Binary Classification: Predicting Yes or No Outcomes

Master binary classification — the foundation of machine learning decision-making. Learn algorithms, evaluation metrics, threshold tuning, class imbalance, and Python implementations.

By Techietory on February 20, 2026
Binary Classification: Predicting Yes or No Outcomes

Binary classification is a supervised machine learning task where the model predicts one of exactly two possible outcomes — yes or no, spam or not spam, fraud or legitimate, sick or healthy. The model learns a decision boundary that separates the two classes in feature space, then assigns new examples to one class based on which side of the boundary they fall on. Binary classification is the most fundamental classification task, and mastering it — including algorithm selection, evaluation metrics, threshold tuning, and handling class imbalance — provides the conceptual foundation for all classification problems.

Introduction: The World of Yes-or-No Decisions

Every day, machine learning systems make millions of binary decisions: Is this transaction fraudulent? Should this loan be approved? Is this X-ray showing a tumor? Will this customer cancel their subscription? Does this image contain a face? Is this review positive or negative?

These are binary classification problems — situations where the answer is one of exactly two possibilities. The output space is discrete and binary: 0 or 1, False or True, negative or positive, class A or class B. Binary classification is the most common and fundamental classification task in machine learning, and getting it right requires more than just fitting a model.

It requires choosing the right algorithm for your data, selecting evaluation metrics that match your problem’s priorities (accuracy alone is often misleading), tuning the decision threshold to balance different types of errors, handling class imbalance when one outcome is rare, and understanding what makes a binary classifier truly useful in practice.

This comprehensive guide covers the complete landscape of binary classification. You’ll learn the formal problem definition, the taxonomy of binary classification algorithms, evaluation metrics and their tradeoffs, threshold optimization, handling imbalanced classes, probability calibration, and complete Python implementations across multiple real-world scenarios.

What is Binary Classification?

The Formal Definition

Binary classification: A supervised learning task where:

  • Input: Feature vector x = [x₁, x₂, …, xₙ]
  • Output: Class label y ∈ {0, 1}
  • Goal: Learn a function f(x) → {0, 1}

The two classes:

Plaintext
Positive class (y=1): The "event of interest"
  Examples: fraud, spam, disease, churn, default

Negative class (y=0): The "baseline" or "absence"
  Examples: legitimate, not spam, healthy, retained, repaid

Convention: Positive class is typically the rarer or more consequential outcome.

Real-World Binary Classification Problems

Finance:

Plaintext
Credit card fraud detection:  Fraud (1) vs. Legitimate (0)
Loan default prediction:      Default (1) vs. Repaid (0)
Stock movement prediction:    Up (1) vs. Down (0)

Healthcare:

Plaintext
Disease diagnosis:            Positive (1) vs. Negative (0)
Tumor classification:         Malignant (1) vs. Benign (0)
Readmission prediction:       Readmitted (1) vs. Not (0)

Technology:

Plaintext
Spam detection:               Spam (1) vs. Ham (0)
Intrusion detection:          Attack (1) vs. Normal (0)
Sentiment analysis:           Positive (1) vs. Negative (0)

Business:

Plaintext
Customer churn:               Churned (1) vs. Retained (0)
Click-through prediction:     Clicked (1) vs. Not clicked (0)
Product defect detection:     Defective (1) vs. Good (0)

How Binary Classifiers Work

The Two-Step Process

Every binary classifier follows the same two-step process:

Step 1: Learn a scoring function

Plaintext
score(x) = some measure of "how much like class 1" is x

Step 2: Apply a threshold

Plaintext
If score(x) ≥ threshold → Predict class 1
If score(x) < threshold → Predict class 0

The scoring function varies by algorithm:

Plaintext
Logistic Regression:   score = σ(wᵀx + b) = probability
Decision Tree:         score = fraction of class-1 examples in leaf
Random Forest:         score = average probability across trees
SVM:                   score = distance from hyperplane
Neural Network:        score = σ(output neuron)
Naive Bayes:           score = P(class 1 | features)

The Decision Boundary

The decision boundary is the surface in feature space where the classifier is exactly uncertain — where score = threshold.

