True)
+    if y.ndim == 1:
+        y = y.reshape(-1, 1)
+
+    n_features = X.shape[1]
+    n_outputs = y.shape[1]
+
+    if n_features_to_select > n_features:
+        raise ValueError(
+            f"n_features_to_select {n_features_to_select} "
+            f"must be <= n_features {n_features}."
+        )
+
+    n_threads = _openmp_effective_n_threads()
+
+    n_to_select_split = np.diff(
+        np.linspace(
+            0, n_features_to_select, num=n_outputs + 1, endpoint=True, dtype=int
+        )
+    )
+    indices_select = np.zeros(0, dtype=int)
+    for i in range(n_outputs):
+        y_i = y[:, i]
+        batch_split_i = np.diff(
+            np.r_[
+                np.arange(n_to_select_split[i], step=batch_size, dtype=int),
+                n_to_select_split[i],
+            ]
+        )
+        for j, batch_size_j in enumerate(batch_split_i):
+            if j == 0:
+                selector_j = FastCan(
+                    batch_size_j, indices_exclude=indices_select, verbose=0
+                ).fit(X, y_i)
+                X_transformed_ = deepcopy(selector_j.X_transformed_)
+                indices = selector_j.indices_
+            else:
+                indices, scores, mask = _prepare_search(
+                    n_features,
+                    batch_size_j,
+                    selector_j.indices_include_,
+                    np.r_[selector_j.indices_exclude_, indices_select],
+                )
+                _forward_search(
+                    X=X_transformed_,
+                    V=selector_j.y_transformed_,
+                    t=batch_size_j,
+                    tol=selector_j.tol,
+                    num_threads=n_threads,
+                    verbose=0,
+                    mask=mask,
+                    indices=indices,
+                    scores=scores,
+                )
+            indices_select = np.r_[indices_select, indices]
+            if verbose == 1:
+                print(
+                    f"Progress: {indices_select.size}/{n_features_to_select}", end="\r"
+                )
+    if verbose == 1:
+        print()
+    return indices_select
diff --git a/fastcan/_narx.py b/fastcan/_narx.py
index 4f9d29a..49562a4 100644
--- a/fastcan/_narx.py
+++ b/fastcan/_narx.py
@@ -4,14 +4,14 @@
 
 import math
 from itertools import combinations_with_replacement
-from numbers import Integral, Real
+from numbers import Integral
 
 import numpy as np
 from scipy.optimize import least_squares
 from scipy.stats import rankdata
 from sklearn.base import BaseEstimator, RegressorMixin
 from sklearn.linear_model import LinearRegression
-from sklearn.utils import check_array, check_X_y
+from sklearn.utils import check_array, check_consistent_length, column_or_1d
 from sklearn.utils._param_validation import Interval, StrOptions, validate_params
 from sklearn.utils.validation import check_is_fitted
 
@@ -52,7 +52,7 @@ def make_time_shift_features(X, ids):
            [5., 3., 4.],
            [7., 5., 6.]])
     """
-    X = check_array(X, ensure_2d=True, dtype=float)
+    X = check_array(X, ensure_2d=True, dtype=float, force_all_finite="allow-nan")
     ids = check_array(ids, ensure_2d=True, dtype=int)
     n_samples = X.shape[0]
     n_outputs = ids.shape[0]
@@ -177,7 +177,7 @@ def make_poly_features(X, ids):
            [ 1.,  5., 25.,  6.],
            [ 1.,  7., 49.,  8.]])
     """
-    X = check_array(X, ensure_2d=True, dtype=float)
+    X = check_array(X, ensure_2d=True, dtype=float, force_all_finite="allow-nan")
     ids = check_array(ids, ensure_2d=True, dtype=int)
     n_samples = X.shape[0]
     n_outputs, degree = ids.shape
@@ -263,6 +263,12 @@ def make_poly_ids(
     return np.delete(ids, const_id, 0)  # remove the constant featrue
 
 
+def _mask_missing_value(*arr):
+    """Remove missing value for all arrays."""
+    mask_nomissing = np.all(np.isfinite(np.c_[arr]), axis=1)
+    return tuple([x[mask_nomissing] for x in arr])
+
+
 class Narx(BaseEstimator, RegressorMixin):
     """Nonlinear Autoregressive eXogenous model.
     For example, a (polynomial) Narx model is like
@@ -392,6 +398,9 @@ def fit(self, X, y, coef_init=None, **params):
             When `coef_init` is an array, the model will be a Multi-Step-Ahead
             Narx whose coefficients and intercept are initialized by the array.
 
