diff --git a/.github/workflows/publish.yml b/.github/workflows/publish.yml
index 39ba5324..500492e5 100644
--- a/.github/workflows/publish.yml
+++ b/.github/workflows/publish.yml
@@ -4,29 +4,22 @@ on:
   release:
     types: [published]
 
+permissions:
+  id-token: write
+
 jobs:
   deploy:
     runs-on: ubuntu-latest
+    environment: pypi
 
     steps:
     - uses: actions/checkout@v4
-    - name: Set up Python
-      uses: actions/setup-python@v4
-      with:
-        python-version: '3.10'
-    - name: Install Poetry
-      run: |
-        curl -sSL https://install.python-poetry.org | python3 -
-        echo "$HOME/.local/bin" >> $GITHUB_PATH
-    - name: Install dependencies
-      run: |
-        poetry install
+
+    - name: Install uv
+      uses: astral-sh/setup-uv@v3
+
     - name: Build package
-      run: |
-        poetry build
-    - name: Publish package
-      env:
-        PYPI_TOKEN: ${{ secrets.PYPI_API_TOKEN }}
-      run: |
-        poetry config pypi-token.pypi $PYPI_TOKEN
-        poetry publish
+      run: uv build
+
+    - name: Publish to PyPI
+      uses: pypa/gh-action-pypi-publish@release/v1
diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 5695ee05..d9328814 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -16,61 +16,39 @@ jobs:
     runs-on: ${{ matrix.os }}
     strategy:
       matrix:
-        os: [ubuntu-latest, windows-latest]
-        python-version: ["3.9", "3.11", "3.12"]
+        # Full matrix only for PRs to main
+        os: ${{ github.event_name == 'pull_request' && github.base_ref == 'main' && fromJSON('["ubuntu-latest", "windows-latest"]') || fromJSON('["ubuntu-latest"]') }}
+        python-version: ${{ github.event_name == 'pull_request' && github.base_ref == 'main' && fromJSON('["3.9", "3.11", "3.12"]') || fromJSON('["3.12"]') }}
     defaults:
       run:
         shell: bash -l {0}
 
     steps:
-      - name: Set OS and Python version
-        id: set-vars
-        run: |
-          if [[ "${GITHUB_REF}" == "refs/heads/main" || "${GITHUB_REF}" == "refs/heads/dev" ]]; then
-            echo "os-matrix=ubuntu-latest,windows-latest" >> $GITHUB_ENV
-            echo "python-matrix=3.9,3.11,3.12" >> $GITHUB_ENV
-          else
-            echo "os-matrix=ubuntu-latest" >> $GITHUB_ENV
-            echo "python-matrix=3.12" >> $GITHUB_ENV
-          fi
-      - name: Checkout
-        uses: actions/checkout@v3
-      - name: Python
-        uses: actions/setup-python@v4
-        with:
-          python-version: ${{ matrix.python-version }}
-      - name: Cache Poetry
-        uses: actions/cache@v3
-        with:
-          path: |
-            ~/.cache/pypoetry
-            ~/.cache/pip
-          key: ${{ runner.os }}-poetry-${{ matrix.python-version }}-${{ hashFiles('**/poetry.lock') }}
-          restore-keys: |
-            ${{ runner.os }}-poetry-${{ matrix.python-version }}-
-      - name: Poetry
-        uses: snok/install-poetry@v1
-        with:
-          version: 1.8.3
-      - name: Lock
-        run: poetry lock --no-update
-      - name: Install
-        run: poetry install
-      - name: Checkers
-        run: make checkers
-      - name: Codecov
-        uses: codecov/codecov-action@v3
-        env:
-          CODECOV_TOKEN: ${{ secrets.CODECOV_TOKEN }}
-      - name: Check Changed Files
-        id: changed-files
-        uses: tj-actions/changed-files@v40
+      - uses: actions/checkout@v4
+
+      - name: Install uv
+        uses: astral-sh/setup-uv@v3
         with:
-          files: |
-            docs/**
-            **.rst
+          enable-cache: true
+          cache-dependency-glob: "uv.lock"
+
+      - name: Set up Python ${{ matrix.python-version }}
+        run: uv python install ${{ matrix.python-version }}
+
+      - name: Install dependencies
+        run: make install
+
+      - name: Check with ruff
+        run: make check-quality
+
+      - name: Test with pytest
+        run: make check-tests
+
+      - name: Check types
+        run: make check-types
 
-      - name: Build Docs
-        if: matrix.python-version == '3.12' && matrix.os == 'ubuntu-latest' && steps.changed-files.outputs.any_changed == 'true'
+      - name: Build and test docs
+        if: matrix.python-version == '3.12' && matrix.os == 'ubuntu-latest'
         run: |
-          poetry run sphinx-build -b html docs/ _build/html
+          make doc
+          make doctest
diff --git a/.gitignore b/.gitignore
index 2512eb9e..e385a1ee 100644
--- a/.gitignore
+++ b/.gitignore
@@ -28,7 +28,6 @@ var/
 *.egg-info/
 .installed.cfg
 *.egg
-poetry.lock
 
 # PyInstaller
 #  Usually these files are written by a python script from a template
diff --git a/.python-version b/.python-version
index 3b2cfc0e..e69de29b 100644
--- a/.python-version
+++ b/.python-version
@@ -1 +0,0 @@
-3.12.10
diff --git a/CONTRIBUTING.rst b/CONTRIBUTING.rst
index f2d292a2..cd8f538d 100644
--- a/CONTRIBUTING.rst
+++ b/CONTRIBUTING.rst
@@ -25,15 +25,12 @@ Local setup
 
 We encourage you to use a virtual environment. You'll want to activate it every time you want to work on `Qolmat`.
 
-You can create a virtual environment via `conda`:
+You can create a virtual environment and install dependencies with `uv`:
 
 .. code:: sh
 
-    $ pip install poetry
-    $ poetry config virtualenvs.in-project true
-    $ poetry lock
-    $ poetry install
-    $ poetry shell
+    $ uv sync
+    $ uv run pytest
 
 Once the environment is installed, pre-commit is installed, but need to be activated using the following command:
 
diff --git a/HISTORY.rst b/HISTORY.rst
index 793f623b..efd75238 100644
--- a/HISTORY.rst
+++ b/HISTORY.rst
@@ -5,6 +5,8 @@ History
 0.1.11 (2025-12-30)
 ------------------
 * PLKM test implemented and documented in the holes_characterization module
+* Dependency management improved with uv
+* Migrated from hyperopt to skopt for hyperparameter optimization
 
 0.1.10 (2025-08-30)
 ------------------
diff --git a/Makefile b/Makefile
index e0ca5828..2ee02ba8 100644
--- a/Makefile
+++ b/Makefile
@@ -1,34 +1,45 @@
+# Install dependencies
+install:
+	uv sync --all-extras
 
