Added metric Brier Score (#275)

* Added metric Brier Score

* added numpy library and reformatter

* Updated the args description.

* examples codes updated.

* word error fixed

* parameter error fixed.

* parameter and reference codes have been updated.

* The print code has been updated.

* output value have been updated.

* Update metrics/brier_score/brier_score.py

Co-authored-by: Leandro von Werra <lvwerra@users.noreply.github.com>

* Update metrics/brier_score/README.md

Co-authored-by: Leandro von Werra <lvwerra@users.noreply.github.com>

* Update metrics/brier_score/README.md

Co-authored-by: Leandro von Werra <lvwerra@users.noreply.github.com>

* Update metrics/brier_score/README.md

Co-authored-by: Leandro von Werra <lvwerra@users.noreply.github.com>

Co-authored-by: Leandro von Werra <lvwerra@users.noreply.github.com>

metrics/brier_score/README.md

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+---
+title: Brier Score
+emoji: 🤗 
+colorFrom: blue
+colorTo: red
+sdk: gradio
+sdk_version: 3.0.2
+app_file: app.py
+pinned: false
+tags:
+- evaluate
+- metric
+description: >-
+  The Brier score is a measure of the error between two probability distributions.
+---
+
+# Metric Card for Brier Score
+
+
+## Metric Description
+Brier score is a type of evaluation metric for classification tasks, where you predict outcomes such as win/lose, spam/ham, click/no-click etc.
+`BrierScore = 1/N * sum( (p_i - o_i)^2 )`
+
+Where `p_i` is the prediction probability of occurrence of the event, and the term `o_i` is equal to 1 if the event occurred and 0 if not. Which means: the lower the value of this score, the better the prediction. 
+## How to Use
+
+At minimum, this metric requires predictions and references as inputs.
+
+```python
+>>> brier_score = evaluate.load("brier_score")
+>>> predictions = np.array([0, 0, 1, 1])
+>>> references = np.array([0.1, 0.9, 0.8, 0.3])
+>>> results = brier_score.compute(predictions=predictions, references=references)
+```
+
+### Inputs
+
+Mandatory inputs: 
+- `predictions`: numeric array-like of shape (`n_samples,`) or (`n_samples`, `n_outputs`), representing the estimated target values.
+
+- `references`: numeric array-like of shape (`n_samples,`) or (`n_samples`, `n_outputs`), representing the ground truth (correct) target values.
+
+Optional arguments:
+- `sample_weight`: numeric array-like of shape (`n_samples,`) representing sample weights. The default is `None`.
+- `pos_label`: the label of the positive class. The default is `1`.
+
+
+### Output Values
+This metric returns a dictionary with the following keys:
+- `brier_score (float)`: the computed Brier score.
+
+
+Output Example(s):
+```python
+{'brier_score': 0.5}
+```
+
+#### Values from Popular Papers
+
+
+### Examples
+```python
+>>> brier_score = evaluate.load("brier_score")
+>>> predictions = np.array([0, 0, 1, 1])
+>>> references = np.array([0.1, 0.9, 0.8, 0.3])
+>>> results = brier_score.compute(predictions=predictions, references=references)
+>>> print(results)
+{'brier_score': 0.3375}
+```
+Example with `y_true` contains string, an error will be raised and `pos_label` should be explicitly specified.
+```python
+>>> brier_score_metric = evaluate.load("brier_score")
+>>> predictions =  np.array(["spam", "ham", "ham", "spam"])
+>>> references = np.array([0.1, 0.9, 0.8, 0.3])
+>>> results = brier_score.compute(predictions, references, pos_label="ham")
+>>> print(results) 
+{'brier_score': 0.0374}
+```
+## Limitations and Bias
+The [brier_score](https://huggingface.co/metrics/brier_score) is appropriate for binary and categorical outcomes that can be structured as true or false, but it is inappropriate for ordinal variables which can take on three or more values.
+## Citation(s)
+```bibtex
+@article{scikit-learn,
+  title={Scikit-learn: Machine Learning in {P}ython},
+  author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.
+         and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.
+         and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and
+         Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},
+  journal={Journal of Machine Learning Research},
+  volume={12},
+  pages={2825--2830},
+  year={2011}
+}
+
+@Article{brier1950verification,
+  title={Verification of forecasts expressed in terms of probability},
+  author={Brier, Glenn W and others},
+  journal={Monthly weather review},
+  volume={78},
+  number={1},
+  pages={1--3},
+  year={1950}
+}
+```
+## Further References
+- [Brier Score - Wikipedia](https://en.wikipedia.org/wiki/Brier_score)