1D case (one feature):

Plaintext
score
1.0 │              ╭─────────
    │           ╭──╯
0.5 │──────────╯←────────────── threshold
    │       ╭──╯
0.0 │──────╯
    └────────────────────────── x
         ↑
      x* = decision boundary
      Left: predict class 0
      Right: predict class 1

2D case (two features):

Plaintext
Feature 2
    │ ● ●
    │  ● ●  ●                 ← Class 1
    │    ●  ● ●
    │───────────────           ← Decision boundary
    │    ○  ○ ○ ○
    │  ○ ○  ○                 ← Class 0
    │ ○ ○
    └─────────────── Feature 1

Binary Classification Algorithms

Logistic Regression

Best for: Linearly separable data, when probabilities matter, interpretability needed

Python
from sklearn.linear_model import LogisticRegression

lr = LogisticRegression(C=1.0, max_iter=1000)
lr.fit(X_train, y_train)
probs = lr.predict_proba(X_test)[:, 1]  # Probability of class 1

Strengths: Fast, interpretable, well-calibrated probabilities, works well with many features Weaknesses: Only linear boundary, needs feature scaling, assumes feature independence

Decision Tree

Best for: Non-linear data, interpretability, mixed feature types

Python
from sklearn.tree import DecisionTreeClassifier

dt = DecisionTreeClassifier(max_depth=5, min_samples_leaf=10)
dt.fit(X_train, y_train)
probs = dt.predict_proba(X_test)[:, 1]

Strengths: Handles non-linearity, no scaling needed, interpretable rules Weaknesses: Prone to overfitting without pruning, unstable (high variance)

Random Forest

Best for: General purpose, when performance matters, handles missing data well

Python
from sklearn.ensemble import RandomForestClassifier

rf = RandomForestClassifier(n_estimators=100, max_depth=10,
                             random_state=42)
rf.fit(X_train, y_train)
probs = rf.predict_proba(X_test)[:, 1]

Strengths: Excellent performance, handles non-linearity, feature importance, robust Weaknesses: Slower training, less interpretable, memory intensive

Gradient Boosting (XGBoost / LightGBM)

Best for: Structured/tabular data, competitions, maximum performance

Python
from sklearn.ensemble import GradientBoostingClassifier

gb = GradientBoostingClassifier(n_estimators=100, learning_rate=0.1,
                                  max_depth=3)
gb.fit(X_train, y_train)
probs = gb.predict_proba(X_test)[:, 1]

Strengths: State-of-the-art on tabular data, handles missing values, feature importance Weaknesses: Many hyperparameters, slower training, prone to overfitting

Support Vector Machine (SVM)

Best for: High-dimensional data, small-medium datasets, text classification

Python
from sklearn.svm import SVC

svm = SVC(kernel='rbf', C=1.0, probability=True)
svm.fit(X_train, y_train)
probs = svm.predict_proba(X_test)[:, 1]

Strengths: Effective in high dimensions, kernel trick for non-linearity Weaknesses: Slow on large datasets, kernel/parameter selection tricky, memory intensive

K-Nearest Neighbors (KNN)

Best for: Small datasets, simple problems, baseline models

Python
from sklearn.neighbors import KNeighborsClassifier

knn = KNeighborsClassifier(n_neighbors=5)
knn.fit(X_train, y_train)
probs = knn.predict_proba(X_test)[:, 1]

Strengths: Simple, no training needed, naturally multi-class Weaknesses: Slow at inference, needs scaling, poor with high dimensions

Naive Bayes

Best for: Text classification, very large datasets, when data is sparse

Python
from sklearn.naive_bayes import GaussianNB

nb = GaussianNB()
nb.fit(X_train, y_train)
probs = nb.predict_proba(X_test)[:, 1]

Strengths: Very fast, works well with small data, text problems, interpretable Weaknesses: Independence assumption often violated, poor probability calibration

Evaluation Metrics: Beyond Accuracy

Accuracy alone is insufficient for binary classification — especially with imbalanced classes.

The Confusion Matrix

Every binary prediction falls into one of four categories:

Plaintext
                    Predicted
                   0               1
Actual  0     True Neg (TN)   False Pos (FP)
        1     False Neg (FN)  True Pos (TP)

TN: Correctly predicted class 0
TP: Correctly predicted class 1
FP: Incorrectly predicted class 1 (False alarm)
FN: Incorrectly predicted class 0 (Missed detection)

Real-world names:

Plaintext
Disease testing:
  TN = Healthy person → Negative test ✓
  TP = Sick person   → Positive test ✓
  FP = Healthy person → Positive test (false alarm — unnecessary treatment)
  FN = Sick person   → Negative test (missed diagnosis — dangerous!)

