Code Breakdown and Explanation

This code utilizes libraries for data manipulation, machine learning, and optimization to analyze marketing spend and its impact on incremental revenue through a predictive model. The key components include data preparation, an adstock transformation function, logistic response curve modeling, and optimization of parameters using Nevergrad.

1. Library Imports

# General Libraries
import numpy as np
import pandas as pd

# Machine Learning
from sklearn.ensemble import RandomForestRegressor
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error

# Optimization
import nevergrad as ng

Explanation:

• NumPy and Pandas: Used for numerical and data manipulation tasks, respectively.
• Scikit-learn: Contains tools for creating and evaluating machine learning models (Random Forest).
• Nevergrad: A library for optimization without the need for gradients, which is beneficial for parameter tuning.

2. Function Definitions

2.1 Adstock Transformation

def adstock_transform(spend, decay_rate):
    adstock = np.zeros_like(spend)
    for t in range(len(spend)):
        if t == 0:
            adstock[t] = spend[t]
        else:
            adstock[t] = spend[t] + decay_rate * adstock[t-1]
    return adstock

Explanation:

• Purpose: This function applies an adstock transformation to marketing spend. Adstock is a marketing concept that accounts for the delayed and diminishing effect of advertising over time.
• Parameters:
  • spend: An array representing marketing expenditures.
  • decay_rate: A factor determining how quickly the previous spend effect diminishes.

2.2 Logistic Response Curve

def logistic_response_curve(x, a, b):
    return 1 / (1 + np.exp(-(a * (x - b))))

Explanation:

• Purpose: This function generates a logistic response curve model to represent the relationship between transformed spend and incremental revenue.
• Parameters:
  • x: Independent variable (adstocked spend).
  • a & b: Parameters that define the shape of the curve.

3. Data Preparation

data = pd.DataFrame({
    'Week': np.arange(1, 101),
    'Region': ['Region1'] * 50 + ['Region2'] * 50,
    'Channel1_Spend': np.random.rand(100) * 1000,
    'Channel2_Spend': np.random.rand(100) * 800,
    'Incremental_Revenue': np.random.rand(100) * 1500
})

Explanation:

• DataFrame Creation: A synthetic dataset of 100 weeks is created with two channels of marketing spend and corresponding incremental revenue. Each column represents a different attribute: week number, region, channel-specific spending, and generated revenue.

4. Objective Function for Optimization

def objective_function(params, spend, revenue):
    decay_rate, a, b = params
    adstocked_spend = adstock_transform(spend, decay_rate)
    transformed_spend = logistic_response_curve(adstocked_spend, a, b)

    X = transformed_spend.reshape(-1, 1)
    y = revenue

    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
    model = RandomForestRegressor(n_estimators=100, random_state=42)
    model.fit(X_train, y_train)

    y_pred = model.predict(X_test)
    return mean_squared_error(y_test, y_pred)

Explanation:

• Purpose: The function calculates the mean squared error of the Random Forest model given the parameters of interest (decay rate, a, b).
• Steps:
  • Transform the spend data using adstock_transform.
  • Apply the logistic_response_curve.
  • Split data into training and testing sets.
  • Fit the Random Forest model and predict outcomes.
  • Return the mean squared error (lower is better).

5. Optimization Process

# Initialize optimizer
optimizer = ng.optimizers.NGOpt(parametrization=3, budget=100)

# Define the parameter bounds
parametrization = ng.p.Array(shape=(3,)).set_bounds(lower=[0, 0, 0], upper=[1, 10, 10])

# Define the optimization process
revenue = data['Incremental_Revenue'].values
spend = data['Channel1_Spend'].values

recommendation = optimizer.minimize(lambda x: objective_function(x, spend, revenue))
best_params = recommendation.value

print("Best Parameters found:", best_params)

Explanation:

• Initialization: The optimizer is set to minimize the objective function. The parameter range is defined for decay rate and curve parameters.
• Optimization: The optimizer searches for the best combination of parameters that minimize the model’s mean squared error. This process iterates up to the defined budget.

6. Applying the Best Parameters

# Apply the best parameters found
decay_rate, a, b = best_params
adstocked_spend = adstock_transform(spend, decay_rate)
transformed_spend = logistic_response_curve(adstocked_spend, a, b)

# Prepare the data for Random Forest
X = transformed_spend.reshape(-1, 1)
y = revenue
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Train the Random Forest model
rf_model = RandomForestRegressor(n_estimators=100, random_state=42)
rf_model.fit(X_train, y_train)

# Predict and evaluate
y_pred = rf_model.predict(X_test)
mse = mean_squared_error(y_test, y_pred)

print(f'Mean Squared Error of the Random Forest Model: {mse}')

Explanation:

• Parameter Application: Once optimal parameters are found, the model uses these to transform the spend data again.
• Model Training: A new Random Forest model is trained using the transformed spend data.
• Evaluation: Predictions are made and the model's performance is measured using mean squared error. The final result is printed for observation.

Summary

This code demonstrates a comprehensive approach to building a model to analyze marketing spend's impact on revenue using adstock transformations, logistic response curves, and machine learning optimization techniques. Each section of the code builds on previous components, demonstrating a structured methodology for predictive analytics in marketing.

For further knowledge in data science and practical applications, consider exploring resources from the Enterprise DNA Platform.