How to Read a Confusion Matrix

                    Predicted Negative   Predicted Positive
Actual Negative  |        TN           |        FP          |
Actual Positive  |        FN           |        TP          |

Rows = actual class
Columns = predicted class
Diagonal = correct predictions
Off-diagonal = errors

from sklearn.metrics import confusion_matrix
import numpy as np

# Warfarin bleeding risk model
# Positive = high bleeding risk (needs dose reduction)
# Negative = normal risk

y_true = np.array([0]*180 + [1]*20)    # 200 patients, 20 high-risk
y_pred = np.array([0]*168 + [1]*12 + [0]*6 + [1]*14)
#                  TN=168   FP=12   FN=6    TP=14

cm = confusion_matrix(y_true, y_pred)
tn, fp, fn, tp = cm.ravel()
print(cm)
# [[168  12]
#  [  6  14]]

# Step 1: Read the diagonal (correct predictions)
print(f"Correctly classified: TN={tn} (safe patients cleared) + TP={tp} (high-risk flagged) = {tn+tp}")

# Step 2: Read the off-diagonal (errors)
print(f"\nErrors:")
print(f"  FP={fp}: {fp} safe patients flagged as high-risk (unnecessary caution)")
print(f"  FN={fn}: {fn} high-risk patients missed (most dangerous error)")

# Step 3: Total counts
total = tn + fp + fn + tp
print(f"\nTotals:")
print(f"  All actual negatives: {tn+fp} ({(tn+fp)/total:.0%})")
print(f"  All actual positives: {fn+tp} ({(fn+tp)/total:.0%})")
print(f"  All predicted negative: {tn+fn} ({(tn+fn)/total:.0%})")
print(f"  All predicted positive: {fp+tp} ({(fp+tp)/total:.0%})")

Warfarin bleeding risk model:

  TN (168): Patient is low-risk, model says low-risk
            → Safe to maintain current dose
            → Correct and no action needed

  TP (14):  Patient is high-risk, model says high-risk
            → Dose reduction recommended
            → Correct — clinical intervention triggered

  FP (12):  Patient is low-risk, model says high-risk
            → Unnecessary dose reduction recommended
            → Outcome: sub-therapeutic anticoagulation, possible clotting event
            → Costly — but at least an action was taken

  FN (6):   Patient is high-risk, model says low-risk
            → No intervention — dose maintained
            → Outcome: patient at risk of bleeding event
            → Most dangerous: no safety net for a patient who needs protection

from sklearn.metrics import confusion_matrix

# Raw counts — useful for understanding scale
cm_raw = confusion_matrix(y_true, y_pred)
print("Raw:\n", cm_raw)

# Normalized by actual class (rows sum to 1.0)
# Tells you: of all actual positives, what fraction was caught?
cm_true = confusion_matrix(y_true, y_pred, normalize="true")
print("Normalized by actual (rows):\n", cm_true.round(3))
# [[0.933, 0.067]  → 93.3% of negatives correctly cleared; 6.7% falsely flagged
#  [0.300, 0.700]] → 70.0% of high-risk patients caught; 30.0% missed

# Normalized by predicted class (columns sum to 1.0)
# Tells you: of all patients flagged as positive, what fraction truly were?
cm_pred = confusion_matrix(y_true, y_pred, normalize="pred")
print("Normalized by predicted (cols):\n", cm_pred.round(3))

# Normalized by total — every cell is fraction of all predictions
cm_all = confusion_matrix(y_true, y_pred, normalize="all")
print("Normalized by total:\n", cm_all.round(3))

# Drug category classification: 4 classes
classes = ["anticoagulant", "antidiabetic", "antihypertensive", "antibiotic"]

y_true = [0, 1, 2, 3, 0, 1, 2, 3, 0, 0, 1, 2, 3, 3, 1, 2]
y_pred = [0, 1, 2, 2, 0, 1, 3, 3, 1, 0, 1, 2, 3, 2, 1, 2]

cm = confusion_matrix(y_true, y_pred)

print("Rows = Actual, Columns = Predicted")
header = "           " + "  ".join(f"{c[:6]:>8}" for c in classes)
print(header)
for i, (row, name) in enumerate(zip(cm, classes)):
    vals = "  ".join(f"{v:>8}" for v in row)
    print(f"{name[:12]:>12}: {vals}")

# How to read:
# Row 0 (anticoagulant): cm[0,0]=correct anticoag, cm[0,1]=anticoag predicted as antidiabetic, ...
# Row 2 (antihypertensive): cm[2,3] — antihypertensives predicted as antibiotics
# This is suspicious: investigate feature overlap between these two classes

import numpy as np

def analyze_confusion_matrix(cm: np.ndarray, class_names: list) -> None:
    n = len(class_names)
    total = cm.sum()

    print("=== Confusion Matrix Analysis ===\n")

    # Per-class accuracy (diagonal / row sum)
    print("Per-class accuracy (recall):")
    for i in range(n):
        row_total = cm[i, :].sum()
        acc = cm[i, i] / row_total if row_total > 0 else 0
        print(f"  {class_names[i]:<20}: {acc:.2%} ({cm[i,i]}/{row_total})")

    # Most confused pairs (off-diagonal)
    print("\nTop confused pairs (off-diagonal errors):")
    errors = []
    for i in range(n):
        for j in range(n):
            if i != j and cm[i, j] > 0:
                errors.append((class_names[i], class_names[j], cm[i, j]))

    for actual, predicted, count in sorted(errors, key=lambda x: -x[2])[:5]:
        print(f"  {actual} → {predicted}: {count} times")

analyze_confusion_matrix(np.array(confusion_matrix(y_true, y_pred)), classes)

import numpy as np
from sklearn.metrics import confusion_matrix

y_proba = model.predict_proba(X_test)[:, 1]

# Lower threshold → more positive predictions → TP and FP increase, FN decreases
print(f"{'Threshold':>10}  {'TN':>6}  {'FP':>6}  {'FN':>6}  {'TP':>6}")
print("-" * 40)
for threshold in [0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8]:
    y_pred_t = (y_proba >= threshold).astype(int)
    tn, fp, fn, tp = confusion_matrix(y_test, y_pred_t).ravel()
    print(f"{threshold:>10.1f}  {tn:>6}  {fp:>6}  {fn:>6}  {tp:>6}")

# As threshold drops: FN shrinks (fewer missed positives), FP grows (more false alarms)
# Pick threshold based on which error is more costly