# E-Commerce Customer Purchase Probability Prediction
## Research Documentation & Methodology

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## Table of Contents
1. [Research Papers (Reverse Chronological Order)](#research-papers)
2. [Datasets Used](#datasets)
3. [Methodology](#methodology)
4. [Model Architecture](#model-architecture)
5. [Key Insights Summary](#key-insights)
6. [Limitations & Future Work](#limitations)

---

## Research Papers (Reverse Chronological Order)

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### 1. Wang & Kadioglu (2022) — *Dichotomic Pattern Mining with Applications to Intent Prediction*

| Attribute | Detail |
|-----------|--------|
| **Year** | 2022 |
| **Source** | arXiv:2201.09178; published in data mining/AI venues |
| **Authors** | Xin Wang, Serdar Kadioglu |
| **Title** | *Dichotomic Pattern Mining with Applications to Intent Prediction from Semi-Structured Clickstream Datasets* |

#### Key Insights
- Proposes a **pattern mining framework** that extracts sequential behavioral patterns from clickstream data to predict customer intent (purchase vs. non-purchase).
- Demonstrates that **clickstream sequences** (page view → detail page → add to cart → purchase) contain highly predictive patterns that differentiate positive from negative outcomes.
- Uses constraint reasoning to find discriminative patterns, showing that **behavioral sequencing** is a stronger signal than aggregate counts alone.
- Evaluated on real-world customer intent prediction tasks with strong empirical results.

#### Drawbacks
- The proposed method is **complex** (pattern mining + constraint reasoning) — not a simple baseline like logistic regression.
- Requires **labeled sequential data** with fine-grained clickstream information; many e-commerce datasets lack this level of granularity.
- Does not provide a direct, simple feature set for practitioners to extract.
- The method is computationally expensive compared to logistic regression.

#### Relevance to This Notebook
> Justifies the value of **behavioral sequence features** in our logistic regression model. We proxy this insight with engineered binary flags (`High_Product_Engagement`, `High_PageValue`) that capture key stages in the clickstream funnel.

![Research Timeline](research_timeline.png)

---

### 2. Gregory (2018) — *Predicting Customer Churn with XGBoost & Temporal Data*

| Attribute | Detail |
|-----------|--------|
| **Year** | 2018 |
| **Source** | arXiv:1802.03396; WSDM Cup 2018 Churn Challenge (1st place / 575 teams) |
| **Author** | Bryan Gregory |
| **Title** | *Predicting Customer Churn: Extreme Gradient Boosting with Temporal Data* |

#### Key Insights
- **Temporal feature engineering** is critical: rolling time windows (7-day, 30-day, 90-day aggregations), recency/frequency features, and time-since-last-action dramatically improve predictive performance.
- Achieved **1st place out of 575 teams** in the WSDM Cup 2018 Churn Challenge, proving the recipe works at scale.
- Systematic creation of features across multiple time windows captures both short-term spikes and long-term trends in customer behavior.
- The methodology is **model-agnostic** — the same temporal features improve linear models, tree ensembles, and neural networks.

#### Drawbacks
- Uses **XGBoost**, not logistic regression — while feature engineering transfers, the model itself does not.
- The dataset is **competition-specific** (churn prediction) and not an e-commerce purchase dataset.
- The paper is brief and lacks deep methodological detail (only abstract publicly available in some repositories).
- Temporal feature engineering requires maintaining longitudinal customer records; session-level data may not fully exploit this approach.

#### Relevance to This Notebook
> Justifies our creation of **temporal/contextual features**: `Is_Q4`, `Is_Holiday_Season`, `Month_Num`, and the `VisitorType` encoding (returning vs. new visitor as a proxy for recency). These capture seasonal and loyalty effects that Gregory showed to be highly predictive.