+            .. note::
+                When coef_init is None, missing values (i.e., np.nan) are allowed.
+
         **params : dict
             Keyword arguments passed to
             `scipy.optimize.least_squares`.
@@ -401,7 +410,9 @@ def fit(self, X, y, coef_init=None, **params):
         self : object
             Fitted Estimator.
         """
-        X, y = self._validate_data(X, y, y_numeric=True, multi_output=False)
+        X = self._validate_data(X, dtype=float, force_all_finite="allow-nan")
+        y = column_or_1d(y, dtype=float, warn=True)
+        check_consistent_length(X, y)
 
         if self.time_shift_ids is None:
             self.time_shift_ids_ = make_time_shift_ids(
@@ -453,10 +464,12 @@ def fit(self, X, y, coef_init=None, **params):
             # fit a one-step-ahead Narx model
             xy_hstack = np.c_[X, y]
             osa_narx = LinearRegression()
-            time_shift_terms = make_time_shift_features(xy_hstack, self.time_shift_ids_)
-            poly_terms = make_poly_features(time_shift_terms, self.poly_ids_)
+            time_shift_vars = make_time_shift_features(xy_hstack, self.time_shift_ids_)
+            poly_terms = make_poly_features(time_shift_vars, self.poly_ids_)
+            # Remove missing values
+            poly_terms_masked, y_masked = _mask_missing_value(poly_terms, y)
 
-            osa_narx.fit(poly_terms, y)
+            osa_narx.fit(poly_terms_masked, y_masked)
             if coef_init is None:
                 self.coef_ = osa_narx.coef_
                 self.intercept_ = osa_narx.intercept_
@@ -516,9 +529,21 @@ def _expression(self, X, y_hat, coef, intercept, k):
     def _predict(expression, X, y_init, coef, intercept, max_delay):
         n_samples = X.shape[0]
         y_hat = np.zeros(n_samples)
-        y_hat[:max_delay] = y_init
-        for k in range(max_delay, n_samples):
-            y_hat[k] = expression(X, y_hat, coef, intercept, k)
+        at_init = True
+        init_k = 0
+        for k in range(n_samples):
+            if ~np.all(np.isfinite(X[k])):
+                at_init = True
+                init_k = k + 1
+                y_hat[k] = np.nan
+                continue
+            if k - init_k == max_delay:
+                at_init = False
+
+            if at_init:
+                y_hat[k] = y_init[k - init_k]
+            else:
+                y_hat[k] = expression(X, y_hat, coef, intercept, k)
             if np.any(y_hat[k] > 1e20):
                 y_hat[k:] = np.inf
                 return y_hat
@@ -535,9 +560,11 @@ def _residual(
         coef = coef_intercept[:-1]
         intercept = coef_intercept[-1]
 
-        return (
-            y - Narx._predict(expression, X, y[:max_delay], coef, intercept, max_delay)
-        ).flatten()
+        y_hat = Narx._predict(expression, X, y[:max_delay], coef, intercept, max_delay)
+
+        y_masked, y_hat_masked = _mask_missing_value(y, y_hat)
+
+        return (y_masked - y_hat_masked).flatten()
 
     @validate_params(
         {
@@ -564,11 +591,11 @@ def predict(self, X, y_init=None):
         """
         check_is_fitted(self)
 