Key Metrics

Accuracy:

Plaintext
Accuracy = (TP + TN) / (TP + TN + FP + FN)

Proportion of all predictions that are correct.

Problem: Misleading with imbalanced classes.
  99% of transactions are legitimate → predict all negative → 99% accuracy!
  But catches 0% of fraud. Useless model.

Precision (Positive Predictive Value):

Plaintext
Precision = TP / (TP + FP)

"Of all examples predicted positive, what fraction are actually positive?"

High precision = few false alarms
Important when: False positives are costly
  Spam filter: Don't want to mark legitimate email as spam
  Legal system: Don't want to convict innocent people

Recall (Sensitivity / True Positive Rate):

Plaintext
Recall = TP / (TP + FN)

"Of all actual positives, what fraction did we correctly identify?"

High recall = few missed detections
Important when: False negatives are costly
  Cancer detection: Don't want to miss a real tumor
  Fraud: Don't want to miss actual fraud

F1 Score:

Plaintext
F1 = 2 × (Precision × Recall) / (Precision + Recall)
   = Harmonic mean of precision and recall

Balances both metrics.
Best single metric when classes are imbalanced.
Range: [0, 1], higher is better.

Specificity (True Negative Rate):

Plaintext
Specificity = TN / (TN + FP)

"Of all actual negatives, what fraction did we correctly identify?"
Complement of false positive rate.

The Precision-Recall Tradeoff:

Plaintext
Lowering the decision threshold:
  → More positives predicted
  → Higher recall (catch more true positives)
  → Lower precision (more false positives)

Raising the decision threshold:
  → Fewer positives predicted
  → Lower recall (miss more true positives)
  → Higher precision (fewer false positives)

Cannot maximize both simultaneously — must choose based on problem needs.

ROC-AUC: Threshold-Independent Performance

ROC Curve: Plots True Positive Rate (Recall) vs. False Positive Rate at every threshold

Plaintext
TPR (Recall)
1.0 │      ╭─────────────
    │   ╭──╯
    │ ╭─╯   ← Good classifier (area = 0.92)
    │╭╯
0.5 │╱
    │╱  ← Random classifier (area = 0.5, diagonal)
    │
0.0 └────────────────── FPR
    0    0.5    1.0

AUC (Area Under Curve):

Plaintext
AUC = 1.0: Perfect classifier
AUC = 0.5: Random classifier (diagonal line)
AUC = 0.0: Perfectly wrong classifier

AUC ≈ probability that model ranks a random positive
      example higher than a random negative example.

Threshold-independent: measures ranking quality, not just a single threshold.

Practical Code: All Metrics at Once

Python
import numpy as np
import pandas as pd
from sklearn.metrics import (
    accuracy_score, precision_score, recall_score,
    f1_score, roc_auc_score, confusion_matrix,
    classification_report, roc_curve,
    precision_recall_curve, average_precision_score
)
import matplotlib.pyplot as plt

def evaluate_binary_classifier(y_true, y_pred, y_prob,
                                 model_name="Model"):
    """
    Comprehensive evaluation of a binary classifier.
    y_true: true labels
    y_pred: predicted labels (after threshold)
    y_prob: predicted probabilities for class 1
    """
    print(f"\n{'='*55}")
    print(f"  {model_name} — Evaluation Report")
    print(f"{'='*55}")

    # Core metrics
    acc  = accuracy_score(y_true, y_pred)
    prec = precision_score(y_true, y_pred)
    rec  = recall_score(y_true, y_pred)
    f1   = f1_score(y_true, y_pred)
    auc  = roc_auc_score(y_true, y_prob)

    print(f"  Accuracy:   {acc:.4f}")
    print(f"  Precision:  {prec:.4f}")
    print(f"  Recall:     {rec:.4f}")
    print(f"  F1 Score:   {f1:.4f}")
    print(f"  ROC-AUC:    {auc:.4f}")

    # Confusion matrix
    cm = confusion_matrix(y_true, y_pred)
    tn, fp, fn, tp = cm.ravel()
    print(f"\n  Confusion Matrix:")
    print(f"    TN={tn:5d}  FP={fp:5d}")
    print(f"    FN={fn:5d}  TP={tp:5d}")