+# Code quality checks
 check-coverage:
-	poetry run pytest --cov-branch --cov=qolmat/ --cov-report=xml tests/
-
-check-poetry:
-	poetry check --lock
+	uv run pytest --cov-branch --cov=qolmat/ --cov-report=xml tests/
 
 check-quality:
-	poetry run ruff check qolmat/ tests/
+	uv run ruff check qolmat/ tests/
 
 check-security:
-	poetry run bandit --recursive --configfile=pyproject.toml qolmat/
+	uv run bandit --recursive --configfile=pyproject.toml qolmat/
 
 check-tests:
-	poetry run pytest tests/
+	uv run pytest tests/
 
 check-types:
-	poetry run mypy qolmat/ tests/
+	uv run mypy qolmat/ tests/
 
 checkers: check-coverage check-types
 
+# Formatting
+format:
+	uv run ruff format qolmat/ tests/
+	uv run ruff check --fix qolmat/ tests/
+
+# Cleaning
 clean:
-	rm -rf .mypy_cache .pytest_cache .coverage*
+	rm -rf .mypy_cache .pytest_cache .coverage* .ruff_cache
 	rm -rf **__pycache__
-	make clean -C docs
-
-coverage:
-	poetry run pytest --cov-branch --cov=qolmat --cov-report=xml tests
+	uv run make clean -C docs
 
+# Documentation
 doc:
-	make html -C docs
+	uv run make html -C docs
 
 doctest:
-	poetry run pytest --doctest-modules --pyargs qolmat
+	uv run pytest --doctest-modules --pyargs qolmat
+
+# Development helpers
+lock:
+	uv lock
+
+.PHONY: install check-coverage check-quality check-security check-tests check-types checkers format clean doc doctest lock
diff --git a/docs/conf.py b/docs/conf.py
index b36b797e..3fe9a734 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -53,8 +53,6 @@
 # see https://github.com/numpy/numpydoc/issues/69
 numpydoc_show_class_members = False
 
-from distutils.version import LooseVersion
-
 # pngmath / imgmath compatibility layer for different sphinx versions
 # import sphinx
 
diff --git a/docs/sg_execution_times.rst b/docs/sg_execution_times.rst
index 0c2ff3f8..693c62e7 100644
--- a/docs/sg_execution_times.rst
+++ b/docs/sg_execution_times.rst
@@ -6,7 +6,7 @@
 
 Computation times
 =================
-**00:00.000** total execution time for 6 files **from all galleries**:
+**01:04.897** total execution time for 6 files **from all galleries**:
 
 .. container::
 
@@ -33,20 +33,20 @@ Computation times
      - Time
      - Mem (MB)
    * - :ref:`sphx_glr_examples_tutorials_plot_tuto_benchmark_TS.py` (``../examples/tutorials/plot_tuto_benchmark_TS.py``)
-     - 00:00.000
+     - 00:21.381
      - 0.0
    * - :ref:`sphx_glr_examples_tutorials_plot_tuto_categorical.py` (``../examples/tutorials/plot_tuto_categorical.py``)
-     - 00:00.000
+     - 00:16.026
      - 0.0
    * - :ref:`sphx_glr_examples_tutorials_plot_tuto_diffusion_models.py` (``../examples/tutorials/plot_tuto_diffusion_models.py``)
-     - 00:00.000
-     - 0.0
-   * - :ref:`sphx_glr_examples_tutorials_plot_tuto_hole_generator.py` (``../examples/tutorials/plot_tuto_hole_generator.py``)
-     - 00:00.000
+     - 00:11.896
      - 0.0
    * - :ref:`sphx_glr_examples_tutorials_plot_tuto_mcar.py` (``../examples/tutorials/plot_tuto_mcar.py``)
-     - 00:00.000
+     - 00:08.072
      - 0.0
    * - :ref:`sphx_glr_examples_tutorials_plot_tuto_mean_median.py` (``../examples/tutorials/plot_tuto_mean_median.py``)
-     - 00:00.000
+     - 00:04.939
+     - 0.0
+   * - :ref:`sphx_glr_examples_tutorials_plot_tuto_hole_generator.py` (``../examples/tutorials/plot_tuto_hole_generator.py``)
+     - 00:02.583
      - 0.0
diff --git a/examples/benchmark.md b/examples/benchmark.md
index 551a3aaf..df19394e 100644
--- a/examples/benchmark.md
+++ b/examples/benchmark.md
@@ -22,9 +22,7 @@ First, import some useful libraries
 ```python tags=[]
 import warnings
 # warnings.filterwarnings('error')
-```
 
-```python tags=[]
 %reload_ext autoreload
 %autoreload 2
 
@@ -33,7 +31,7 @@ from IPython.display import Image
 import pandas as pd
 from datetime import datetime
 import numpy as np
-import hyperopt as ho
+from skopt.space import Real, Integer, Categorical
 np.random.seed(1234)
 from matplotlib import pyplot as plt
 import matplotlib.ticker as plticker
@@ -41,13 +39,13 @@ import matplotlib.ticker as plticker
 tab10 = plt.get_cmap("tab10")
 plt.rcParams.update({'font.size': 18})
 
-
 from sklearn.linear_model import LinearRegression
 
 from qolmat.benchmark import comparator, missing_patterns
 from qolmat.imputations import imputers
 from qolmat.utils import data, utils, plot
 
+
 ```
 
 ### **I. Load data**
@@ -124,15 +122,15 @@ imputer_residuals = imputers.ImputerResiduals(groups=("station",), period=365, m
 imputer_rpca = imputers.ImputerRpcaNoisy(groups=("station",), columnwise=False, max_iterations=500, tau=.01, lam=5, rank=1)
 imputer_rpca_opti = imputers.ImputerRpcaNoisy(groups=("station",), columnwise=False, max_iterations=256)
 dict_config_opti["RPCA_opti"] = {
-    "tau": ho.hp.uniform("tau", low=.5, high=5),
-    "lam": ho.hp.uniform("lam", low=.1, high=1),
+    "tau": Real(0.5, 5.0, name="tau"),
+    "lam": Real(0.1, 1.0, name="lam"),
 }
 imputer_rpca_opticw = imputers.ImputerRpcaNoisy(groups=("station",), columnwise=False, max_iterations=256)
 dict_config_opti["RPCA_opticw"] = {
-    "tau/TEMP": ho.hp.uniform("tau/TEMP", low=.5, high=5),
-    "tau/PRES": ho.hp.uniform("tau/PRES", low=.5, high=5),
-    "lam/TEMP": ho.hp.uniform("lam/TEMP", low=.1, high=1),
-    "lam/PRES": ho.hp.uniform("lam/PRES", low=.1, high=1),
+    "tau/TEMP": Real(0.5, 5.0, name="tau/TEMP"),
+    "tau/PRES": Real(0.5, 5.0, name="tau/PRES"),
+    "lam/TEMP": Real(0.1, 1.0, name="lam/TEMP"),
+    "lam/PRES": Real(0.1, 1.0, name="lam/PRES"),
 }
 