-        X = self._validate_data(X, reset=False)
+        X = self._validate_data(X, reset=False, force_all_finite="allow-nan")
         if y_init is None:
             y_init = np.zeros(self.max_delay_)
         else:
-            y_init = check_array(y_init, ensure_2d=False, dtype=np.float64)
+            y_init = column_or_1d(y_init, dtype=float)
             if y_init.shape[0] != self.max_delay_:
                 raise ValueError(
                     "`y_init` should have the shape of "
@@ -586,6 +613,9 @@ def predict(self, X, y_init=None):
             self.max_delay_,
         )
 
+    def _more_tags(self):
+        return {"allow_nan": True}
+
 
 @validate_params(
     {
@@ -644,6 +674,7 @@ def print_narx(
     | X[k-0,9] | 68  |
     """
     check_is_fitted(narx)
+
     def _get_variable_str(time_shift_id):
         if time_shift_id[0] < narx.n_features_in_:
             variable_str = f"X[k-{time_shift_id[1]},{time_shift_id[0]}]"
@@ -720,10 +751,10 @@ def make_narx(
     Parameters
     ----------
     X : array-like of shape (n_samples, n_features)
-            Feature matrix.
+        Feature matrix.
 
     y : array-like of shape (n_samples,)
-        Target matrix.
+        Target vector.
 
     n_features_to_select : int
         The parameter is the absolute number of features to select.
@@ -799,14 +830,15 @@ def make_narx(
     | X[k-1,0]*X[k-3,0]  |  1.999   |
     | X[k-2,0]*X[k-0,1]  |  1.527   |
     """
-    X, y = check_X_y(X, y, dtype=Real, multi_output=False)
+    X = check_array(X, dtype=float, ensure_2d=True, force_all_finite="allow-nan")
+    y = column_or_1d(y, dtype=float)
+    check_consistent_length(X, y)
 
     xy_hstack = np.c_[X, y]
     n_features = X.shape[1]
-    n_outputs = xy_hstack.shape[1] - n_features
 
     if include_zero_delay is None:
-        include_zero_delay = [True] * n_features + [False] * n_outputs
+        include_zero_delay = [True] * n_features + [False]
 
     time_shift_ids_all = make_time_shift_ids(
         n_features=xy_hstack.shape[1],
@@ -822,19 +854,22 @@ def make_narx(
         ),
         0,
     )
-    time_shift_terms = make_time_shift_features(xy_hstack, time_shift_ids_all)
+    time_shift_vars = make_time_shift_features(xy_hstack, time_shift_ids_all)
 
     poly_ids_all = make_poly_ids(
         time_shift_ids_all.shape[0],
         poly_degree,
     )
-    poly_terms = make_poly_features(time_shift_terms, poly_ids_all)
+    poly_terms = make_poly_features(time_shift_vars, poly_ids_all)
+
+    # Remove missing values
+    poly_terms_masked, y_masked = _mask_missing_value(poly_terms, y)
 