    # Classification report
    print(f"\n{classification_report(y_true, y_pred)}")

    return {'accuracy': acc, 'precision': prec,
            'recall': rec, 'f1': f1, 'auc': auc}

Complete Binary Classification Pipeline

Problem: Credit Card Fraud Detection

Python
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split, StratifiedKFold
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LogisticRegression
from sklearn.ensemble import RandomForestClassifier, GradientBoostingClassifier
from sklearn.pipeline import Pipeline

# ── 1. Simulate credit card fraud dataset ─────────────────────
np.random.seed(42)
X_fraud, y_fraud = make_classification(
    n_samples=10000,
    n_features=20,
    n_informative=10,
    n_redundant=5,
    weights=[0.97, 0.03],    # 97% legitimate, 3% fraud
    flip_y=0.01,
    random_state=42
)

print(f"Total examples:        {len(y_fraud):,}")
print(f"Legitimate (class 0):  {(y_fraud==0).sum():,} ({(y_fraud==0).mean()*100:.1f}%)")
print(f"Fraud (class 1):       {(y_fraud==1).sum():,} ({(y_fraud==1).mean()*100:.1f}%)")
print(f"\nClass imbalance: {(y_fraud==0).sum() / (y_fraud==1).sum():.0f}:1")

# ── 2. Split ────────────────────────────────────────────────────
X_tr, X_te, y_tr, y_te = train_test_split(
    X_fraud, y_fraud, test_size=0.2,
    random_state=42, stratify=y_fraud    # Preserve class ratio
)

# ── 3. Build and compare multiple classifiers ──────────────────
classifiers = {
    'Logistic Regression': Pipeline([
        ('scaler', StandardScaler()),
        ('clf', LogisticRegression(C=1.0, max_iter=1000))
    ]),
    'Random Forest': Pipeline([
        ('scaler', StandardScaler()),
        ('clf', RandomForestClassifier(n_estimators=100,
                                        max_depth=8,
                                        random_state=42))
    ]),
    'Gradient Boosting': Pipeline([
        ('scaler', StandardScaler()),
        ('clf', GradientBoostingClassifier(n_estimators=100,
                                            learning_rate=0.1,
                                            max_depth=4,
                                            random_state=42))
    ])
}

results = {}
for name, pipe in classifiers.items():
    pipe.fit(X_tr, y_tr)
    y_pred  = pipe.predict(X_te)
    y_prob  = pipe.predict_proba(X_te)[:, 1]
    metrics = evaluate_binary_classifier(y_te, y_pred,
                                          y_prob, name)
    results[name] = {'pipe': pipe, 'y_prob': y_prob,
                     'metrics': metrics}

Comparing ROC Curves

Python
fig, axes = plt.subplots(1, 2, figsize=(14, 5))

# ── ROC curves ─────────────────────────────────────────────────
ax = axes[0]
colors = ['steelblue', 'coral', 'seagreen']

for (name, res), color in zip(results.items(), colors):
    fpr, tpr, _ = roc_curve(y_te, res['y_prob'])
    auc = res['metrics']['auc']
    ax.plot(fpr, tpr, color=color, linewidth=2,
            label=f"{name} (AUC={auc:.3f})")

ax.plot([0, 1], [0, 1], 'k--', linewidth=1, label='Random')
ax.set_xlabel('False Positive Rate')
ax.set_ylabel('True Positive Rate (Recall)')
ax.set_title('ROC Curves — Fraud Detection')
ax.legend(loc='lower right')
ax.grid(True, alpha=0.3)

# ── Precision-Recall curves (better for imbalanced) ────────────
ax = axes[1]
for (name, res), color in zip(results.items(), colors):
    prec_c, rec_c, _ = precision_recall_curve(y_te, res['y_prob'])
    ap = average_precision_score(y_te, res['y_prob'])
    ax.plot(rec_c, prec_c, color=color, linewidth=2,
            label=f"{name} (AP={ap:.3f})")

ax.axhline(y=y_te.mean(), color='black', linestyle='--',
           linewidth=1, label=f'Baseline (={y_te.mean():.3f})')
ax.set_xlabel('Recall')
ax.set_ylabel('Precision')
ax.set_title('Precision-Recall Curves — Fraud Detection\n'
             '(Better metric for imbalanced classes)')
ax.legend()
ax.grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

Threshold Optimization

The default threshold of 0.5 is rarely optimal. Choose it based on your problem’s costs.