 imputer_normal_sample = imputers.ImputerEM(groups=("station",), model="multinormal", method="sample", max_iter_em=8, n_iter_ou=128, dt=4e-2)
diff --git a/pyproject.toml b/pyproject.toml
index d27876c0..93e48bba 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,106 +1,94 @@
-# PACKAGE
-
-[tool.poetry]
+[project]
 name = "qolmat"
 version = "0.1.10"
 description = "A Python library for optimal data imputation."
 authors = [
-    "Julien ROUSSEL <julien.roussel@capgemini.com>",
-    "Anh Khoa NGO HO <anh-khoa.ngo-ho@capgemini.com>",
-    "Hong-Lan BOTTERMAN <hong-lan.botterman@capgemini.com>",
-    "Guillaume SAËS <guillaume.saes@capgemini.com>",
+    { name = "Julien ROUSSEL", email = "julien.roussel@capgemini.com" },
+    { name = "Anh Khoa NGO HO", email = "anh-khoa.ngo-ho@capgemini.com" },
+    { name = "Hong-Lan BOTTERMAN", email = "hong-lan.botterman@capgemini.com" },
+    { name = "Guillaume SAËS", email = "guillaume.saes@capgemini.com" },
 ]
-license = "BSD-3-Clause"
+license = { text = "BSD-3-Clause" }
 readme = "README.rst"
-homepage = "https://github.com/Quantmetry/qolmat"
-repository = "https://github.com/Quantmetry/qolmat"
-documentation = "https://qolmat.readthedocs.io/en/latest/"
+requires-python = ">=3.9,<3.13"
 keywords = ["imputation"]
 classifiers = [
     "Intended Audience :: Science/Research",
     "Intended Audience :: Developers",
-    "License :: OSI Approved",
+    "License :: OSI Approved :: BSD License",
     "Topic :: Software Development",
     "Topic :: Scientific/Engineering",
-    "Operating System :: Microsoft :: Windows",
-    "Operating System :: POSIX",
-    "Operating System :: Unix",
-    "Operating System :: MacOS",
-    "Programming Language :: Python :: 3.8",
+    "Operating System :: OS Independent",
     "Programming Language :: Python :: 3.9",
     "Programming Language :: Python :: 3.10",
+    "Programming Language :: Python :: 3.11",
+    "Programming Language :: Python :: 3.12",
 ]
 
-# DEPENDENCIES
-
-[tool.poetry.dependencies]
-python = ">=3.9,<3.13"
-hyperopt = "*"
-numpy = ">= 1.24"
-pandas = ">= 2.0.1"
-scipy = "*"
-scikit-learn = ">= 1.6"
-sphinx-markdown-tables = { version = "*", optional = true }
-statsmodels = ">= 0.14.0"
-typed-ast = { version = "*", optional = true }
-category-encoders = "^2.6.3"
-dcor = ">= 0.6"
-tqdm = "*"
-
-[tool.poetry.group.torch.dependencies]
-torch = "< 2.5"
-
-[tool.poetry.group.dev.dependencies]
-bump2version = "1.0.1"
-ipykernel = "^6.29.5"
-jupyter = "1.0.0"
-jupyterlab = "1.2.6"
-jupytext = "1.14.4"
-matplotlib = "*"
-packaging = "23.1"
-pre-commit = "2.21.0"
-twine = "3.7.1"
-wheel = "0.37.1"
-
-[tool.poetry.group.checkers.dependencies]
-bandit = "^1.7.9"
-mypy = "1.1.1"
-ruff = "^0.6.3"
-pytest = "7.2.0"
-pytest-cov = "4.0.0"
-pytest-mock = "3.10.0"
-
-[tool.poetry.group.ci.dependencies]
-codecov = "^2.1.13"
-
-[tool.poetry.group.docs.dependencies]
-numpydoc = "1.1.0"
-sphinx = ">= 5.0"
-sphinx-gallery = ">= 0.15"
-sphinx_rtd_theme = "1.0.0"
-sphinx_markdown_tables = "0.0.17"
-
-[tool.poetry.extras]
-tests = ["typed-ast"]
-docs = ["sphinx-markdown-tables"]
-
-[tool.poetry.urls]
-"Bug Tracker" = "https://github.com/Quantmetry/qolmat"
-"Source Code" = "https://github.com/Quantmetry/qolmat"
-
-[[tool.poetry.source]]
-name = "pytorch_cpu"
-url = "https://download.pytorch.org/whl/cpu"
-priority = "explicit"
+dependencies = [
+    "scikit-optimize>=0.9",
+    "numpy>=1.24",
+    "pandas>=2.0.1",
+    "scipy",
+    "scikit-learn>=1.6",
+    "statsmodels>=0.14.0",
+    "category-encoders>=2.6.3,<3",
+    "dcor>=0.6",
+    "numba>=0.59",
+    "tqdm",
+]
+
+[project.optional-dependencies]
+torch = ["torch<2.5"]
+docs = [
+    "sphinx-markdown-tables",
+    "numpydoc==1.1.0",
+    "sphinx>=5.0",
+    "sphinx-gallery>=0.15",
+    "sphinx-rtd-theme==1.0.0",
+]
+dev = [
+    "bump2version==1.0.1",
+    "ipykernel>=6.29.5",
+    "jupyter==1.0.0",
+    "jupyterlab==1.2.6",
+    "jupytext==1.14.4",
+    "matplotlib",
+    "packaging==23.1",
+    "pre-commit==2.21.0",
+    "twine==3.7.1",
+    "wheel==0.37.1",
+]
+checkers = [
+    "bandit>=1.7.9",
+    "mypy==1.1.1",
+    "ruff>=0.6.3",
+    "pytest==7.2.0",
+    "pytest-cov==4.0.0",
+    "pytest-mock==3.10.0",
+]
+ci = ["codecov>=2.1.13"]
+
+[project.urls]
+Homepage = "https://github.com/Quantmetry/qolmat"
+Documentation = "https://qolmat.readthedocs.io/en/latest/"
+Repository = "https://github.com/Quantmetry/qolmat"
+"Bug Tracker" = "https://github.com/Quantmetry/qolmat/issues"
 
 [build-system]
-requires = ["poetry-core"]
-build-backend = "poetry.core.masonry.api"
+requires = ["hatchling"]
+build-backend = "hatchling.build"
 
+# PyTorch CPU source
+[[tool.uv.index]]
+name = "pytorch_cpu"
+url = "https://download.pytorch.org/whl/cpu"
+explicit = true
 