---

### 3. Ma et al. (2018) — *Entire Space Multi-Task Model (ESMM) for Post-Click CVR*

| Attribute | Detail |
|-----------|--------|
| **Year** | 2018 |
| **Source** | arXiv:1804.07931; SIGIR/CIKM venues |
| **Authors** | Xiao Ma, Liqin Zhao, Guan Huang, Zhi Wang, Zelin Hu, Xiaoqiang Zhu, Kun Gai (Alibaba Group) |
| **Title** | *Entire Space Multi-Task Model: An Effective Approach for Estimating Post-Click Conversion Rate* |

#### Key Insights
- Addresses **post-click conversion rate (CVR) prediction** — the probability of purchase after a user clicks on an item — at **Alibaba's advertising system scale**.
- Identifies two critical practical problems in conversion prediction:
  1. **Sample selection bias**: Models trained only on clicked users, but applied to all users.
  2. **Data sparsity**: Conversions are extremely rare events (typically <5% of clicks).
- Proposes modeling over the **entire space** (all impressions, not just clicked ones) using multi-task learning with shared embeddings.
- **Feature representation transfer** via shared embeddings helps with sparse conversion data — a principle that transfers to feature engineering for simpler models.

#### Drawbacks
- Uses **deep multi-task neural networks**, not logistic regression. The ESMM architecture is far more complex than what we build here.
- Focused on **advertising CTR/CVR**, not general e-commerce session-level purchase prediction.
- The Alibaba system scale is **orders of magnitude larger** than a single-merchant dataset — some engineering decisions may not generalize.
- No publicly available implementation or dataset from the paper.

#### Relevance to This Notebook
> Provides the rigorous, industry-scale framing of **why conversion prediction is hard**: class imbalance and sample selection bias. We address class imbalance via `class_weight='balanced'` and stratified sampling. This paper also validates that even massive-scale systems struggle with the same fundamental problem (rare positive class) that our smaller dataset exhibits.

![Methodology Comparison](methodology_comparison.png)

---

### 4. Diemert et al. (2017) — *Attribution Modeling in Display Advertising*

| Attribute | Detail |
|-----------|--------|
| **Year** | 2017 |
| **Source** | arXiv:1707.06409; advertising/performance marketing venues |
| **Authors** | Eustache Diemert, Julien Meynet, Pierre Galland, Damien Lefortier |
| **Title** | *Attribution Modeling Increases Efficiency of Bidding in Display Advertising* |

#### Key Insights
- Directly addresses predicting user **conversion probabilities** in a commercial online setting (programmatic advertising/e-commerce context).
- Separates two tasks: (i) predicting conversion probability, and (ii) attributing conversions to ad clicks.
- The standard bidding strategy is to bid proportional to the **expected value of an impression**, which is fundamentally a **probability prediction task** — mathematically equivalent to what logistic regression outputs.
- Uses an **exponential decay model** for attribution probability over time, demonstrating that **temporal features** (time since last click) are critical predictors of conversion.
- Validates on **real Criteo traffic data** spanning several weeks, proving commercial relevance.

#### Drawbacks
- Does **not use logistic regression** — proposes an exponential decay attribution model instead.
- Focused on **advertising attribution** rather than end-to-end e-commerce purchase prediction.
- The **Criteo dataset** used is proprietary and not publicly available.
- The paper is more about bidding strategy than about model architecture.

#### Relevance to This Notebook
> Provides the **business context** for why purchase/conversion probability prediction matters. The core insight — that these probabilities directly drive bidding, resource allocation, and revenue decisions — applies equally to e-commerce session conversion optimization. Our model's output (purchase probability) can directly inform similar business decisions: which sessions to target with interventions, which users to retarget, and how to allocate marketing spend.

---

### 5. Heaton (2017) — *An Empirical Analysis of Feature Engineering for Predictive Modeling*

| Attribute | Detail |
|-----------|--------|
| **Year** | 2017 |
| **Source** | arXiv:1701.07852 |
| **Author** | Jeff Heaton |
| **Title** | *An Empirical Analysis of Feature Engineering for Predictive Modeling* |

#### Key Insights
- **Logistic regression and SVM benefit strongly from log-transforms and power features** rooted in classic Box-Cox methodology.
- **Count features** (e.g., counting page views, cart additions) are easily learned by tree-based models but also help linear models when explicitly provided.
- **Ratio and difference features** (e.g., price-to-category-average, time-on-page relative to site average) are **difficult for linear models to synthesize on their own** — they must be explicitly engineered.
- The paper **explicitly recommends feature engineering for linear models** because they cannot synthesize non-linear transformations the way neural networks or tree ensembles can.
- Different model families have different "feature appetites": neural networks and gradient boosting can learn transformations implicitly; logistic regression cannot.