Finding the Optimal Threshold

Python
def find_optimal_threshold(y_true, y_prob, metric='f1'):
    """
    Find the decision threshold that maximizes a given metric.

    metric: 'f1', 'recall', 'precision', or custom cost function
    """
    thresholds = np.linspace(0.01, 0.99, 200)
    scores = []

    for t in thresholds:
        y_pred_t = (y_prob >= t).astype(int)
        if metric == 'f1':
            score = f1_score(y_true, y_pred_t, zero_division=0)
        elif metric == 'recall':
            score = recall_score(y_true, y_pred_t, zero_division=0)
        elif metric == 'precision':
            score = precision_score(y_true, y_pred_t, zero_division=0)
        scores.append(score)

    best_idx = np.argmax(scores)
    best_threshold = thresholds[best_idx]
    best_score = scores[best_idx]

    return best_threshold, best_score, thresholds, scores


# Apply to best model (Gradient Boosting)
gb_probs = results['Gradient Boosting']['y_prob']

best_t, best_f1, thresholds, f1_scores = find_optimal_threshold(
    y_te, gb_probs, metric='f1'
)

print(f"Default threshold (0.5) F1: "
      f"{f1_score(y_te, (gb_probs>=0.5).astype(int)):.4f}")
print(f"Optimal threshold ({best_t:.2f}) F1: {best_f1:.4f}")

# Visualise threshold vs metrics
precs, recs, pr_thresholds = precision_recall_curve(y_te, gb_probs)

plt.figure(figsize=(10, 5))
plt.plot(thresholds, f1_scores, 'b-', linewidth=2, label='F1 Score')
# Align precision/recall to same threshold axis
plt.plot(pr_thresholds,
         precs[:-1], 'g--', linewidth=1.5, label='Precision')
plt.plot(pr_thresholds,
         recs[:-1],  'r--', linewidth=1.5, label='Recall')
plt.axvline(x=best_t, color='purple', linestyle=':',
            linewidth=2, label=f'Optimal t={best_t:.2f}')
plt.axvline(x=0.5, color='gray', linestyle=':',
            linewidth=1.5, label='Default t=0.5')
plt.xlabel('Decision Threshold')
plt.ylabel('Score')
plt.title('Metrics vs. Decision Threshold')
plt.legend()
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()

Cost-Based Threshold Selection

Python
def cost_based_threshold(y_true, y_prob,
                          cost_fp=1, cost_fn=5):
    """
    Select threshold minimizing total misclassification cost.

    cost_fp: Cost of a false positive (predict fraud, is legitimate)
    cost_fn: Cost of a false negative (miss actual fraud)
    """
    thresholds = np.linspace(0.01, 0.99, 200)
    costs = []

    for t in thresholds:
        y_pred_t = (y_prob >= t).astype(int)
        cm = confusion_matrix(y_true, y_pred_t)
        tn, fp, fn, tp = cm.ravel()
        total_cost = cost_fp * fp + cost_fn * fn
        costs.append(total_cost)

    best_t = thresholds[np.argmin(costs)]
    print(f"Cost-minimizing threshold: {best_t:.3f}")
    print(f"  FP cost={cost_fp}, FN cost={cost_fn}")
    print(f"  (Fraud missed {cost_fn}x more costly than false alarm)")
    return best_t

# Fraud: missing fraud (FN) is 10x more costly than false alarm (FP)
cost_threshold = cost_based_threshold(y_te, gb_probs,
                                        cost_fp=1, cost_fn=10)

Handling Class Imbalance

Imbalanced datasets — where one class is rare — require special treatment.

Why Imbalance is Problematic

Plaintext
Fraud dataset: 97% legitimate (0), 3% fraud (1)

Naive model: "Always predict 0"
  Accuracy: 97% ← Looks great!
  Fraud caught: 0  ← Completely useless!

The majority class dominates training.
Model learns to predict majority class for everything.