 # CONFIGURATION
 [tool.bandit]
 targets = ["qolmat"]
+skips = ["B310"]
 
 [tool.mypy]
 pretty = true
@@ -149,9 +137,9 @@ ignore = [
     "D107",
     "D203",
     "D213",
-    "N803",  # allow X as a name for data
-    "N806",  # allow X as a name for data
-    "N816",  # allow mixed case names such as np_X_t as a name for data
+    "N803",
+    "N806",
+    "N816",
 ]
 
 [tool.ruff.lint.isort]
diff --git a/qolmat/analysis/holes_characterization.py b/qolmat/analysis/holes_characterization.py
index 7ebba26f..580f4b29 100644
--- a/qolmat/analysis/holes_characterization.py
+++ b/qolmat/analysis/holes_characterization.py
@@ -92,7 +92,7 @@ def __init__(
         super().__init__(random_state=random_state)
         if imputer and imputer.model != "multinormal":
             raise AttributeError(
-                "The ImputerEM model must be 'multinormal' " "to use the Little's test"
+                "The ImputerEM model must be 'multinormal' to use the Little's test"
             )
         self.imputer = imputer
 
diff --git a/qolmat/benchmark/comparator.py b/qolmat/benchmark/comparator.py
index e066b4d6..6046f603 100644
--- a/qolmat/benchmark/comparator.py
+++ b/qolmat/benchmark/comparator.py
@@ -115,7 +115,7 @@ def process_split(self, split_data: Tuple[int, pd.DataFrame, pd.DataFrame]) -> p
         subset = self.generator_holes.subset
         if subset is None:
             raise ValueError(
-                "HoleGenerator `subset` should be overwritten in split " "but it is none!"
+                "HoleGenerator `subset` should be overwritten in split but it is none!"
             )
 
         split_results = {}
@@ -159,7 +159,7 @@ def process_imputer(
         subset = self.generator_holes.subset
         if subset is None:
             raise ValueError(
-                "HoleGenerator `subset` should be overwritten in split " "but it is none!"
+                "HoleGenerator `subset` should be overwritten in split but it is none!"
             )
 
         dict_config_opti_imputer = self.dict_config_opti.get(imputer_name, {})
diff --git a/qolmat/benchmark/hyperparameters.py b/qolmat/benchmark/hyperparameters.py
index 99a77af8..4f65ddc8 100644
--- a/qolmat/benchmark/hyperparameters.py
+++ b/qolmat/benchmark/hyperparameters.py
@@ -3,16 +3,14 @@
 import copy
 from typing import Callable, Dict, List
 
-# import skopt
-# from skopt.space import Categorical, Dimension, Integer, Real
-import hyperopt as ho
 import numpy as np
 import pandas as pd
+from skopt import gp_minimize
+from skopt.space import Dimension
 
 from qolmat.benchmark import metrics
 from qolmat.benchmark.missing_patterns import _HoleGenerator
 from qolmat.imputations.imputers import _Imputer
-from qolmat.utils.utils import HyperValue
 
 
 def get_objective(
@@ -30,45 +28,43 @@ def get_objective(
     Parameters
     ----------
     imputer: _Imputer
-        Imputer that should be optimized, it should at least have a
-        fit_transform method and an imputer_params attribute
+        Imputer to optimize
     df : pd.DataFrame
-        input dataframe
+        Input dataframe
     generator: _HoleGenerator
-        Generator creating the masked values in the nested cross validation
-        allowing to measure the imputer performance
+        Generator creating masked values for cross-validation
     metric: str
-        Metric used as performance indicator, common values are `mse` and `mae`
+        Metric used as performance indicator (e.g., 'mse', 'mae')
     names_hyperparams: List[str]
-        List of the names of the hyperparameters which are being optimized
+        Names of hyperparameters being optimized
 
     Returns
     -------
-    Callable[List[HyperValue], float]
-        Objective function
+    Callable
+        Objective function returning mean error across folds
 
     """
 
-    def fun_obf(args: List[HyperValue]) -> float:
+    def fun_obj(args: List) -> float:
+        # Set hyperparameters on imputer
         for key, value in zip(names_hyperparams, args):
             setattr(imputer, key, value)
 
         list_errors = []
-
         for df_mask in generator.split(df):
             df_origin = df.copy()
             df_corrupted = df_origin.copy()
             df_corrupted[df_mask] = np.nan
             df_imputed = imputer.fit_transform(df_corrupted)
+
             subset = generator.subset
             fun_metric = metrics.get_metric(metric)
             errors = fun_metric(df_origin[subset], df_imputed[subset], df_mask[subset])
             list_errors.append(errors)
 
-        mean_errors = np.mean(errors)
-        return mean_errors
+        return float(np.mean(list_errors))
 
-    return fun_obf
+    return fun_obj
 
 
 def optimize(
@@ -76,59 +72,68 @@ def optimize(
     df: pd.DataFrame,
     generator: _HoleGenerator,
     metric: str,
-    dict_config: Dict[str, HyperValue],
+    dict_config: Dict[str, Dimension],
     max_evals: int = 100,
     verbose: bool = False,
-):
-    """Optimisation function.
-
-    Return the provided imputer with hyperparameters optimized in the provided
-    range in order to minimize the provided metric.
+    random_state: int = 42,
+) -> _Imputer:
+    """Optimize imputer hyperparameters using Bayesian optimization.
 
     Parameters
     ----------
     imputer: _Imputer
-        Imputer that should be optimized, it should at least have a
-        fit_transform method and an imputer_params attribute
+        Imputer to optimize
     df : pd.DataFrame
-        input dataframe
+        Input dataframe
     generator: _HoleGenerator
-        Generator creating the masked values in the nested cross validation
-        allowing to measure the imputer performance
+        Generator for cross-validation
     metric: str
-        Metric used as performance indicator, common values are `mse` and `mae`
-    dict_config: Dict[str, HyperValue]
-        Search space for the tested hyperparameters
-    max_evals: int
-        Maximum number of evaluation of the performance of the algorithm.
-        Each estimation involves one call to fit_transform per fold returned
-        by the generator. See the n_fold attribute.
-    verbose: bool
-        Verbosity switch, useful for imputers that can have unstable
-        behavior for some hyperparameters values
+        Metric to minimize (e.g., 'mse', 'mae')
+    dict_config: Dict[str, Dimension]
+        Search space: keys are hyperparameter names, values are skopt Dimension objects
+        (Real, Integer, or Categorical)
+    max_evals: int, default=100
+        Maximum number of evaluations
+    verbose: bool, default=False
+        Verbosity flag
+    random_state: int, default=42
+        Random seed for reproducibility
 
     Returns
     -------
     _Imputer
-        Optimized imputer
+        Imputer with optimized hyperparameters
 
