Designing Trustworthy ML Models: Alan & Aida Discover Monotonicity in Machine Learning

Machine studying fashions are highly effective, however typically they produce predictions that break human instinct.

Think about this: you’re predicting home costs. A 2,000 sq. ft. house is predicted cheaper than a 1,500 sq. ft. residence. Sounds unsuitable, proper?

That is the place monotonicity constraints step in. They ensure that fashions observe the logical enterprise guidelines we anticipate.

Let’s observe two colleagues, Alan and Aida, on their journey to find why monotonicity issues in machine studying.

The Story: Alan & Aida’s Discovery

Alan is a sensible engineer. Aida is a principled scientist. Collectively, they’re constructing a home value prediction mannequin.

Alan proudly reveals Aida his mannequin outcomes:

“Look! R² is nice, the error is low. We’re able to deploy!”

Aida takes the mannequin out for testing: 

• For a home with 1500 sq ft → Mannequin predicts $300,000
• For a home with 2000 sq ft → Mannequin predicts $280,000 😮

Aida frowns as she appears to be like on the predictions:

“Wait a second… Why is that this 2,000 sq. ft. residence predicted cheaper than a 1,500 sq. ft. residence? That doesn’t make sense.”

Alan shrugs:

“That’s as a result of the mannequin discovered noise within the coaching knowledge. It’s not all the time logical. However, the accuracy is nice general. Isn’t that sufficient?”

Aida shakes her head:

“Probably not. A reliable mannequin should not solely be correct but in addition observe logic individuals can belief. Clients gained’t belief us if greater properties typically look cheaper. We want a assure. This can be a monotonicity downside.”

And similar to that, Alan learns his subsequent large ML lesson: metrics aren’t the whole lot.

What’s Monotonicity in ML?

Aida explains:

“Monotonicity means predictions transfer in a constant path as inputs change. It’s like telling the mannequin: as sq. footage goes up, value ought to by no means go down. We name it Monotone rising. Or, as one other instance, as a home age will get older, predicted costs mustn’t go up. We name this Monotone lowering.”

Alan concludes that: 

“So monotonicity right here issues as a result of it:

• Aligns with enterprise logic, and
• Improves belief & interpretability.”

Aida nodded:

• “Sure, Plus, it helps meet equity & regulatory expectations.”

Visualizing the Drawback

Aida creates a toy dataset in Pandas to point out the issue:

import pandas as pd

# Instance toy dataset
knowledge = pd.DataFrame({
   "sqft": [1200, 1500, 1800, 2000, 2200, 2250],
   "predicted_price": [250000, 270000, 260000, 280000, 290000, 285000]  # Discover dip at 1800 sqft and 2250 sqft
})

# Kind by sqft
data_sorted = knowledge.sort_values("sqft")

# Verify variations in goal
data_sorted["price_diff"] = data_sorted["predicted_price"].diff()

# Discover monotonicity violations (the place value decreases as sqft will increase)
violations = data_sorted[data_sorted["price_diff"] < 0]
print("Monotonicity violations:n", violations)

Monotonicity violations:
    sqft   value  price_diff
2  1800  260000    -10000.0
5  2250  285000     -5000.0

After which she plots the violations:

import matplotlib.pyplot as plt
plt.determine(figsize=(7,5))
plt.plot(knowledge["sqft"], knowledge["predicted_price"], marker="o", linestyle="-.", shade="steelblue", label="Predicted Worth")


# Spotlight the dips
for sqft, value, price_diff in violations.values:
 plt.scatter(sqft, value, shade="crimson", zorder=5)
 plt.textual content(x=sqft, y=price-3000, s="Dip!", shade="crimson", ha="middle")


# Labels and title
plt.title("Predicted Home Costs vs. Sq. Footage")
plt.xlabel("Sq. Footage (sqft)")
plt.ylabel("Predicted Worth ($)")
plt.grid(True, linestyle="--", alpha=0.6)
plt.legend()

Aida factors to the Dips: “Right here’s the issue: 1,800 sq. ft. is priced decrease than 1,500 sq. ft. and a couple of,250 sq. ft. is priced decrease than 2,200 sq. ft.”

