Repository: sktime/sktime (python)

Issue:
[BUG] ConformalInterval Memory Usage
**Describe the bug**
Disclaimer: Not sure if really a bug or more a request.

Currently, the ConformalInterval is not very memory efficient, since it constructs internally a dataframe with the size of len(time series) x len(time series) (line 420). However, the matrix represented by this dataframe is sparse for two reasons:
1. It is an upper triangular matrix by definition.
2. Due to the `sample_frac` parameter, multiple rows will stay completely empty. 

Thus, I would propose to use a sparse matrix here instead of a normal dataframe. Thus, the definition of the dataframe would need to be replaced with: 

```python
residuals_matrix = pd.DataFrame.sparse.from_spmatrix(scipy.sparse.csr_array((len(full_y_index), len(full_y_index))), 
                                                             index=full_y_index, columns=full_y_index)
```


Pull request description:
[ENN] Improve memory efficiency of `ConformalIntervals` using sparse matrices
#### Reference Issues/PRs
Fixes #5569 

#### What does this implement/fix? Explain your changes.
This PR is using a sparse matrix representation instead of directly a dataframe in `ConformalIntervals` to save the residuals. 


#### Does your contribution introduce a new dependency? If yes, which one?
No
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#### Did you add any tests for the change?
No
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Patch:
diff --git a/sktime/forecasting/conformal.py b/sktime/forecasting/conformal.py
index 175e75437..b63176813 100644
--- a/sktime/forecasting/conformal.py
+++ b/sktime/forecasting/conformal.py
@@ -11,6 +11,7 @@ from math import floor
 
 import numpy as np
 import pandas as pd
+import scipy
 from joblib import Parallel, delayed
 from sklearn.base import clone
 
@@ -417,8 +418,10 @@ class ConformalIntervals(BaseForecaster):
 
         full_y_index = y.iloc[n_initial_window:].index
 
-        residuals_matrix = pd.DataFrame(
-            columns=full_y_index, index=full_y_index, dtype="float"
+        residuals_matrix = pd.DataFrame.sparse.from_spmatrix(
+            scipy.sparse.csr_array((len(full_y_index), len(full_y_index))),
+            index=full_y_index,
+            columns=full_y_index,
         )
 
         if update and hasattr(self, "residuals_matrix_") and not sample_frac:
@@ -427,9 +430,9 @@ class ConformalIntervals(BaseForecaster):
                 overlapping_index = pd.Index(
                     self.residuals_matrix_.index.intersection(full_y_index)
                 ).sort_values()
-                residuals_matrix.loc[
+                residuals_matrix = self.residuals_matrix_.loc[
                     overlapping_index, overlapping_index
-                ] = self.residuals_matrix_.loc[overlapping_index, overlapping_index]
+                ].combine_first(residuals_matrix)
             else:
                 overlapping_index = None
             y_index = remaining_y_index
@@ -466,8 +469,10 @@ class ConformalIntervals(BaseForecaster):
             delayed(_get_residuals_matrix_row)(forecaster.clone(), y, X, id)
             for id in y_index
         )
-        for idx, id in enumerate(y_index):
-            residuals_matrix.loc[id] = all_residuals[idx]
+        all_residuals = pd.concat(all_residuals, axis=1, ignore_index=True).T
+        all_residuals.index = y_index
+        all_residuals = all_residuals.astype(pd.SparseDtype("float", 0))
+        residuals_matrix = all_residuals.combine_first(residuals_matrix)
 
         if overlapping_index is not None:
 
@@ -494,9 +499,10 @@ class ConformalIntervals(BaseForecaster):
                 delayed(_extend_residuals_matrix_row)(y, X, id)
                 for id in overlapping_index
             )
-
-            for idx, id in enumerate(overlapping_index):
-                residuals_matrix.loc[id] = extend_residuals[idx]
+            extend_residuals = pd.concat(extend_residuals, axis=1, ignore_index=True).T
+            extend_residuals.index = overlapping_index
+            extend_residuals = extend_residuals.astype(pd.SparseDtype("float", 0))
+            residuals_matrix = extend_residuals.combine_first(residuals_matrix)
 
