Decision Tree Concepts

This document explains the core concepts behind decision tree models in SQL Server Analysis Services (SSAS) Data Mining.

Introduction

Decision trees are a widely used data mining technique that creates a model in the form of a tree structure. This structure is used to classify or predict outcomes based on a set of input attributes. Each node in the tree represents a test on an attribute, and each branch represents the outcome of the test. The leaves of the tree represent the final classification or prediction.

How Decision Trees Work

Decision tree algorithms work by recursively partitioning the data into subsets based on the values of input attributes. The goal is to create partitions that are as "pure" as possible, meaning that each partition contains data points that are predominantly of the same class or outcome. The algorithm typically uses a measure of impurity, such as Gini impurity or entropy, to determine the best attribute to split on at each node.

The process starts with the entire dataset at the root node. The algorithm selects an attribute that best splits the data, creating child nodes for each possible value or range of values of that attribute. This process is repeated for each child node until a stopping criterion is met, such as:

All data points in a node belong to the same class.
A predefined minimum number of data points are in a node.
A predefined maximum depth of the tree is reached.

Components of a Decision Tree

Root Node: The starting point of the tree, representing the entire dataset.
Internal Nodes (Decision Nodes): Represent a test on an attribute. Each internal node has branches leading to child nodes.
Branches: Represent the possible outcomes or values of the test performed at an internal node.
Leaf Nodes (Terminal Nodes): Represent the final classification or prediction for the data points that reach this node.

Example Structure

Consider a decision tree used to predict whether a customer will purchase a product:

In this example:

The root node might test "Age < 30".
If true, a branch leads to a child node testing "Income > $50,000".
If false (Age ≥ 30), a branch might lead to a leaf node predicting "No Purchase".
Further branches and tests would lead to leaf nodes predicting "Purchase" or "No Purchase".

Algorithm Details

SQL Server Analysis Services typically implements the Microsoft Decision Trees algorithm, which is based on CART (Classification and Regression Trees) principles but offers extensions. Key aspects include:

Splitting Criteria: Uses Gini index by default to measure the purity of a split.
Tree Pruning: Employs strategies to prevent overfitting, ensuring the model generalizes well to new data.
Handling Missing Values: Incorporates methods to deal with incomplete data.
Predictive Capabilities: Can be used for classification (predicting a category) and regression (predicting a numerical value).

Example of Tree Splitting Logic

Imagine a dataset with attributes like 'Age', 'Income', 'Gender', and a target column 'Purchased' (Yes/No).


-- Pseudocode illustrating the concept
IF Age < 25 THEN
    IF Income > 60000 THEN
        RETURN Purchase
    ELSE
        RETURN No Purchase
ELSE IF Age >= 25 AND Age < 50 THEN
    IF Gender = 'Female' THEN
        RETURN Purchase
    ELSE
        RETURN No Purchase
ELSE -- Age >= 50
    RETURN No Purchase

Common Use Cases

Decision trees are versatile and can be applied in various scenarios:

Customer Churn Prediction: Identifying customers likely to leave a service.
Sales Forecasting: Predicting sales volumes based on market conditions and customer demographics.
Fraud Detection: Identifying potentially fraudulent transactions.
Medical Diagnosis: Assisting in diagnosing diseases based on symptoms.
Risk Assessment: Evaluating credit risk for loan applicants.

Interpreting Results

Interpreting a decision tree model involves understanding the sequence of decisions represented by the nodes and branches, and the probability or prediction associated with each leaf node.

Visualizing the decision tree in SQL Server Management Studio (SSMS) or Analysis Services projects is crucial for understanding its structure and the rules it has learned.

Key metrics to consider when evaluating a decision tree model include accuracy, precision, recall, and AUC (Area Under the ROC Curve).

SQL Server Analysis Services Documentation