     csf = FastCan(
         n_features_to_select,
         eta=eta,
         verbose=0,
-    ).fit(poly_terms, y)
+    ).fit(poly_terms_masked, y_masked)
     if drop is not None:
         indices, _ = refine(csf, drop=drop, max_iter=max_iter, verbose=verbose)
         support = np.zeros(shape=csf.n_features_in_, dtype=bool)
diff --git a/pixi.lock b/pixi.lock
index 8531b61..dbad1be 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -57,7 +57,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/pycodestyle-2.12.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/pyproject-metadata-0.9.0-pyh2cfa8aa_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/pyproject_hooks-1.2.0-pyh7850678_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/pytest-8.3.3-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/pytest-8.3.4-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/pytest-cov-6.0.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/python-3.12.7-hc5c86c4_0_cpython.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/python-build-1.2.2.post1-pyhff2d567_0.conda
@@ -66,21 +66,21 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/python_abi-3.12-5_cp312.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/pytz-2024.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/readline-8.2-h8228510_1.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/ruff-0.8.0-py312h2156523_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/ruff-0.8.1-py312h2156523_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/scikit-learn-1.5.2-py312h7a48858_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/scipy-1.14.1-py312h62794b6_1.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/setuptools-75.6.0-pyhff2d567_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/setuptools-75.6.0-pyhff2d567_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/six-1.16.0-pyh6c4a22f_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/threadpoolctl-3.5.0-pyhc1e730c_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/tk-8.6.13-noxft_h4845f30_101.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/tokenize-rt-6.1.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/toml-0.10.2-pyhd8ed1ab_0.tar.bz2
-      - conda: https://conda.anaconda.org/conda-forge/noarch/tomli-2.1.0-pyhff2d567_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/tomli-2.2.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/typing_extensions-4.12.2-pyha770c72_0.conda
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/uv-0.5.4-h0f3a69f_0.conda
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-  md5: 51a01bd7e637556f33e14695983fcd02
+  url: https://conda.anaconda.org/conda-forge/osx-arm64/ruff-0.8.1-py313heab95af_0.conda
+  sha256: 0f4b82f2cb83af93c2b4a7964749b82799e51a126db4fd81a72574f8b661c6cb
+  md5: 2ac10bad59722af27f61b12c26106e01
   depends:
   - __osx >=11.0
   - libcxx >=18
@@ -5088,8 +5092,8 @@ packages:
   license_family: MIT
   purls:
   - pkg:pypi/ruff?source=hash-mapping
-  size: 6960999
-  timestamp: 1732286297576
+  size: 6949768
+  timestamp: 1732870522684
 - kind: conda
   name: scikit-learn
   version: 1.5.2
@@ -5308,20 +5312,21 @@ packages:
 - kind: conda
   name: setuptools
   version: 75.6.0
-  build: pyhff2d567_0
+  build: pyhff2d567_1
+  build_number: 1
   subdir: noarch
   noarch: python
-  url: https://conda.anaconda.org/conda-forge/noarch/setuptools-75.6.0-pyhff2d567_0.conda
-  sha256: eeec4645f70ce0ed03348397dced9d218a650a42df98592419af61d2689163ed
-  md5: 68d7d406366926b09a6a023e3d0f71d7
+  url: https://conda.anaconda.org/conda-forge/noarch/setuptools-75.6.0-pyhff2d567_1.conda
+  sha256: abb12e1dd515b13660aacb5d0fd43835bc2186cab472df25b7716cd65e095111
