F1 Score

Eval

F1 Score | The harmonic mean of precision and recall

Created: Last updated: Read time: 2 min
まとめ
  • F1 Score | The harmonic mean of precision and recallの概要を押さえ、評価対象と読み取り方を整理します。
  • Python 3.13 のコード例で算出・可視化し、手順と実務での確認ポイントを確認します。
  • 図表や補助指標を組み合わせ、モデル比較や閾値調整に活かすヒントをまとめます。

1. Definition #

With precision \(P\) and recall \(R\), F1 is defined as F_1 = 2 \cdot \frac{P \cdot R}{P + R}. The general Fβ score gives more weight to recall (\(\beta > 1\)) or precision (\(\beta < 1\)): F_\beta = (1 + \beta^2) \cdot \frac{P \cdot R}{\beta^2 P + R}.

2. Computing F1 in Python 3.13 #

python --version        # e.g. Python 3.13.0
pip install scikit-learn matplotlib

import numpy as np
from sklearn.datasets import make_classification
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import classification_report, f1_score, fbeta_score
from sklearn.model_selection import train_test_split
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler
X, y = make_classification(
    n_samples=40_000,
    n_features=20,
    n_informative=6,
    weights=[0.95, 0.05],
    random_state=42,
)
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.25, stratify=y, random_state=42
)
model = make_pipeline(
    StandardScaler(),
    LogisticRegression(max_iter=2000, class_weight="balanced"),
)
model.fit(X_train, y_train)
y_pred = model.predict(X_test)
print(classification_report(y_test, y_pred, digits=3))
print("F1:", f1_score(y_test, y_pred))
print("F0.5:", fbeta_score(y_test, y_pred, beta=0.5))
print("F2:", fbeta_score(y_test, y_pred, beta=2.0))

classification_report displays precision, recall, and F1 per class in one table.

3. How F1 varies with the threshold #

Using probability outputs we can plot how F1 evolves as the decision threshold changes.

from sklearn.metrics import f1_score, precision_recall_curve
proba = model.predict_proba(X_test)[:, 1]
precision, recall, thresholds = precision_recall_curve(y_test, proba)
thresholds = np.append(thresholds, 1.0)
f1_scores = [
    f1_score(y_test, (proba >= t).astype(int))
    for t in thresholds
]
F1 score vs threshold

Use the curve to locate the threshold that maximises F1, or to trade precision for recall as requirements change.

  • The peak indicates the best trade-off between precision and recall when both are equally important.
  • Use F0.5 or F2 when you want to bias the trade-off toward precision or recall respectively.

4. Averaging strategies for multiclass #

scikit-learn’s verage parameter lets you aggregate F1 for multiclass or multilabel data:

  • macro — compute F1 per class and take the (unweighted) mean.
  • weighted — average per-class F1 weighted by class support.
  • micro — pool all predictions and recompute from the global confusion matrix.
from sklearn.metrics import f1_score
f1_macro = f1_score(y_test, y_pred, average="macro")
f1_weighted = f1_score(y_test, y_pred, average="weighted")

For multilabel problems verage=“samples” reports the mean per sample.

Summary #

  • F1 balances precision and recall; plotting it across thresholds helps you choose the operating point.
  • Fβ scores adapt the balance when either recall (β>1) or precision (β<1) must dominate.
  • On multiclass tasks, specify the averaging strategy and review precision, recall, F1, and PR curves together to understand the classifier’s behaviour.