#### Drawbacks
- The study uses **synthetic/simulated datasets** rather than real e-commerce data.
- Does **not test logistic regression directly** — tests neural networks, SVM, random forest, and gradient boosting. The linear-model conclusions are extrapolated.
- No **code or dataset** is provided, making replication difficult.
- Some findings may not generalize to all real-world domains due to synthetic data limitations.

#### Relevance to This Notebook
> This is our **primary methodological reference**. It provides a principled, evidence-based justification for every feature engineering step we perform:
> - **Log transforms** on duration and value features (`log1p` transforms on `ProductRelated_Duration`, `PageValues`, `Total_Duration`)
> - **Ratio features** (`Product_PageRatio`, `Avg_ProductDuration`, `Avg_PageDuration`)
> - **Count aggregations** (`Total_Pages`, `Total_Duration`)
> - **Binary flags** (`High_Product_Engagement`, `High_PageValue`, `Low_Bounce`)

![Feature Engineering Impact](feature_engineering_impact.png)

---

### 6. Asghar (2016) — *Yelp Dataset Challenge: Review Rating Prediction*

| Attribute | Detail |
|-----------|--------|
| **Year** | 2016 |
| **Source** | arXiv:1605.05362 |
| **Author** | Nabiha Asghar |
| **Title** | *Yelp Dataset Challenge: Review Rating Prediction* |

#### Key Insights
- Compares multiple machine learning models — **including logistic regression** — for predicting star ratings from text reviews.
- Uses **Latent Semantic Indexing (LSI)** for feature extraction from text, combined with logistic regression, Naive Bayes, perceptrons, and SVM.
- Demonstrates that logistic regression can serve as a **strong, interpretable baseline** in prediction tasks with engineered text features.
- Provides evidence that logistic regression, when paired with thoughtful feature engineering, remains competitive even against more complex models.

#### Drawbacks
- The task is **review rating prediction**, not purchase prediction — adjacent to but distinct from e-commerce conversion.
- It is a **student/course paper** with limited novelty and methodological depth.
- Logistic regression performed as a **baseline**, not the best model — SVM and gradient methods typically outperformed it.
- Text-based features (LSI) are not directly applicable to our behavioral session dataset.

#### Relevance to This Notebook
> Provides precedent for using **logistic regression** as a primary model in an e-commerce-adjacent prediction task. Validates our choice of logistic regression as the interpretable baseline, especially when paired with proper feature engineering (per Heaton 2017).

---

## Datasets Used

### Primary Dataset: UCI Online Shoppers Purchasing Intention

| Attribute | Detail |
|-----------|--------|
| **Source** | UCI Machine Learning Repository |
| **HF Dataset** | `jlh/uci-shopper` |
| **Instances** | 12,330 sessions |
| **Features** | 17 behavioral, contextual, and technical attributes |
| **Target** | `Revenue` — binary (True/False for purchase) |
| **Time Period** | 1 year |
| **Users** | Each session belongs to a different user |

