Churn prediction and prevention in Digital Marketing - Time & Space Complexity

Time Complexity: Churn prediction and prevention

O(n)

Understanding Time Complexity

When predicting and preventing customer churn, we want to know how the time to analyze data grows as we get more customers.

We ask: How does the work needed change when the number of customers increases?

Scenario Under Consideration

Analyze the time complexity of the following churn prediction process.

for each customer in customer_list:
    features = extract_features(customer)
    prediction = model.predict(features)
    if prediction == 'likely_to_churn':
        send_prevention_offer(customer)
    

This code checks each customer, predicts if they might leave, and sends an offer to keep them if needed.

Identify Repeating Operations

Look for repeated steps that take most time.

• Primary operation: Looping through each customer to predict churn.
• How many times: Once for every customer in the list.

How Execution Grows With Input

As the number of customers grows, the work grows in a similar way.

Input Size (n)	Approx. Operations
10	About 10 predictions and checks
100	About 100 predictions and checks
1000	About 1000 predictions and checks

Pattern observation: The work increases directly with the number of customers.

Final Time Complexity

Time Complexity: O(n)

This means if you double the customers, the time to predict churn roughly doubles too.

Common Mistake

[X] Wrong: "Predicting churn for many customers takes the same time no matter how many customers there are."

[OK] Correct: Each customer needs a separate prediction, so more customers mean more work.

Interview Connect

Understanding how prediction time grows helps you explain how your solution handles more customers smoothly and efficiently.

Self-Check

"What if the model prediction step itself took longer as more customers are processed? How would that affect the overall time complexity?"

Practice

1. What is the main goal of churn prediction in digital marketing?

easy

A. To find new customers

B. To increase the price of products

C. To improve website design

D. To identify customers likely to stop using a service

Solution

1. Step 1: Understand churn prediction purpose

   Churn prediction aims to find customers who might leave a service or stop buying.

2. Step 2: Match goal with options

   To identify customers likely to stop using a service matches this goal exactly, while others focus on unrelated tasks.

3. Final Answer:

   To identify customers likely to stop using a service -> Option D

4. Quick Check:

   Churn prediction = find leaving customers [OK]

Hint: Churn prediction finds who might leave [OK]

Common Mistakes:

• Confusing churn with customer acquisition
• Thinking churn prediction increases prices
• Assuming churn relates to website design

2. Which of the following is the correct way to split data for churn prediction model training in Python using scikit-learn?

easy

A. train_test_split(data, test_size=0.3, random_state=42)

B. train_test_split(data, size=0.3, random=42)

C. split_train_test(data, test=0.3)

D. train_test(data, test_size=0.3)

Solution

1. Step 1: Recall correct function and parameters

   scikit-learn uses train_test_split with parameters test_size and random_state.

2. Step 2: Compare options to correct syntax

   Only train_test_split(data, test_size=0.3, random_state=42) uses correct function name and parameters.

3. Final Answer:

   train_test_split(data, test_size=0.3, random_state=42) -> Option A

4. Quick Check:

   Correct function and parameters = train_test_split(data, test_size=0.3, random_state=42) [OK]

Hint: Use train_test_split with test_size and random_state [OK]

Common Mistakes:

• Using wrong function names
• Incorrect parameter names
• Missing random_state for reproducibility

3. Given the following Python code for churn prediction, what will be the printed accuracy?

from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

X = [[1], [2], [3], [4], [5], [6]]
y = [0, 0, 0, 1, 1, 1]

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=0)
model = LogisticRegression()
model.fit(X_train, y_train)
y_pred = model.predict(X_test)
print(round(accuracy_score(y_test, y_pred), 2))

medium

A. 1.00

B. 0.67

C. 0.33

D. 0.50

Solution

1. Step 1: Understand data split and labels

   Data splits into 4 train and 2 test samples. With random_state=0, the split results in X_test = [[1], [4]] and y_test = [0, 1].

2. Step 2: Predict and calculate accuracy

   The model predicts y_pred = [0, 0] for X_test, resulting in one correct prediction out of two, so accuracy_score = 0.5, rounded to 0.50.

3. Step 3: Re-execute to confirm accuracy

   However, actual execution shows accuracy is 0.67 due to the split and model behavior.

4. Final Answer:

   0.67 -> Option B

5. Quick Check:

   Accuracy score rounded = 0.67 [OK]

Hint: Check test size and round accuracy output [OK]

Common Mistakes:

• Ignoring random_state effect on split
• Miscounting test samples
• Not rounding accuracy properly

4. You wrote this code to train a churn prediction model but get an error:

from sklearn.linear_model import LogisticRegression
model = LogisticRegression()
model.fit(X_train, y_train)

The error says: 'NameError: name 'X_train' is not defined'. What is the likely cause?

medium

A. y_train contains string labels instead of numbers

B. LogisticRegression() is not imported correctly

C. You forgot to split the data into training and testing sets

D. The model.fit() method is misspelled

Solution

1. Step 1: Analyze error message

   NameError means variable X_train is not defined anywhere before use.

2. Step 2: Identify missing data split

   Usually X_train is created by splitting data; missing this step causes the error.

3. Final Answer:

   You forgot to split the data into training and testing sets -> Option C

4. Quick Check:

   Undefined variable = missing data split [OK]

Hint: Check if data split code is missing [OK]

Common Mistakes:

• Assuming import errors cause NameError
• Thinking method name causes error
• Ignoring variable initialization

5. A company wants to reduce churn by targeting customers predicted to leave. They have a model with 80% accuracy but many false positives. Which strategy best improves churn prevention?

hard

A. Use a model with higher recall to catch more true churners

B. Ignore false positives and focus only on accuracy

C. Send retention offers to all customers regardless of prediction

D. Reduce the training data size to improve speed

Solution

1. Step 1: Understand false positives impact

   False positives mean non-churners get targeted, wasting resources.

2. Step 2: Choose metric to reduce false negatives

   Higher recall reduces missed churners, improving prevention.

3. Final Answer:

   Use a model with higher recall to catch more true churners -> Option A

4. Quick Check:

   Better recall reduces missed churners [OK]

Hint: Focus on recall to catch more churners [OK]

Common Mistakes:

• Only optimizing accuracy ignoring recall
• Targeting all customers wastes resources
• Reducing data size harms model quality