+  md5: fc80f7995e396cbaeabd23cf46c413dc
   depends:
   - python >=3.9
   license: MIT
   license_family: MIT
   purls:
   - pkg:pypi/setuptools?source=hash-mapping
-  size: 774304
-  timestamp: 1732216189406
+  size: 774252
+  timestamp: 1732632769210
 - kind: conda
   name: sigtool
   version: 0.1.3
@@ -5602,21 +5607,21 @@ packages:
 - kind: conda
   name: tbb
   version: 2021.13.0
-  build: hc790b64_0
+  build: h62715c5_1
+  build_number: 1
   subdir: win-64
-  url: https://conda.anaconda.org/conda-forge/win-64/tbb-2021.13.0-hc790b64_0.conda
-  sha256: 990dbe4fb42f14700c22bd434d8312607bf8d0bd9f922b054e51fda14c41994c
-  md5: 28496a1e6af43c63927da4f80260348d
+  url: https://conda.anaconda.org/conda-forge/win-64/tbb-2021.13.0-h62715c5_1.conda
+  sha256: 03cc5442046485b03dd1120d0f49d35a7e522930a2ab82f275e938e17b07b302
+  md5: 9190dd0a23d925f7602f9628b3aed511
   depends:
-  - libhwloc >=2.11.1,<2.11.2.0a0
+  - libhwloc >=2.11.2,<2.11.3.0a0
   - ucrt >=10.0.20348.0
   - vc >=14.2,<15
   - vc14_runtime >=14.29.30139
   license: Apache-2.0
-  license_family: APACHE
   purls: []
-  size: 151494
-  timestamp: 1725532984828
+  size: 151460
+  timestamp: 1732982860332
 - kind: conda
   name: threadpoolctl
   version: 3.5.0
@@ -5737,21 +5742,20 @@ packages:
   timestamp: 1604308660817
 - kind: conda
   name: tomli
-  version: 2.1.0
-  build: pyhff2d567_0
+  version: 2.2.1
+  build: pyhd8ed1ab_0
   subdir: noarch
   noarch: python
-  url: https://conda.anaconda.org/conda-forge/noarch/tomli-2.1.0-pyhff2d567_0.conda
-  sha256: 354b8a64d4f3311179d85aefc529ca201a36afc1af090d0010c46be7b79f9a47
-  md5: 3fa1089b4722df3a900135925f4519d9
+  url: https://conda.anaconda.org/conda-forge/noarch/tomli-2.2.1-pyhd8ed1ab_0.conda
+  sha256: 706f35327a1b433fb57bb99e9fef878e90317fd6ea8cbcd454fb4af1a2e3f035
+  md5: ee8ab0fe4c8dfc5a6319f7f8246022fc
   depends:
   - python >=3.9
   license: MIT
-  license_family: MIT
   purls:
   - pkg:pypi/tomli?source=hash-mapping
-  size: 18741
-  timestamp: 1731426862834
+  size: 19129
+  timestamp: 1732988289555
 - kind: conda
   name: typing_extensions
   version: 4.12.2
@@ -5811,12 +5815,12 @@ packages:
   requires_python: '>=3.8'
 - kind: conda
   name: uv
-  version: 0.5.4
+  version: 0.5.5
   build: h0f3a69f_0
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/uv-0.5.4-h0f3a69f_0.conda
-  sha256: 826c427524d1930d66bdbbe9f2a380d46abc02e06b4b9870e4c5eb661a292156
-  md5: ecce7c2d83da66eaabf8ba4961a4c828
+  url: https://conda.anaconda.org/conda-forge/linux-64/uv-0.5.5-h0f3a69f_0.conda
+  sha256: d5e7c70e8fd6c328e9a61b6f003f32eb67f9fb4548e266310a1cca8afd9afc4a
+  md5: 8991c763ef7e46ea36acd42c8af4ebef
   depends:
   - __glibc >=2.17,<3.0.a0
   - libgcc >=13
@@ -5825,16 +5829,16 @@ packages:
   - __glibc >=2.17
   license: Apache-2.0 OR MIT
   purls: []
-  size: 10061197
-  timestamp: 1732159190433
+  size: 10298311
+  timestamp: 1732748322896
 - kind: conda
   name: uv
-  version: 0.5.4
+  version: 0.5.5
   build: h668ec48_0
   subdir: osx-arm64
-  url: https://conda.anaconda.org/conda-forge/osx-arm64/uv-0.5.4-h668ec48_0.conda
-  sha256: 85b61a53c0f39339c67a4f11b708fa1f59ad5f0a85d907f3c5ff001c88914b31
-  md5: baad04fb088c4c66acf74a870bdb4536
+  url: https://conda.anaconda.org/conda-forge/osx-arm64/uv-0.5.5-h668ec48_0.conda
+  sha256: 2e5e109a631845b307a054d6f04c7dc834eb5a0c0477fbecfec9f5850a6e36e1
+  md5: 022b347422968f5d454b397193fe28ee
   depends:
   - __osx >=11.0
   - libcxx >=18
@@ -5842,16 +5846,16 @@ packages:
   - __osx >=11.0
   license: Apache-2.0 OR MIT
   purls: []
-  size: 8942315
-  timestamp: 1732160450871
+  size: 8997490
+  timestamp: 1732748956120
 - kind: conda
   name: uv
-  version: 0.5.4
+  version: 0.5.5
   build: h8de1528_0