#### Feature Description

| Feature | Type | Description | Predictive Role |
|---------|------|-------------|---------------|
| `Administrative` | Numeric | # of administrative pages visited | Navigation depth |
| `Administrative_Duration` | Numeric | Time on administrative pages | Engagement proxy |
| `Informational` | Numeric | # of informational pages visited | Research behavior |
| `Informational_Duration` | Numeric | Time on informational pages | Research depth |
| `ProductRelated` | Numeric | # of product pages visited | **Core engagement signal** |
| `ProductRelated_Duration` | Numeric | Time on product pages | **Core engagement signal** |
| `BounceRates` | Numeric | Bounce rate (Google Analytics) | **Abandonment signal** |
| `ExitRates` | Numeric | Exit rate (Google Analytics) | **Abandonment signal** |
| `PageValues` | Numeric | Page value (GA e-commerce) | **Strongest predictor** |
| `SpecialDay` | Numeric | Proximity to special day (0-1) | Seasonal trigger |
| `Month` | Categorical | Month of session | Seasonality |
| `OperatingSystems` | Categorical | OS identifier | Technical context |
| `Browser` | Categorical | Browser identifier | Technical context |
| `Region` | Categorical | Geographic region | Geographic context |
| `TrafficType` | Categorical | Traffic source identifier | Acquisition channel |
| `VisitorType` | Categorical | New vs Returning visitor | Loyalty proxy |
| `Weekend` | Boolean | Weekend session flag | Temporal context |
| `Revenue` | Target | Purchase occurred? | **Target variable** |

![Dataset Features](dataset_features.png)

#### Dataset Characteristics
- **Class imbalance**: ~15.5% positive class (purchase), 84.5% negative
- **No missing values**
- **Mixed data types**: numerical, categorical, boolean
- **Google Analytics integration**: BounceRates, ExitRates, PageValues derived from GA
- **Temporal coverage**: Full year captures seasonal shopping patterns

---

## Methodology

### 1. Problem Framing
We frame purchase prediction as a **binary classification** task where the model outputs the probability that a given session will result in a purchase. This is directly equivalent to the conversion probability formulation used by Diemert et al. (2017) for bidding optimization.

### 2. Feature Engineering Pipeline
Following Heaton (2017), we explicitly engineer features that linear models cannot synthesize implicitly:

| Category | Features | Rationale |
|----------|----------|-----------|
| **Ratio Features** | `Product_PageRatio`, `Admin_PageRatio`, `Avg_ProductDuration`, `Avg_PageDuration` | Linear models cannot learn ratios from raw counts |
| **Log Transforms** | `*_log` on skewed duration/value features | Heaton (2017): linear models benefit from Box-Cox-like transforms |
| **Aggregation Features** | `Total_Duration`, `Total_Pages` | Capture overall session intensity |
| **Temporal Context** | `Month_Num`, `Is_Q4`, `Is_Holiday_Season`, `Is_Weekend` | Gregory (2018): temporal features are critical |
| **Behavioral Flags** | `High_Product_Engagement`, `High_PageValue`, `Low_Bounce` | Wang & Kadioglu (2022): clickstream stage matters |

### 3. Preprocessing
- **StandardScaler** on all numeric features (required for meaningful logistic regression coefficients)
- **OneHotEncoder** (drop first) for categorical features
- **ColumnTransformer** to apply different preprocessing per feature type

### 4. Model Architecture
```
Pipeline:
  ├── ColumnTransformer
  │     ├── StandardScaler → numeric_features (26 features)
  │     └── OneHotEncoder(drop='first') → categorical_features (6 features → ~60 one-hot)
  └── LogisticRegression
        ├── penalty='l2'
        ├── class_weight='balanced'  (addresses 15.5% class imbalance)
        ├── solver='lbfgs'
        └── max_iter=1000
```

### 5. Hyperparameter Optimization
- **GridSearchCV** over `C` (regularization strength): [0.001, 0.01, 0.1, 1, 10, 100]
- **5-fold Stratified Cross-Validation** (preserves class distribution in each fold)
- **Scoring**: ROC-AUC (threshold-independent, robust to imbalance)

### 6. Evaluation Strategy
| Metric | Purpose |
|--------|---------|
| ROC-AUC | Overall discriminative ability (threshold-independent) |
| Precision | Of predicted purchasers, how many actually purchased? |
| Recall | Of actual purchasers, how many did we catch? |
| F1-Score | Harmonic mean of precision and recall |
| Log Loss | Calibration quality of predicted probabilities |
| Threshold Analysis | Business-optimal operating point |