Fixing It with Monotonicity Constraints in XGBoost

Alan retrains the mannequin and units a monotonic rising constraint on sq. footage and monotonic lowering constraint on home age.
This forces the mannequin to all the time 

• improve (or keep the identical) when sq. footage will increase given all different options are mounted. 
• lower (or keep the identical) when home age will increase given all different options are mounted. 

He makes use of XGBoost that makes it simple to implement monotonicity:

import xgboost as xgb
from sklearn.model_selection import train_test_split

df = pd.DataFrame({
   "sqft": [1200, 1500, 1800, 2000, 2200],
   "house_age": [30, 20, 15, 10, 5],
   "value": [250000, 270000, 280000, 320000, 350000]
})

X = df[["sqft", "house_age"]]
y = df["price"]

X_train, X_test, y_train, y_test = train_test_split(X, y, 
                                    test_size=0.2, random_state=42)

monotone_constraints = {
   "sqft": 1,        # Monotone rising
   "house_age": -1   # Monotone lowering
}

mannequin = xgb.XGBRegressor(
   monotone_constraints=monotone_constraints,
   n_estimators=200,
   learning_rate=0.1,
   max_depth=4,
   random_state=42
)

mannequin.match(X_train, y_train)

print(X_test)
print("Predicted value:", mannequin.predict(X_test.values))

  sqft  house_age
1  1500         20
Predicted value: [250000.84]

Alan fingers over the brand new mannequin to Aida. “Now the mannequin respects area data. Predictions for bigger homes won’t ever dip beneath smaller ones.”

Aida assessments the mannequin once more:

• 1500 sq ft → $300,000
• 2000 sq ft → $350,000
• 2500 sq ft → $400,000

Now she sees a smoother plot of home costs vs sq. footage.

import matplotlib.pyplot as plt

data2 = pd.DataFrame({
  "sqft": [1200, 1500, 1800, 2000, 2200, 2250],
  "predicted_price": [250000, 270000, 275000, 280000, 290000, 292000]
})

plt.determine(figsize=(7,5))
plt.plot(data2["sqft"], data2["predicted_price"], marker="o", 
                     linestyle="-.", shade="inexperienced", label="Predicted Worth")

plt.title("Monotonic Predicted Home Costs vs. Sq. Footage")
plt.xlabel("Sq. Footage (sqft)")
plt.ylabel("Predicted Worth ($)")
plt.grid(True, linestyle="--", alpha=0.6)
plt.legend()

Aida: “Excellent! When properties are of the identical age, a bigger measurement constantly results in a better or equal value. Conversely, properties of the identical sq. footage will all the time be priced decrease if they’re older.”

Alan: “Sure — we gave the mannequin guardrails that align with area data.”

Actual-World Examples

Alan: what different domains can profit from monotonicity constraints? 

Aida: Wherever prospects or cash are concerned, monotonicity can influence belief. Some domains the place monotonicity actually issues are:

• Home pricing → Bigger properties shouldn’t be priced decrease.
• Mortgage approvals → Increased revenue mustn’t scale back approval likelihood.
• Credit score scoring → Longer reimbursement historical past mustn’t decrease the rating.
• Buyer lifetime worth (CLV) → Extra purchases shouldn’t decrease CLV predictions.
• Insurance coverage pricing → Extra protection mustn’t scale back the premium.

Takeaways

• Accuracy alone doesn’t assure trustworthiness.
• Monotonicity ensures predictions align with widespread sense and enterprise guidelines.
• Clients, regulators, and stakeholders usually tend to settle for and use fashions which might be each correct and logical.

As Aida reminds Alan:

“Make fashions not simply sensible, however wise.”

Closing Ideas

Subsequent time you construct a mannequin, don’t simply ask: How correct is it? Additionally ask: Does it make sense to the individuals who’ll use it?

Monotonicity constraints are one in every of many instruments for designing reliable ML fashions — alongside explainability, equity constraints, and transparency.

. . .

Thanks for studying! I usually share insights on sensible AI/ML strategies—let’s join on LinkedIn when you’d wish to proceed the dialog.