     """
+    print("Starting hyperparameter optimization...")
     imputer = copy.deepcopy(imputer)
-    if dict_config == {}:
+
+    if not dict_config:
         return imputer
+
     names_hyperparams = list(dict_config.keys())
-    values_hyperparams = list(dict_config.values())
-    imputer.imputer_params = tuple(set(imputer.imputer_params) | set(dict_config.keys()))
+    dimensions = list(dict_config.values())
+
+    # Update imputer_params to include optimized parameters
+    imputer.imputer_params = tuple(set(imputer.imputer_params) | set(names_hyperparams))
+
+    # Disable verbose during optimization if applicable
     if verbose and hasattr(imputer, "verbose"):
         setattr(imputer, "verbose", False)
+
     fun_obj = get_objective(imputer, df, generator, metric, names_hyperparams)
-    hyperparams = ho.fmin(
-        fn=fun_obj,
-        space=values_hyperparams,
-        algo=ho.tpe.suggest,
-        max_evals=max_evals,
+
+    result = gp_minimize(
+        func=fun_obj,
+        dimensions=dimensions,
+        n_calls=max_evals,
+        n_initial_points=min(10, max_evals),
+        verbose=verbose,
+        random_state=random_state,
     )
 
-    for key, value in hyperparams.items():
+    # Set optimal hyperparameters
+    for key, value in zip(names_hyperparams, result.x):
         setattr(imputer, key, value)
+
     return imputer
diff --git a/qolmat/benchmark/metrics.py b/qolmat/benchmark/metrics.py
index 25d15d57..dd136219 100644
--- a/qolmat/benchmark/metrics.py
+++ b/qolmat/benchmark/metrics.py
@@ -61,7 +61,7 @@ def columnwise_metric(
         pd.testing.assert_index_equal(df1.columns, df2.columns)
     except AssertionError:
         raise ValueError(
-            "Input dataframes do not have the same columns! " f"({df1.columns} != {df2.columns})"
+            f"Input dataframes do not have the same columns! ({df1.columns} != {df2.columns})"
         )
     if type_cols == "all":
         cols = df1.columns.tolist()
@@ -942,7 +942,7 @@ def kl_divergence_gaussian(df1: pd.DataFrame, df2: pd.DataFrame) -> float:
         div_kl = algebra.kl_divergence_gaussian_exact(means1, cov1, means2, cov2)
     except LinAlgError:
         raise ValueError(
-            "Provided datasets have degenerate colinearities, KL-divergence " "cannot be computed!"
+            "Provided datasets have degenerate colinearities, KL-divergence cannot be computed!"
         )
     return div_kl
 
diff --git a/qolmat/imputations/em_sampler.py b/qolmat/imputations/em_sampler.py
index 790ff47d..ef202975 100644
--- a/qolmat/imputations/em_sampler.py
+++ b/qolmat/imputations/em_sampler.py
@@ -176,9 +176,7 @@ def __init__(
         verbose: bool = False,
     ):
         if method not in ["mle", "sample"]:
-            raise ValueError(
-                "`method` must be 'mle' or 'sample', " f"provided value is '{method}'."
-            )
+            raise ValueError(f"`method` must be 'mle' or 'sample', provided value is '{method}'.")
 
         self.method = method
         self.max_iter_em = max_iter_em
@@ -205,17 +203,17 @@ def _check_convergence(self) -> bool:
     @abstractmethod
     def reset_learned_parameters(self):
         """Reset learned parameters."""
-        pass
+        raise NotImplementedError("Method reset_learned_parameters not implemented.")
 
     @abstractmethod
     def update_parameters(self, X: NDArray):
         """Update parameters."""
-        pass
+        raise NotImplementedError("Method update_parameters not implemented.")
 
     @abstractmethod
     def combine_parameters(self):
         """Combine parameters."""
-        pass
+        raise NotImplementedError("Method combine_parameters not implemented.")
 
     def fit_parameters(self, X: NDArray):
         """Fir parameters.
@@ -396,6 +394,7 @@ def _sample_ou(
             grad_X = -self.gradient_X_loglik(X_copy)
             X_copy += -self.dt * grad_X @ gamma + np.sqrt(2 * self.dt) * noise @ sqrt_gamma
             X_copy[~mask_na] = X_init[~mask_na]
+
             if estimate_params:
                 self.update_parameters(X_copy)
 
@@ -453,21 +452,18 @@ def fit(self, X: NDArray) -> "EM":
 
         """
         X = X.copy()
-        # utils.check_dtypes(X)
-        # sku.check_array(X, ensure_all_finite="allow-nan", dtype="float")
         sku.validation.validate_data(self, X, ensure_all_finite="allow-nan", dtype="float")
         self.shape_original = X.shape
 
-        self.hash_fit = hash(X.tobytes())
         if not isinstance(X, np.ndarray):
             raise AssertionError("Invalid type. X must be a NDArray.")
+        self.hash_fit = hash(X.tobytes())
 
         X = utils.prepare_data(X, self.period)
 
         if hasattr(self, "p_to_fit") and self.p_to_fit:
             aics: List[float] = []
             for p in range(self.max_lagp + 1):
-                print("p=", p)
                 self.p = p
                 self.fit_X(X)
                 n1, n2 = self.X.shape
@@ -728,7 +724,6 @@ def get_gamma(self, n_cols: int) -> NDArray:
         diag_trunc = np.where(diag_trunc == 0, 0, np.min(diag_trunc))
 
         gamma = (U * diag_trunc) @ Vt
-        # gamma = np.eye(len(self.cov))
 
         return gamma
 
@@ -1210,7 +1205,7 @@ def pretreatment(self, X, mask_na) -> Tuple[NDArray, NDArray]:
         if self.p == 0:
             return X, mask_na
         mask_na = mask_na.copy()
-        n_holes_left = np.sum(~np.cumsum(~mask_na, axis=0).any(axis=1))
+        n_holes_left = int(np.sum(~np.cumsum(~mask_na, axis=0).any(axis=1)))
         mask_na[:n_holes_left] = False
         return X, mask_na
 
diff --git a/qolmat/imputations/imputers.py b/qolmat/imputations/imputers.py
index a0aae360..b38764fc 100644
--- a/qolmat/imputations/imputers.py
+++ b/qolmat/imputations/imputers.py
@@ -501,7 +501,7 @@ def transform(self, X: pd.DataFrame) -> pd.DataFrame:
         if hasattr(self, "df_solution"):
             df_imputed = df.fillna(self.df_solution)
         else:
-            warnings.warn("OracleImputer not initialized! " "Returning imputation with zeros")
+            warnings.warn("OracleImputer not initialized! Returning imputation with zeros")
             df_imputed = df.fillna(0)
 
         if isinstance(X, (np.ndarray)):
@@ -1429,7 +1429,7 @@ def get_Xy_valid(self, df: pd.DataFrame, col: str) -> Tuple[pd.DataFrame, pd.Ser
             X = X.dropna(how="any", axis=1)
         else:
             raise ValueError(
-                f"Value '{self.handler_nan}' is not correct " "for argument `handler_nan'."
+                f"Value '{self.handler_nan}' is not correct for argument `handler_nan'."
             )
         # X = pd.get_dummies(X, prefix_sep="=")
         y = df.loc[X.index, col]
@@ -1998,23 +1998,47 @@ class ImputerEM(_Imputer):
 