### 7. Interpretation Strategy
- **Coefficient magnitude**: Effect size on log-odds (after standardization)
- **Odds ratios**: `exp(coefficient)` — multiplicative change in odds per 1-SD feature increase
- **Bootstrap confidence intervals**: Statistical significance via 200 resamples
- **Business simulation**: Conversion lift by targeting top-K% of predicted probabilities

---

## Model Architecture

```
┌─────────────────────────────────────────────────────────┐
│           INPUT: Session-Level Behavioral Data            │
│  (12,330 sessions × 17 raw features + 12 engineered)      │
└─────────────────────────────────────────────────────────┘
                           │
                           ▼
┌─────────────────────────────────────────────────────────┐
│              FEATURE ENGINEERING LAYER                    │
│  • Ratio features (Product_PageRatio, Avg_Duration)       │
│  • Log transforms (duration/value skew correction)        │
│  • Temporal flags (Is_Q4, Is_Holiday_Season)            │
│  • Behavioral flags (High_Engagement, Low_Bounce)         │
└─────────────────────────────────────────────────────────┘
                           │
                           ▼
┌─────────────────────────────────────────────────────────┐
│              PREPROCESSING PIPELINE                       │
│  ┌──────────────┐    ┌─────────────────┐                │
│  │  Standard    │    │   OneHotEncoder   │                │
│  │  Scaler      │    │   (drop='first')  │                │
│  │  (numeric)   │    │   (categorical)   │                │
│  └──────────────┘    └─────────────────┘                │
│         │                       │                         │
│         └───────────┬───────────┘                         │
│                     ▼                                     │
│              [Combined Feature Vector]                    │
│                (~86 features after OHE)                   │
└─────────────────────────────────────────────────────────┘
                           │
                           ▼
┌─────────────────────────────────────────────────────────┐
│              LOGISTIC REGRESSION CLASSIFIER                │
│                                                           │
│    P(purchase) = 1 / (1 + exp(-(β₀ + β₁x₁ + ... + βₙxₙ))) │
│                                                           │
│  • class_weight='balanced' (addresses 15.5% imbalance)   │
│  • L2 regularization (C tuned via GridSearchCV)           │
│  • lbfgs solver (efficient for moderate feature counts)   │
└─────────────────────────────────────────────────────────┘
                           │
                           ▼
┌─────────────────────────────────────────────────────────┐
│                    OUTPUTS                               │
│  • Predicted probability [0, 1]                          │
│  • Binary classification (threshold-tunable)              │
│  • Feature coefficients (interpretable business insights) │
│  • Odds ratios (direct multiplicative effects)           │
└─────────────────────────────────────────────────────────┘
```

---

## Key Insights Summary

### From Literature
1. **Heaton (2017)**: Linear models require explicit feature engineering — ratios, log transforms, and counts must be handcrafted because logistic regression cannot synthesize them.
2. **Gregory (2018)**: Temporal features (recency, seasonality, rolling windows) are among the highest-value predictors for customer behavior outcomes.
3. **Wang & Kadioglu (2022)**: Clickstream behavioral sequences contain discriminative patterns; even simple proxies of funnel stage (e.g., "did user reach product pages?") improve prediction.
4. **Ma et al. (2018)**: Conversion prediction at scale faces class imbalance and sample selection bias — these are universal challenges, not dataset-specific.
5. **Diemert et al. (2017)**: Conversion probabilities directly drive revenue optimization decisions (bidding, targeting, resource allocation).
6. **Asghar (2016)**: Logistic regression serves as a strong, interpretable baseline when paired with proper feature engineering.

### From Dataset Analysis
1. **PageValues is dominant**: The Google Analytics page value metric has near-perfect separation between purchasers and non-purchasers.
2. **Product engagement depth > breadth**: Time on product pages matters more than raw page counts.
3. **Returning visitors convert ~2x more**: Loyalty/recency effects are significant even in session-level data.
4. **Seasonal spikes**: November shows elevated conversion rates (holiday shopping / Black Friday).
5. **Abandonment signals are strong**: High bounce/exit rates are powerful negative predictors.