         return residuals_matrix
 
diff --git a/sktime/utils/sklearn/__init__.py b/sktime/utils/sklearn/__init__.py
new file mode 100644
index 000000000..5b1546d33
--- /dev/null
+++ b/sktime/utils/sklearn/__init__.py
@@ -0,0 +1,21 @@
+"""Sklearn related utility functionality."""
+
+from sktime.utils.sklearn._adapt_df import prep_skl_df
+from sktime.utils.sklearn._scitype import (
+    is_sklearn_classifier,
+    is_sklearn_clusterer,
+    is_sklearn_estimator,
+    is_sklearn_regressor,
+    is_sklearn_transformer,
+    sklearn_scitype,
+)
+
+__all__ = [
+    "prep_skl_df",
+    "is_sklearn_estimator",
+    "is_sklearn_transformer",
+    "is_sklearn_classifier",
+    "is_sklearn_regressor",
+    "is_sklearn_clusterer",
+    "sklearn_scitype",
+]
diff --git a/sktime/utils/sklearn/_adapt_df.py b/sktime/utils/sklearn/_adapt_df.py
new file mode 100644
index 000000000..300764c1b
--- /dev/null
+++ b/sktime/utils/sklearn/_adapt_df.py
@@ -0,0 +1,31 @@
+"""Utility functions for adapting to sklearn."""
+# copyright: sktime developers, BSD-3-Clause License (see LICENSE file)
+
+import numpy as np
+
+
+def prep_skl_df(df, copy_df=False):
+    """Make df compatible with sklearn input expectations.
+
+    Changes:
+    turns column index into a list of strings
+
+    Parameters
+    ----------
+    df : pd.DataFrame
+        list of indices to sample from
+    copy_df : bool, default=False
+        whether to mutate df or return a copy
+        if False, index of df is mutated
+        if True, original df is not mutated. If index is not a list of strings,
+        a copy is made and the copy is mutated. Otherwise, the original df is returned.
+    """
+    cols = df.columns
+    str_cols = cols.astype(str)
+
+    if not np.all(str_cols == cols):
+        if copy_df:
+            df = df.copy()
+        df.columns = str_cols
+
+    return df