Strategy 1: Adjust Class Weights

Python
from sklearn.linear_model import LogisticRegression

# class_weight='balanced' automatically weights classes
# inversely proportional to their frequency
lr_balanced = Pipeline([
    ('scaler', StandardScaler()),
    ('clf', LogisticRegression(class_weight='balanced',
                                max_iter=1000))
])
lr_balanced.fit(X_tr, y_tr)
y_pred_bal = lr_balanced.predict(X_te)
y_prob_bal = lr_balanced.predict_proba(X_te)[:, 1]

print("With class_weight='balanced':")
print(f"  Recall (fraud):    {recall_score(y_te, y_pred_bal):.4f}")
print(f"  Precision (fraud): {precision_score(y_te, y_pred_bal):.4f}")
print(f"  F1:                {f1_score(y_te, y_pred_bal):.4f}")

Strategy 2: Oversampling (SMOTE)

Python
# pip install imbalanced-learn
from imblearn.over_sampling import SMOTE
from imblearn.pipeline import Pipeline as ImbPipeline

# SMOTE: Synthetic Minority Over-sampling Technique
# Creates synthetic examples of the minority class
smote_pipe = ImbPipeline([
    ('scaler',  StandardScaler()),
    ('smote',   SMOTE(random_state=42)),
    ('clf',     LogisticRegression(max_iter=1000))
])
smote_pipe.fit(X_tr, y_tr)
y_pred_smote = smote_pipe.predict(X_te)
y_prob_smote = smote_pipe.predict_proba(X_te)[:, 1]

print("With SMOTE oversampling:")
print(f"  Recall:    {recall_score(y_te, y_pred_smote):.4f}")
print(f"  Precision: {precision_score(y_te, y_pred_smote):.4f}")
print(f"  F1:        {f1_score(y_te, y_pred_smote):.4f}")

Strategy 3: Undersampling

Python
from imblearn.under_sampling import RandomUnderSampler

# Reduce majority class to balance ratio
under_pipe = ImbPipeline([
    ('scaler',  StandardScaler()),
    ('under',   RandomUnderSampler(sampling_strategy=0.5,
                                    random_state=42)),
    ('clf',     LogisticRegression(max_iter=1000))
])
under_pipe.fit(X_tr, y_tr)

Strategy 4: Use AUC/F1 Instead of Accuracy

Python
# Always evaluate with imbalance-aware metrics
from sklearn.model_selection import cross_val_score

for name, pipe in classifiers.items():
    # F1 score (handles imbalance)
    f1_cv = cross_val_score(pipe, X_fraud, y_fraud,
                             cv=5, scoring='f1').mean()
    # ROC-AUC (threshold-independent)
    auc_cv = cross_val_score(pipe, X_fraud, y_fraud,
                              cv=5, scoring='roc_auc').mean()
    print(f"{name:25s}: F1={f1_cv:.4f}  AUC={auc_cv:.4f}")

Strategy 5: Stratified Sampling

Python
# Always use stratify=y when splitting imbalanced data
X_tr, X_te, y_tr, y_te = train_test_split(
    X_fraud, y_fraud,
    test_size=0.2,
    random_state=42,
    stratify=y_fraud    # Preserves class ratio in both splits
)

print("Training set class ratio:")
print(f"  Class 0: {(y_tr==0).mean()*100:.1f}%")
print(f"  Class 1: {(y_tr==1).mean()*100:.1f}%")

Cross-Validation for Binary Classification

Python
from sklearn.model_selection import StratifiedKFold, cross_validate

# Stratified K-Fold preserves class balance across folds
cv = StratifiedKFold(n_splits=5, shuffle=True, random_state=42)

# Evaluate multiple metrics simultaneously
scoring = {
    'accuracy':  'accuracy',
    'precision': 'precision',
    'recall':    'recall',
    'f1':        'f1',
    'roc_auc':   'roc_auc'
}

best_model = classifiers['Gradient Boosting']
cv_results  = cross_validate(best_model, X_fraud, y_fraud,
                               cv=cv, scoring=scoring)

print("5-Fold Cross-Validation Results (Gradient Boosting):")
for metric, scores in cv_results.items():
    if metric.startswith('test_'):
        name = metric.replace('test_', '')
        print(f"  {name:12s}: {scores.mean():.4f} ± {scores.std():.4f}")

The Probability-vs-Label Decision

A critical design choice: does your application need probabilities or just labels?

When You Need Probabilities

Plaintext
Use case: Fraud risk scoring
  Don't want binary "fraud/not fraud"
  Want "risk score: 89% probability of fraud"
  → Allows prioritization (investigate highest risk first)
  → Allows different thresholds for different contexts

Use case: Medical diagnosis
  Don't want binary "sick/healthy"
  Want "73% probability of disease"
  → Doctor can weigh against clinical judgment
  → Risk communication to patient

When You Need Labels

Plaintext
Use case: Email spam filter
  Just need: "Move to spam? Yes/No"
  Binary label sufficient

Use case: Production alert
  Just need: "Trigger alert? Yes/No"
  Binary action is the end result

Probability Calibration

Some models produce poorly calibrated probabilities — the predicted probability doesn’t match true frequency.