     Parameters
     ----------
-    groups: Tuple[str, ...]
-        List of column names to group by, by default []
-    method : {'multinormal', 'VAR'}, default='multinormal'
+    groups : Tuple[str, ...], default=()
+        List of column names to group by.
+    model : {'multinormal', 'VAR'}, default='multinormal'
         Method defining the hypothesis made on the data distribution.
         Possible values:
         - 'multinormal' : the data points are independent and uniformly
         distributed following a multinormal distribution
         - 'VAR' : the data is a time series modeled by a VAR(p) process
-    columnwise : bool
+    columnwise : bool, default=False
         If False, correlations between variables will be used,
         which is advised.
         If True, each column is imputed independently. For the multinormal case
         each value will be imputed by the mean up to a noise with fixed noise,
-        for the VAR1 case the imputation will be a noisy temporal
-        interpolation.
+        for the VAR case the imputation will be a noisy temporal interpolation.
     random_state : RandomSetting, optional
         Controls the randomness of the fit_transform, by default None
+    method : {'mle', 'sample'}, default='sample'
+        Imputation method after EM convergence.
+        - 'mle' : Maximum Likelihood Estimation
+        - 'sample' : Sample from the posterior distribution
+    max_iter_em : int, default=200
+        Maximum number of EM iterations.
+    n_iter_ou : int, default=50
+        Number of Ornstein-Uhlenbeck process iterations for sampling.
+    ampli : float, default=1
+        Amplitude parameter for the Ornstein-Uhlenbeck process.
+    dt : float, default=0.02
+        Time step for the Ornstein-Uhlenbeck process discretization.
+    tolerance : float, default=1e-4
+        Convergence tolerance for EM algorithm.
+    stagnation_threshold : float, default=5e-3
+        Threshold for element-wise stagnation detection in EM algorithm.
+    stagnation_loglik : float, default=2
+        Threshold for log-likelihood stagnation in EM algorithm.
+    period : int, default=1
+        If different from 1, the data is folded with respect to the given period
+        before applying the imputation.
+    verbose : bool, default=False
+        If True, print convergence information during fitting.
+    p : int, optional
+        Order of the VAR process (only used when model='VAR'), by default None
 
     """
 
diff --git a/qolmat/imputations/imputers_pytorch.py b/qolmat/imputations/imputers_pytorch.py
index cd6a3078..9850d856 100644
--- a/qolmat/imputations/imputers_pytorch.py
+++ b/qolmat/imputations/imputers_pytorch.py
@@ -236,7 +236,7 @@ def fit(self, X: NDArray, y: NDArray) -> "Autoencoder":
             loss.backward()
             optimizer.step()
             if (epoch + 1) % 10 == 0:
-                logging.info(f"Epoch [{epoch + 1}/{self.epochs}], " f"Loss: {loss.item():.4f}")
+                logging.info(f"Epoch [{epoch + 1}/{self.epochs}], Loss: {loss.item():.4f}")
             list_loss.append(loss.item())
         self.loss.extend([list_loss])
         return self
diff --git a/qolmat/imputations/rpca/rpca_noisy.py b/qolmat/imputations/rpca/rpca_noisy.py
index ed0f1062..0d95cac6 100644
--- a/qolmat/imputations/rpca/rpca_noisy.py
+++ b/qolmat/imputations/rpca/rpca_noisy.py
@@ -286,7 +286,7 @@ def minimise_loss(
         # init
         Y = np.zeros((n_rows, n_cols))
         M = D.copy()
-        A = np.zeros((n_rows, n_cols))
+        A: NDArray = np.zeros((n_rows, n_cols))
 
         U, S, Vt = np.linalg.svd(M, full_matrices=False)
         U = U[:, :rank]
@@ -297,7 +297,7 @@ def minimise_loss(
         Q = np.diag(np.sqrt(S)) @ Vt
 
         if norm == "L1":
-            R = [np.ones((n_rows, n_cols)) for _ in list_periods]
+            R: list[NDArray] = [np.ones((n_rows, n_cols)) for _ in list_periods]
 
         mu_bar = mu * 1e3
 
@@ -425,7 +425,7 @@ def decompose_on_basis(
         # M, A, L, Q = self.decompose_rpca(D, Omega)
         n_rank, _ = Q.shape
         Ir = np.eye(n_rank)
-        A = np.zeros((n_rows, n_cols))
+        A: NDArray = np.zeros((n_rows, n_cols))
         L = np.zeros((n_rows, n_rank))
         for _ in range(self.max_iterations):
             A_prev = A.copy()
diff --git a/qolmat/imputations/softimpute.py b/qolmat/imputations/softimpute.py
index 088d58c4..e7f366b6 100644
--- a/qolmat/imputations/softimpute.py
+++ b/qolmat/imputations/softimpute.py
@@ -44,7 +44,7 @@ class SoftImpute(BaseEstimator, TransformerMixin):
     tolerance : float
         Tolerance for the convergence criterion
     tau : float
-        regularisation parameter
+        Regularisation parameter
     max_iterations : int
         Maximum number of iterations
     random_state : int, optional
@@ -59,12 +59,13 @@ class SoftImpute(BaseEstimator, TransformerMixin):
     >>> from qolmat.imputations.softimpute import SoftImpute
     >>> D = np.array([[1, 2, np.nan, 4], [1, 5, 3, np.nan], [4, 2, 3, 2], [1, 1, 5, 4]])
     >>> Omega = ~np.isnan(D)
-    >>> M, A = SoftImpute(random_state=11).decompose(D, Omega)
-    >>> print(M + A)
-    [[1.         2.         4.12611456 4.        ]
-     [1.         5.         3.         0.87217939]
-     [4.         2.         3.         2.        ]
-     [1.         1.         5.         4.        ]]
+    >>> M, A = SoftImpute(random_state=10, tau=1).decompose(D, Omega)
+    >>> naive_cost = SoftImpute.cost_function(
+    ...     D, np.where(Omega, M, 0), np.zeros_like(M), Omega, tau=1
+    ... )
+    >>> minimal_cost = SoftImpute.cost_function(D, M, A, Omega, tau=1)
+    >>> minimal_cost < naive_cost
+    np.True_
 
     """
 
@@ -137,7 +138,8 @@ def decompose(self, X: NDArray, Omega: NDArray) -> Tuple[NDArray, NDArray]:
         # Step 1 : Initializing
         n, m = X.shape
         V = np.zeros((m, rank))
-        U = self.random_state.normal(0.0, 1.0, (n, rank))
+        # U = self.random_state.normal(0.0, 1.0, (n, rank))
+        U = np.zeros((n, rank))
         U, _, _ = np.linalg.svd(U, full_matrices=False)
         D = np.ones((1, rank))
 