   subdir: osx-64
-  url: https://conda.anaconda.org/conda-forge/osx-64/uv-0.5.4-h8de1528_0.conda
-  sha256: 7ee578a9944f39c7d249c18fcde7f8a6d3131c3788c9dc6b8b3c36c0784b3340
-  md5: 0cf1dbd494c85fd0730a27b9c335b2ea
+  url: https://conda.anaconda.org/conda-forge/osx-64/uv-0.5.5-h8de1528_0.conda
+  sha256: 1fd02edd93c39676024211b32a04880e9579bd5534e694ae6bc6cef6453dc865
+  md5: 863a10750b4ee2d02ae8dafdafdc4fdb
   depends:
   - __osx >=10.13
   - libcxx >=18
@@ -5859,24 +5863,24 @@ packages:
   - __osx >=10.13
   license: Apache-2.0 OR MIT
   purls: []
-  size: 9694051
-  timestamp: 1732159860536
+  size: 9798812
+  timestamp: 1732748791519
 - kind: conda
   name: uv
-  version: 0.5.4
+  version: 0.5.5
   build: ha08ef0e_0
   subdir: win-64
-  url: https://conda.anaconda.org/conda-forge/win-64/uv-0.5.4-ha08ef0e_0.conda
-  sha256: 493bece8c71254c2f9002fe5f53dd71265ce38d9dee2842286120e86acc2e523
-  md5: 9fc38b02b5c4fa1be9a42c1b951d98e1
+  url: https://conda.anaconda.org/conda-forge/win-64/uv-0.5.5-ha08ef0e_0.conda
+  sha256: 4daaf55e417b790b1bb5cf4cded0ed241dbd0b513933601b2be6fc8d55d13f53
+  md5: 7efee2c95bdad3ec4df7b9d66471106e
   depends:
   - ucrt >=10.0.20348.0
   - vc >=14.2,<15
   - vc14_runtime >=14.29.30139
   license: Apache-2.0 OR MIT
   purls: []
-  size: 10797785
-  timestamp: 1732160258909
+  size: 11162866
+  timestamp: 1732749609026
 - kind: conda
   name: vc
   version: '14.3'
@@ -5985,20 +5989,21 @@ packages:
 - kind: conda
   name: zipp
   version: 3.21.0
-  build: pyhd8ed1ab_0
+  build: pyhd8ed1ab_1
+  build_number: 1
   subdir: noarch
   noarch: python
-  url: https://conda.anaconda.org/conda-forge/noarch/zipp-3.21.0-pyhd8ed1ab_0.conda
-  sha256: 232a30e4b0045c9de5e168dda0328dc0e28df9439cdecdfb97dd79c1c82c4cec
-  md5: fee389bf8a4843bd7a2248ce11b7f188
+  url: https://conda.anaconda.org/conda-forge/noarch/zipp-3.21.0-pyhd8ed1ab_1.conda
+  sha256: 567c04f124525c97a096b65769834b7acb047db24b15a56888a322bf3966c3e1
+  md5: 0c3cc595284c5e8f0f9900a9b228a332
   depends:
-  - python >=3.8
+  - python >=3.9
   license: MIT
   license_family: MIT
   purls:
   - pkg:pypi/zipp?source=hash-mapping
-  size: 21702
-  timestamp: 1731262194278
+  size: 21809
+  timestamp: 1732827613585
 - kind: conda
   name: zlib
   version: 1.3.1
diff --git a/tests/test_extend.py b/tests/test_extend.py
deleted file mode 100644
index b37e990..0000000
--- a/tests/test_extend.py
+++ /dev/null
@@ -1,84 +0,0 @@
-"""Test feature selection extend"""
-import numpy as np
-import pytest
-from numpy.testing import assert_array_equal
-from sklearn.datasets import make_classification
-
-from fastcan import FastCan, extend
-
-
-def test_select_extend_cls():
-    # Test whether refine work correctly with random samples.
-    n_samples = 200
-    n_features = 30
-    n_informative = 20
-    n_classes = 8
-    n_repeated = 5
-    n_to_select = 18
-
-    X, y = make_classification(
-        n_samples=n_samples,
-        n_features=n_features,
-        n_informative=n_informative,
-        n_repeated=n_repeated,
-        n_classes=n_classes,
-        n_clusters_per_class=1,
-        flip_y=0.0,
-        class_sep=10,
-        shuffle=False,
-        random_state=0,
-    )
-
-    n_features_to_select = 2
-    selector = FastCan(n_features_to_select).fit(X, y)
-    indices = extend(selector, n_to_select, batch_size=3)
-    selector_inc = FastCan(n_features_to_select, indices_include=[10]).fit(X, y)
-    indices_inc = extend(selector_inc, n_to_select, batch_size=3)
-    selector_exc = FastCan(
-        n_features_to_select, indices_include=[10], indices_exclude=[0]
-    ).fit(X, y)
-    indices_exc = extend(selector_exc, n_to_select, batch_size=3)
-
-