Python
from sklearn.calibration import CalibratedClassifierCV, calibration_curve

# Random Forest: often overconfident (probabilities near 0 or 1)
rf_pipe  = results['Random Forest']['pipe']
rf_probs = results['Random Forest']['y_prob']

# Calibrate using Platt scaling (sigmoid) or isotonic regression
rf_calibrated = CalibratedClassifierCV(
    rf_pipe.named_steps['clf'],
    method='sigmoid',
    cv=5
)
# Note: need to transform X first since we're bypassing pipeline
scaler_standalone = StandardScaler().fit(X_tr)
rf_calibrated.fit(scaler_standalone.transform(X_tr), y_tr)
rf_cal_probs = rf_calibrated.predict_proba(
    scaler_standalone.transform(X_te)
)[:, 1]

# Compare calibration
fig, ax = plt.subplots(figsize=(7, 5))

for probs, label, color in [
        (rf_probs,     'RF (uncalibrated)', 'coral'),
        (rf_cal_probs, 'RF (calibrated)',   'steelblue')]:
    prob_true, prob_pred = calibration_curve(y_te, probs, n_bins=10)
    ax.plot(prob_pred, prob_true, 's-', color=color,
            linewidth=2, label=label)

ax.plot([0, 1], [0, 1], 'k--', linewidth=1.5,
        label='Perfect calibration')
ax.set_xlabel('Mean Predicted Probability')
ax.set_ylabel('Fraction of Positives (True Probability)')
ax.set_title('Calibration Curves')
ax.legend()
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()

Algorithm Selection Guide

AlgorithmData SizeLinearityInterpretabilitySpeedBest Use Case
Logistic Reg.AnyLinear onlyHighVery fastBaseline, interpretable, probabilities needed
Decision TreeSmall-MediumNon-linearHighFastRules needed, mixed features
Random ForestMedium-LargeNon-linearMediumMediumGeneral purpose, tabular data
Gradient BoostingMedium-LargeNon-linearLowSlowMax performance, tabular data
SVMSmall-MediumNon-linear (kernel)LowSlowHigh-dim, text, small data
KNNSmallNon-linearMediumVery slowBaseline, simple problems
Naive BayesAnyLinear (feature indep.)HighVery fastText classification, sparse data
Neural NetworkLargeAny shapeVery lowSlowImages, text, complex patterns

Conclusion: The Building Block of Classification

Binary classification is the foundation of all machine learning classification work. Every concept introduced here — decision boundaries, probability outputs, precision-recall tradeoffs, threshold optimization, class imbalance handling — generalizes directly to multi-class classification, sequence labeling, object detection, and virtually every other classification task.

The most important lessons from this guide:

Accuracy alone is dangerous. With imbalanced classes — which describe most real-world classification problems — accuracy is misleading. A model that predicts the majority class for everything achieves high accuracy while being completely useless. Always evaluate with precision, recall, F1, and ROC-AUC.

Threshold 0.5 is rarely optimal. The default threshold is a starting point, not a decision. Every classification problem has different costs for false positives and false negatives. Tune the threshold based on what matters in your specific application — medical screening demands high recall, fraud alerting may need high precision, and most problems require a deliberate balance.

Class imbalance requires active handling. Don’t let the majority class dominate. Use class weights, SMOTE, stratified sampling, and imbalance-aware metrics to ensure the minority class receives appropriate attention during training.

Probabilities are more valuable than labels. Whenever possible, preserve probability outputs. They enable flexible threshold selection, risk ranking, calibration assessment, and combination with domain knowledge in ways that hard labels never can.

Start simple, then add complexity. Logistic regression is fast, interpretable, and surprisingly powerful. It should be your first classifier on any new problem. Only escalate to Random Forest, Gradient Boosting, or neural networks when logistic regression genuinely falls short.

Binary classification is where machine learning meets real decisions. Master it, and you have the tools to build systems that catch fraud, diagnose diseases, filter spam, and make countless other yes-or-no decisions that create real value in the world.

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