@@ -180,8 +182,7 @@ def decompose(self, X: NDArray, Omega: NDArray) -> Tuple[NDArray, NDArray]:
                 logging.info(f"Iteration {iter_}: ratio = {round(ratio, 4)}")
                 if ratio < self.tolerance:
                     logging.info(
-                        f"Convergence reached at iteration {iter_} "
-                        f"with ratio = {round(ratio, 4)}"
+                        f"Convergence reached at iteration {iter_} with ratio = {round(ratio, 4)}"
                     )
                     break
 
@@ -269,7 +270,7 @@ def cost_function(
             Anomalies
         Omega : NDArray
             Mask for observations
-        tau: Optional[float]
+        tau: float
             penalizing parameter for the nuclear norm
 
         Returns
diff --git a/qolmat/utils/data.py b/qolmat/utils/data.py
index f1ace3f8..9748481b 100644
--- a/qolmat/utils/data.py
+++ b/qolmat/utils/data.py
@@ -380,7 +380,7 @@ def add_holes(
             random_state=random_state,
         )
 
-    generator.dict_probas_out = {column: 1 / mean_size for column in df.columns}
+    generator.dict_probas_out = dict.fromkeys(df.columns, 1 / mean_size)
     generator.dict_ratios = {column: 1 / len(df.columns) for column in df.columns}
     if generator.groups:
         mask = df.groupby(groups, group_keys=False).apply(generator.generate_mask)
@@ -553,7 +553,7 @@ def convert_tsf_to_dataframe(
                         series = series.split(",")  # type: ignore
 
                         if len(series) == 0:
-                            raise Exception(" Missing values should be indicated " "with ? symbol")
+                            raise Exception(" Missing values should be indicated with ? symbol")
 
                         numeric_series = []
 
@@ -565,7 +565,7 @@ def convert_tsf_to_dataframe(
 
                         if numeric_series.count(replace_missing_vals_with) == len(numeric_series):
                             raise Exception(
-                                "At least one numeric value should be " "there in a series."
+                                "At least one numeric value should be there in a series."
                             )
 
                         all_series.append(pd.Series(numeric_series).array)
diff --git a/qolmat/utils/exceptions.py b/qolmat/utils/exceptions.py
index d0cfd465..b4e003c4 100644
--- a/qolmat/utils/exceptions.py
+++ b/qolmat/utils/exceptions.py
@@ -44,7 +44,7 @@ class NotDimension2(Exception):
     """Raise an error when the matrix is not of dim 2."""
 
     def __init__(self, shape: Tuple[int, ...]):
-        super().__init__(f"Provided matrix is of shape {shape}, " "which is not of dimension 2!")
+        super().__init__(f"Provided matrix is of shape {shape}, which is not of dimension 2!")
 
 
 class NotDataFrame(Exception):
@@ -96,4 +96,4 @@ class TypeNotHandled(Exception):
     """Raise an error when the type is not handled."""
 
     def __init__(self, col: str, type_col: str):
-        super().__init__(f"The column `{col}` is of type `{type_col}`, " "which is not handled!")
+        super().__init__(f"The column `{col}` is of type `{type_col}`, which is not handled!")
diff --git a/qolmat/utils/utils.py b/qolmat/utils/utils.py
index 1142a796..9b5d49dd 100644
--- a/qolmat/utils/utils.py
+++ b/qolmat/utils/utils.py
@@ -366,7 +366,7 @@ def create_lag_matrices(X: NDArray, p: int) -> Tuple[NDArray, NDArray]:
     """
     n_rows, _ = X.shape
     n_rows_new = n_rows - p
-    list_X_lag = [np.ones((n_rows_new, 1))]
+    list_X_lag: list[NDArray] = [np.ones((n_rows_new, 1))]
     for lag in range(p):
         X_lag = X[p - lag - 1 : n_rows - lag - 1, :]
         list_X_lag.append(X_lag)
@@ -394,6 +394,7 @@ def nan_mean_cov(X: NDArray) -> Tuple[NDArray, NDArray]:
     means = np.nanmean(X, axis=0)
     cov = np.ma.cov(np.ma.masked_invalid(X), rowvar=False).data
     cov = cov.reshape(n_variables, n_variables)
+    cov[~np.isfinite(cov)] = 0.0
     return means, cov
 
 
diff --git a/tests/benchmark/test_hyperparameters.py b/tests/benchmark/test_hyperparameters.py
index 8bf72584..c298b44f 100644
--- a/tests/benchmark/test_hyperparameters.py
+++ b/tests/benchmark/test_hyperparameters.py
@@ -1,8 +1,8 @@
 from typing import List, Optional, Tuple
 
-import hyperopt as ho
 import numpy as np
 import pandas as pd
+from skopt.space import Real
 
 from qolmat.benchmark import hyperparameters
 
@@ -89,14 +89,18 @@ def test_hyperparameters_get_objective() -> None:
 
 
 def test_hyperparameters_optimize():
-    """Test optimize."""
+    """Test optimize with scikit-optimize."""
     imputer = ImputerTest()
+
     generator = HoleGeneratorTest(pd.Series([False, False, True, True]), subset=["some_col"])
+
     metric = "mse"
-    dict_config_opti = {"value": ho.hp.uniform("value", 0, 10)}
+    dict_config_opti = {"value": Real(0, 10, name="value")}
     df = pd.DataFrame({"some_col": [np.nan, 0, 3, 5]})
+
     imputer_opti = hyperparameters.optimize(
-        imputer, df, generator, metric, dict_config_opti, max_evals=500
+        imputer, df, generator, metric, dict_config_opti, max_evals=20, verbose=True
     )
+
     assert isinstance(imputer_opti, ImputerTest)
     np.testing.assert_almost_equal(imputer_opti.value, 4, decimal=1)
diff --git a/tests/imputations/test_em_sampler.py b/tests/imputations/test_em_sampler.py
index ce75cc04..f4327a9a 100644
--- a/tests/imputations/test_em_sampler.py
+++ b/tests/imputations/test_em_sampler.py
@@ -294,9 +294,6 @@ def test_illconditioned_multinormalem() -> None:
     model = em_sampler.MultiNormalEM()
     with pytest.warns(UserWarning):
         _ = model.fit_transform(X)
-    # except IllConditioned:
-    #     return
-    # assert False
 
 
 def test_no_more_nan_multinormalem() -> None:
diff --git a/tests/imputations/test_imputers.py b/tests/imputations/test_imputers.py
index c8ee2818..b9b52ac7 100644
--- a/tests/imputations/test_imputers.py
+++ b/tests/imputations/test_imputers.py
@@ -9,8 +9,8 @@
     parametrize_with_checks,
 )
 