metrics/brier_score/app.py

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+import evaluate
+from evaluate.utils import launch_gradio_widget
+
+
+module = evaluate.load("brier_score")
+launch_gradio_widget(module)

metrics/brier_score/brier_score.py

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+# Copyright 2022 The HuggingFace Datasets Authors and the current dataset script contributor.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""Brier Score Metric"""
+
+import datasets
+from sklearn.metrics import brier_score_loss
+
+import evaluate
+
+
+_CITATION = """\
+@article{scikit-learn,
+ title={Scikit-learn: Machine Learning in {P}ython},
+ author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.
+         and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.
+         and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and
+         Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},
+ journal={Journal of Machine Learning Research},
+ volume={12},
+ pages={2825--2830},
+ year={2011}
+}
+"""
+
+_DESCRIPTION = """\
+Brier score is a type of evaluation metric for classification tasks, where you predict outcomes such as win/lose, spam/ham, click/no-click etc.
+`BrierScore = 1/N * sum( (p_i - o_i)^2 )`
+"""
+
+
+_KWARGS_DESCRIPTION = """
+Args:
+    y_true : array of shape (n_samples,)
+        True targets.
+
+    y_prob : array of shape (n_samples,)
+        Probabilities of the positive class.
+
+    sample_weight : array-like of shape (n_samples,), default=None
+        Sample weights.
+
+    pos_label : int or str, default=None
+        Label of the positive class. `pos_label` will be inferred in the
+        following manner:
+
+        * if `y_true` in {-1, 1} or {0, 1}, `pos_label` defaults to 1;
+        * else if `y_true` contains string, an error will be raised and
+          `pos_label` should be explicitly specified;
+        * otherwise, `pos_label` defaults to the greater label,
+          i.e. `np.unique(y_true)[-1]`.
+
+Returns
+    score : float
+        Brier score loss.
+Examples:
+    Example-1: if y_true in {-1, 1} or {0, 1}, pos_label defaults to 1.
+        >>> import numpy as np
+        >>> brier_score = evaluate.load("brier_score")
+        >>> references = np.array([0, 0, 1, 1])
+        >>> predictions = np.array([0.1, 0.9, 0.8, 0.3])
+        >>> results = brier_score.compute(references=references, predictions=predictions)
+        >>> print(round(results["brier_score"], 4))
+        0.3375
+
+    Example-2: if y_true contains string, an error will be raised and pos_label should be explicitly specified.
+        >>> import numpy as np
+        >>> brier_score = evaluate.load("brier_score")
+        >>> references =  np.array(["spam", "ham", "ham", "spam"])
+        >>> predictions = np.array([0.1, 0.9, 0.8, 0.3])
+        >>> results = brier_score.compute(references=references, predictions=predictions, pos_label="ham")
+        >>> print(round(results["brier_score"], 4))
+        0.0375
+"""
+
+
+@evaluate.utils.file_utils.add_start_docstrings(_DESCRIPTION, _KWARGS_DESCRIPTION)
+class BrierScore(evaluate.Metric):
+    def _info(self):
+        return evaluate.MetricInfo(
+            description=_DESCRIPTION,
+            citation=_CITATION,
+            inputs_description=_KWARGS_DESCRIPTION,
+            features=self._get_feature_types(),
+            reference_urls=["https://scikit-learn.org/stable/modules/generated/sklearn.metrics.brier_score_loss.html"],
+        )
+
+    def _get_feature_types(self):
+        if self.config_name == "multilist":
+            return [
+                datasets.Features(
+                    {
+                        "references": datasets.Sequence(datasets.Value("float")),
+                        "predictions": datasets.Sequence(datasets.Value("float")),
+                    }
+                ),
+                datasets.Features(
+                    {
+                        "references": datasets.Sequence(datasets.Value("string")),
+                        "predictions": datasets.Sequence(datasets.Value("float")),
+                    }
+                ),
+            ]
+        else:
+            return [
+                datasets.Features(
+                    {
+                        "references": datasets.Value("float"),
+                        "predictions": datasets.Value("float"),
+                    }
+                ),
+                datasets.Features(
+                    {
+                        "references": datasets.Value("string"),
+                        "predictions": datasets.Value("float"),
+                    }
+                ),
+            ]
+
+    def _compute(self, references, predictions, sample_weight=None, pos_label=1):
+
+        brier_score = brier_score_loss(references, predictions, sample_weight=sample_weight, pos_label=pos_label)
+
+        return {"brier_score": brier_score}

metrics/brier_score/requirements.txt

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+git+https://github.com/huggingface/evaluate@{COMMIT_PLACEHOLDER}
+sklearn