-    assert np.unique(indices).size == n_to_select
-    assert_array_equal(indices[:n_features_to_select], selector.indices_)
-    assert np.unique(indices_inc).size == n_to_select
-    assert_array_equal(indices_inc[:n_features_to_select], selector_inc.indices_)
-    assert np.unique(indices_exc).size == n_to_select
-    assert_array_equal(indices_exc[:n_features_to_select], selector_exc.indices_)
-    assert ~np.isin(0, indices_exc)
-
-
-def test_extend_error():
-    # Test refine raise error.
-    n_samples = 200
-    n_features = 20
-    n_informative = 10
-    n_classes = 8
-    n_repeated = 5
-
-    X, y = make_classification(
-        n_samples=n_samples,
-        n_features=n_features,
-        n_informative=n_informative,
-        n_repeated=n_repeated,
-        n_classes=n_classes,
-        n_clusters_per_class=1,
-        flip_y=0.0,
-        class_sep=10,
-        shuffle=False,
-        random_state=0,
-    )
-
-    n_features_to_select = 2
-
-    selector = FastCan(n_features_to_select, indices_include=[0]).fit(X, y)
-
-    with pytest.raises(ValueError, match=r"n_features_to_select .*"):
-        _ = extend(selector, n_features+1, batch_size=3)
-
-    with pytest.raises(ValueError, match=r"The number of features to select .*"):
-        _ = extend(selector, n_features_to_select, batch_size=3)
-
-    with pytest.raises(ValueError, match=r"The size of mini batch without .*"):
-        _ = extend(selector, n_features, batch_size=1)
diff --git a/tests/test_minibatch.py b/tests/test_minibatch.py
new file mode 100644
index 0000000..9018a09
--- /dev/null
+++ b/tests/test_minibatch.py
@@ -0,0 +1,64 @@
+"""Test feature selection with mini-batch"""
+import numpy as np
+import pytest
+from sklearn.datasets import make_classification
+from sklearn.preprocessing import OneHotEncoder
+
+from fastcan import minibatch
+
+
+def test_select_minibatch_cls():
+    # Test whether refine work correctly with random samples.
+    n_samples = 200
+    n_features = 30
+    n_informative = 20
+    n_classes = 8
+    n_repeated = 5
+    n_to_select = 18
+
+    X, y = make_classification(
+        n_samples=n_samples,
+        n_features=n_features,
+        n_informative=n_informative,
+        n_repeated=n_repeated,
+        n_classes=n_classes,
+        n_clusters_per_class=1,
+        flip_y=0.0,
+        class_sep=10,
+        shuffle=False,
+        random_state=0,
+    )
+
+    indices = minibatch(X, y, n_to_select, batch_size=3)
+    assert np.unique(indices).size == n_to_select
+    assert indices.size == n_to_select
+
+    Y = OneHotEncoder(sparse_output=False).fit_transform(y.reshape(-1, 1))
+
+    indices = minibatch(X, Y, n_to_select, batch_size=2)
+    assert np.unique(indices).size == n_to_select
+    assert indices.size == n_to_select
+
+def test_minibatch_error():
+    # Test refine raise error.
+    n_samples = 200
+    n_features = 20
+    n_informative = 10
+    n_classes = 8
+    n_repeated = 5
+
+    X, y = make_classification(
+        n_samples=n_samples,
+        n_features=n_features,
+        n_informative=n_informative,
+        n_repeated=n_repeated,
+        n_classes=n_classes,
+        n_clusters_per_class=1,
+        flip_y=0.0,
+        class_sep=10,
+        shuffle=False,
+        random_state=0,
+    )
+
+    with pytest.raises(ValueError, match=r"n_features_to_select .*"):
+        _ = minibatch(X, y, n_features+1, batch_size=3)
diff --git a/tests/test_narx.py b/tests/test_narx.py
index bb4544a..ef5f9ed 100644
--- a/tests/test_narx.py
+++ b/tests/test_narx.py
@@ -19,7 +19,8 @@ def test_time_ids():
     with pytest.raises(ValueError, match=r"The length of `include_zero_delay`.*"):
         make_time_shift_ids(3, 2, [False, True, False, True])
 