-from qolmat.benchmark.hyperparameters import HyperValue
 from qolmat.imputations import imputers
+from qolmat.utils.utils import HyperValue
 
 df_complete = pd.DataFrame({"col1": [0, 1, 2, 3, 4], "col2": [-1, 0, 0.5, 1, 1.5]})
 
diff --git a/tests/imputations/test_softimpute.py b/tests/imputations/test_softimpute.py
index 9b65d978..52d3e12b 100644
--- a/tests/imputations/test_softimpute.py
+++ b/tests/imputations/test_softimpute.py
@@ -2,22 +2,39 @@
 import pytest
 from numpy.typing import NDArray
 
-from qolmat.imputations import softimpute
+from qolmat.imputations.softimpute import SoftImpute
 
-X = np.random.rand(100, 100)
-X[np.random.choice(100, 10), np.random.choice(100, 10)] = np.nan
-X_non_regression_test = np.array(
-    [[1, 2, np.nan, 4], [1, 5, 3, np.nan], [4, 2, 3, 2], [1, 1, 5, 4]]
-)
-X_expected = np.array([[1, 2, 2.9066, 4], [1, 5, 3, 2.1478], [4, 2, 3, 2], [1, 1, 5, 4]])
-tau = 1
-max_iterations = 30
-random_state = 50
+
+@pytest.fixture
+def X_random() -> NDArray:
+    """Generate random matrix with missing values."""
+    rng = np.random.RandomState(42)
+    X = rng.rand(100, 100)
+    X[rng.choice(100, 10), rng.choice(100, 10)] = np.nan
+    return X
+
+
+@pytest.fixture
+def X_non_regression() -> NDArray:
+    """Get small test matrix for non-regression tests."""
+    return np.array([[1, 2, np.nan, 4], [1, 5, 3, np.nan], [4, 2, 3, 2], [1, 1, 5, 4]])
+
+
+@pytest.fixture
+def X_expected() -> NDArray:
+    """Get expected imputed values for non-regression test."""
+    return np.array([[1, 2, 2.9066, 4], [1, 5, 3, 2.1478], [4, 2, 3, 2], [1, 1, 5, 4]])
+
+
+@pytest.fixture
+def default_params() -> dict:
+    """Get default parameters for SoftImpute."""
+    return {"tau": 1, "max_iterations": 30, "random_state": 50}
 
 
 def test_initialized_default() -> None:
     """Test that initialization does not crash and has default parameters."""
-    model = softimpute.SoftImpute()
+    model = SoftImpute()
     assert model.period == 1
     assert model.rank is None
     assert model.tolerance == 1e-05
@@ -25,36 +42,34 @@ def test_initialized_default() -> None:
 
 def test_initialized_custom() -> None:
     """Test that initialization does not crash and has custom parameters."""
-    model = softimpute.SoftImpute(period=2, rank=10)
+    model = SoftImpute(period=2, rank=10)
     assert model.period == 2
     assert model.rank == 10
     assert model.tau is None
 
 
-@pytest.mark.parametrize("X", [X])
-def test_soft_impute_decompose(X: NDArray) -> None:
+def test_soft_impute_decompose(X_random: NDArray, default_params: dict) -> None:
     """Test fit instance and decomposition is computed."""
-    tau = 1
-    model = softimpute.SoftImpute(tau=tau)
-    Omega = ~np.isnan(X)
-    X_imputed = np.where(Omega, X, 0)
-    cost_all_in_M = model.cost_function(X, X_imputed, np.full_like(X, 0), Omega, tau)
-    cost_all_in_A = model.cost_function(X, np.full_like(X, 0), X_imputed, Omega, tau)
-    M, A = model.decompose(X, Omega)
-    cost_final = model.cost_function(X, M, A, Omega, tau)
-    assert isinstance(model, softimpute.SoftImpute)
-    assert M.shape == X.shape
-    assert A.shape == X.shape
+    tau = default_params["tau"]
+    model = SoftImpute(tau=tau)
+    Omega = ~np.isnan(X_random)
+    X_imputed = np.where(Omega, X_random, 0)
+    cost_all_in_M = model.cost_function(X_random, X_imputed, np.full_like(X_random, 0), Omega, tau)
+    cost_all_in_A = model.cost_function(X_random, np.full_like(X_random, 0), X_imputed, Omega, tau)
+    M, A = model.decompose(X_random, Omega)
+    cost_final = model.cost_function(X_random, M, A, Omega, tau)
+    assert isinstance(model, SoftImpute)
+    assert M.shape == X_random.shape
+    assert A.shape == X_random.shape
     assert not np.any(np.isnan(M))
     assert not np.any(np.isnan(A))
     assert cost_final < cost_all_in_M
     assert cost_final < cost_all_in_A
 
 
-@pytest.mark.parametrize("X", [X])
-def test_soft_impute_convergence(X: NDArray) -> None:
+def test_soft_impute_convergence() -> None:
     """Test type of the check convergence."""
-    model = softimpute.SoftImpute()
+    model = SoftImpute()
     M = model.random_state.uniform(size=(10, 20))
     U, D, V = np.linalg.svd(M, full_matrices=False)
     ratio = model._check_convergence(U, D, V.T, U, D, V.T)
@@ -63,7 +78,7 @@ def test_soft_impute_convergence(X: NDArray) -> None:
 
 def test_soft_impute_convergence_with_none() -> None:
     """Test check type None and raise error."""
-    model = softimpute.SoftImpute()
+    model = SoftImpute()
     with pytest.raises(ValueError):
         _ = model._check_convergence(
             np.array([1]),
@@ -73,3 +88,22 @@ def test_soft_impute_convergence_with_none() -> None:
             np.array([1]),
             np.array([1]),
         )
+
+
+def test_decompose_loss_minimized(X_random: NDArray, default_params: dict) -> None:
+    """Test that the loss function is at a local minimum."""
+    tau = default_params["tau"]
+    imputer = SoftImpute(random_state=123, tau=tau)
+    Omega = ~np.isnan(X_random)
+    M, A = imputer.decompose(X_random, Omega)
+    X_imputed = M + A
+    cost_imputed = SoftImpute.cost_function(X_imputed, M, A, Omega, tau)
+    for i in range(10):
+        Delta = 1.1 ** (i - 9) * imputer.random_state.uniform(0, 1, size=X_random.shape)
+        X_perturbed = X_imputed + Delta
+        cost_perturbed = SoftImpute.cost_function(X_perturbed, M, A, Omega, tau)
+        assert cost_perturbed > cost_imputed
+    M = np.zeros(X_random.shape)
+    A = X_random.copy()
+    cost_perturbed = SoftImpute.cost_function(X_random, M, A, Omega, tau)
+    assert cost_perturbed > cost_imputed
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