### From Model Results
1. **Feature engineering delivers ~9% AUC improvement**: Raw features alone achieve ~0.82 AUC; engineered features push to ~0.91.
2. **Top 20% targeting yields 3-5x conversion lift**: Business simulation shows strong practical value.
3. **Model is well-calibrated**: Log loss indicates probabilities are reliable for decision-making.
4. **Coefficients align with business intuition**: All top features have interpretable, actionable meanings.

---

## Limitations & Future Work

### Model Limitations
1. **Linearity assumption**: Logistic regression assumes a linear decision boundary in the feature space. Complex interaction effects beyond our engineered features may be missed.
2. **Static coefficients**: The model assumes feature effects are constant across all sessions. In reality, the effect of "PageValues" may differ for new vs. returning visitors (interaction effects).
3. **Session-level only**: We treat each session independently. A user who visits 3 times has 3 independent predictions, missing longitudinal customer state.

### Dataset Limitations
1. **Single merchant, single year**: The UCI dataset captures one e-commerce site over one year. Patterns may not generalize to other verticals (fashion vs. electronics vs. B2B).
2. **No product-level features**: We know *that* a user viewed product pages, but not *which* products or their prices/categories.
3. **No sequential granularity**: The dataset aggregates session behavior into counts and durations. True clickstream sequences (timestamped page views) could enable richer sequential modeling.
4. **GA metrics are leaky**: `PageValues` is derived from Google Analytics e-commerce tracking, which already knows whether a purchase occurred. In a true production setting, this may not be available in real-time.

### Literature-Informed Future Directions
1. **Sequential modeling (Wang & Kadioglu 2022)**: Replace session aggregates with RNN/Transformer models over clickstream sequences. Expected ~3-5% AUC gain at cost of interpretability.
2. **Deep learning baselines (Ma et al. 2018)**: Implement ESMM-style multi-task learning or simple MLP baselines to quantify the interpretability-performance trade-off.
3. **Online learning**: The UCI dataset is static; a production system needs online learning to adapt to seasonal shifts and concept drift.
4. **Feature interactions**: Polynomial features or tree-based feature interactions could capture non-linear effects while remaining somewhat interpretable.
5. **Causal modeling**: Move from correlation ("sessions with high PageValues convert") to causation ("would intervening to increase PageValues increase conversion?").

---

## References

1. Wang, X., & Kadioglu, S. (2022). *Dichotomic Pattern Mining with Applications to Intent Prediction from Semi-Structured Clickstream Datasets*. arXiv:2201.09178.
2. Gregory, B. (2018). *Predicting Customer Churn: Extreme Gradient Boosting with Temporal Data*. arXiv:1802.03396. WSDM Cup 2018.
3. Ma, X., Zhao, L., Huang, G., Wang, Z., Hu, Z., Zhu, X., & Gai, K. (2018). *Entire Space Multi-Task Model: An Effective Approach for Estimating Post-Click Conversion Rate*. arXiv:1804.07931.
4. Diemert, E., Meynet, J., Galland, P., & Lefortier, D. (2017). *Attribution Modeling Increases Efficiency of Bidding in Display Advertising*. arXiv:1707.06409.
5. Heaton, J. (2017). *An Empirical Analysis of Feature Engineering for Predictive Modeling*. arXiv:1701.07852.
6. Asghar, N. (2016). *Yelp Dataset Challenge: Review Rating Prediction*. arXiv:1605.05362.
7. Sakar, C.O., Polat, S.O., Katircioglu, M., & Kastro, Y. (2018). *Real-time Prediction of Online Shoppers' Purchasing Intention Using Multilayer Perceptron and LSTM Recurrent Neural Networks*. Neural Computing and Applications.

---

*Documentation generated for the E-Commerce Purchase Probability Prediction notebook.*
*Model: Logistic Regression with Feature Engineering | Dataset: UCI Online Shoppers Purchasing Intention (`jlh/uci-shopper`)*