-def test_narx():
+@pytest.mark.parametrize("nan", [False, True])
+def test_narx(nan):
     rng = np.random.default_rng(12345)
     n_samples = 1000
     max_delay = 3
@@ -32,8 +33,14 @@ def test_narx():
     y = y[max_delay:]+e
     X = np.c_[u0[max_delay:], u1]
 
+    if nan:
+        X_nan_ids = rng.choice(n_samples, 20, replace=False)
+        y_nan_ids = rng.choice(n_samples, 10, replace=False)
+        X[X_nan_ids] = np.nan
+        y[y_nan_ids] = np.nan
+
     params = {
-        "n_features_to_select": rng.integers(low=1, high=4),
+        "n_features_to_select": rng.integers(low=2, high=4),
         "max_delay": rng.integers(low=0, high=10),
         "poly_degree": rng.integers(low=2, high=5),
     }
@@ -46,14 +53,19 @@ def test_narx():
     params["include_zero_delay"] = [False, True, False]
     narx_0_delay = make_narx(X=X, y=y, **params)
     time_shift_ids = narx_0_delay.time_shift_ids
-    assert ~np.isin(0, time_shift_ids[time_shift_ids[:, 0] == 0][:, 1])
-    assert np.isin(0, time_shift_ids[time_shift_ids[:, 0] == 1][:, 1])
-    assert ~np.isin(0, time_shift_ids[time_shift_ids[:, 0] == 2][:, 1])
+    time_ids_u0 = time_shift_ids[time_shift_ids[:, 0] == 0]
+    time_ids_u1 = time_shift_ids[time_shift_ids[:, 0] == 1]
+    time_ids_y = time_shift_ids[time_shift_ids[:, 0] == 2]
+    assert ~np.isin(0, time_ids_u0[:, 1]) or (time_ids_u0.size == 0)
+    assert np.isin(0, time_ids_u1[:, 1]) or (time_ids_u1.size == 0)
+    assert ~np.isin(0, time_ids_y[:, 1]) or (time_ids_y.size == 0)
 
     params["static_indices"] = [1]
     narx_static = make_narx(X=X, y=y, **params)
     time_shift_ids = narx_static.time_shift_ids
-    assert time_shift_ids[time_shift_ids[:, 0] == 1][0, 1] == 0
+    time_ids_u1 = time_shift_ids[time_shift_ids[:, 0] == 1]
+    if time_ids_u1.size != 0:
+        assert time_ids_u1[0, 1] == 0
 
     params["drop"] = 1
     params["max_iter"] = 10
@@ -112,3 +124,5 @@ def test_narx():
     poly_ids = make_poly_ids(time_shift_ids.shape[0]+1, 2)
     with pytest.raises(ValueError, match=r"The element x of poly_ids should .*"):
         narx_osa = Narx(time_shift_ids=time_shift_ids, poly_ids=poly_ids).fit(X, y)
+
+test_narx(True)