Test patch:
diff --git a/sktime/utils/_testing/deep_equals.py b/sktime/utils/_testing/deep_equals.py
index 84494ad59..0616cc81a 100644
--- a/sktime/utils/_testing/deep_equals.py
+++ b/sktime/utils/_testing/deep_equals.py
@@ -98,11 +98,67 @@ def deep_equals(x, y, return_msg=False):
         else:
             return ret(x.equals(y), ".series_equals, x = {} != y = {}", [x, y])
     elif isinstance(x, pd.DataFrame):
+        # check column names for equality
         if not x.columns.equals(y.columns):
             return ret(
                 False, f".columns, x.columns = {x.columns} != y.columns = {y.columns}"
             )
-        # if columns are equal and at least one is object, recurse over Series
+        # check dtypes for equality
+        if not x.dtypes.equals(y.dtypes):
+            return ret(
+                False, f".dtypes, x.dtypes = {x.dtypes} != y.dtypes = {y.dtypes}"
+            )
+        # check index for equality
+        # we are not recursing due to ambiguity in integer index types
+        # which may differ from pandas version to pandas version
+        # and would upset the type check, e.g., RangeIndex(2) vs Index([0, 1])
+        xix = x.index
+        yix = y.index
+        if hasattr(xix, "dtype") and hasattr(xix, "dtype"):
+            if not xix.dtype == yix.dtype:
+                return ret(
+                    False,
+                    ".index.dtype, x.index.dtype = {} != y.index.dtype = {}",
+                    [xix.dtype, yix.dtype],
+                )
+        if hasattr(xix, "dtypes") and hasattr(yix, "dtypes"):
+            if not x.dtypes.equals(y.dtypes):
+                return ret(
+                    False,
+                    ".index.dtypes, x.dtypes = {} != y.index.dtypes = {}",
+                    [xix.dtypes, yix.dtypes],
+                )
+        ix_eq = xix.equals(yix)
+        if not ix_eq:
+            if not len(xix) == len(yix):
+                return ret(
+                    False,
+                    ".index.len, x.index.len = {} != y.index.len = {}",
+                    [len(xix), len(yix)],
+                )
+            if hasattr(xix, "name") and hasattr(yix, "name"):
+                if not xix.name == yix.name:
+                    return ret(
+                        False,
+                        ".index.name, x.index.name = {} != y.index.name = {}",
+                        [xix.name, yix.name],
+                    )
+            if hasattr(xix, "names") and hasattr(yix, "names"):
+                if not len(xix.names) == len(yix.names):
+                    return ret(
+                        False,
+                        ".index.names, x.index.names = {} != y.index.name = {}",
+                        [xix.names, yix.names],
+                    )
+                if not np.all(xix.names == yix.names):
+                    return ret(
+                        False,
+                        ".index.names, x.index.names = {} != y.index.name = {}",
+                        [xix.names, yix.names],
+                    )
+            elts_eq = np.all(xix == yix)
+            return ret(elts_eq, ".index.equals, x = {} != y = {}", [xix, yix])
+        # if columns, dtypes are equal and at least one is object, recurse over Series
         if sum(x.dtypes == "object") > 0:
             for c in x.columns:
                 is_equal, msg = deep_equals(x[c], y[c], return_msg=True)
@@ -112,6 +168,14 @@ def deep_equals(x, y, return_msg=False):
         else:
             return ret(x.equals(y), ".df_equals, x = {} != y = {}", [x, y])
     elif isinstance(x, pd.Index):
+        if hasattr(x, "dtype") and hasattr(y, "dtype"):
+            if not x.dtype == y.dtype:
+                return ret(False, f".dtype, x.dtype = {x.dtype} != y.dtype = {y.dtype}")
+        if hasattr(x, "dtypes") and hasattr(y, "dtypes"):
+            if not x.dtypes.equals(y.dtypes):
+                return ret(
+                    False, f".dtypes, x.dtypes = {x.dtypes} != y.dtypes = {y.dtypes}"
+                )
         return ret(x.equals(y), ".index_equals, x = {} != y = {}", [x, y])
     elif isinstance(x, np.ndarray):
         if x.dtype != y.dtype:
diff --git a/sktime/utils/sklearn.py b/sktime/utils/sklearn/_scitype.py
similarity index 100%
rename from sktime/utils/sklearn.py
rename to sktime/utils/sklearn/_scitype.py
diff --git a/sktime/utils/sklearn/tests/__init__.py b/sktime/utils/sklearn/tests/__init__.py
new file mode 100644
index 000000000..1d9b760fe
--- /dev/null
+++ b/sktime/utils/sklearn/tests/__init__.py
@@ -0,0 +1,1 @@
+"""Tests for sklearn related utility functionality."""
diff --git a/sktime/utils/sklearn/tests/test_sklearn_df_adapt.py b/sktime/utils/sklearn/tests/test_sklearn_df_adapt.py
new file mode 100644
index 000000000..57b36ebcd
--- /dev/null
+++ b/sktime/utils/sklearn/tests/test_sklearn_df_adapt.py
@@ -0,0 +1,33 @@
+"""Tests for sklearn dataframe coercion."""
+
+__author__ = ["fkiraly"]
+
+import numpy as np
+import pandas as pd
+import pytest
+
+from sktime.utils.sklearn._adapt_df import prep_skl_df
+
+
+@pytest.mark.parametrize("copy_df", [True, False])
+def test_prep_skl_df_coercion(copy_df):
+    """Test that prep_skl_df behaves correctly on the coercion case."""
+    mixed_example = pd.DataFrame({0: [1, 2, 3], "b": [1, 2, 3]})
+
+    res = prep_skl_df(mixed_example, copy_df=copy_df)
+
+    assert np.all(res.columns == ["0", "b"])
+
+    if not copy_df:
+        assert res is mixed_example
+
+
+@pytest.mark.parametrize("copy_df", [True, False])
+def test_prep_skl_df_non_coercion(copy_df):
+    """Test that prep_skl_df behaves correctly on the non-coercion case."""
+    mixed_example = pd.DataFrame({"a": [1, 2, 3], "b": [1, 2, 3]})
+
+    res = prep_skl_df(mixed_example, copy_df=copy_df)
+
+    assert np.all(res.columns == ["a", "b"])
+    assert res is mixed_example