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Decision Trees: Bias and Variance

 

Decision Trees: Bias and Variance Explained

Quick Recap: What are Decision Trees?

Decision trees are rule-based algorithms that make predictions by asking a series of yes/no questions, splitting data at each node until reaching a decision.

Note: This is not Neural Networks Yet.  We are still talking about Rule Based Systems - that includes "Decision Trees" 




Bias in Decision Trees

Single Decision Trees: Generally LOW BIAS

Decision trees have low bias because they're very flexible and can create complex decision boundaries. They can:

  • Fit almost any pattern in the data
  • Create very detailed rules
  • Capture non-linear relationships easily
  • Keep splitting until they perfectly classify training data

Why Low Bias?

  • They don't make strong assumptions about data structure
  • Can model complex relationships with enough depth
  • Flexible enough to fit training data very closely

Example: If predicting house prices, a deep tree can capture intricate rules like: "IF location=downtown AND bedrooms>3 AND year>2010 AND garage=yes AND school_rating>8 THEN price=high"

Variance in Decision Trees

Single Decision Trees: Generally HIGH VARIANCE

Decision trees have high variance because small changes in training data can create completely different trees.

Why High Variance?

  • Different split points can lead to entirely different tree structures
  • Sensitive to which data points are in training set
  • One different sample at the top can change the entire tree
  • Prone to overfitting on training data

Example: Train on two slightly different datasets of the same problem:

  • Dataset 1: Tree splits first on "Age > 30"
  • Dataset 2: Tree splits first on "Income > 50000" → Completely different tree structures and rules!

The Bias-Variance Profile

Tree Type Bias Variance Problem
Shallow Tree (depth=2-3) HIGH LOW Underfitting
Deep Tree (depth=20+) LOW HIGH Overfitting
Unpruned Tree VERY LOW VERY HIGH Severe Overfitting
Pruned Tree MODERATE MODERATE Balanced

Visual Analogy

Think of it like giving directions:

High Bias (Shallow Tree): "Just go north" - Too simple, misses important turns

High Variance (Deep Tree): "Turn left at the red house with the broken mailbox that the Johnson family painted last Tuesday" - Too specific, won't work if anything changes

Controlling Bias and Variance

To Reduce Variance (usual problem):

  1. Pruning - Cut back overly specific branches
  2. Set minimum samples per leaf
  3. Limit maximum depth
  4. Require minimum samples to split

To Reduce Bias (if tree is too simple):

  1. Increase depth
  2. Reduce minimum samples per leaf
  3. Use more features
  4. Allow more complex splits

Ensemble Methods Solution

Since single trees have high variance, we use ensembles:

Random Forests:

  • Multiple trees with random subsets
  • Reduces variance while keeping low bias
  • Averages out the individual tree variations

Gradient Boosting:

  • Sequential trees that correct errors
  • Reduces both bias and variance
  • Each tree learns from previous mistakes

Real-World Example

Predicting Customer Churn:

Shallow Tree (High Bias):

IF contract_length < 12 months
  THEN predict: CHURN
ELSE predict: STAY

Too simple - misses many patterns

Deep Tree (High Variance):

IF contract=12 AND age=33 AND city="Houston" 
   AND last_call_duration=5.2 minutes 
   AND payment_method="credit" 
   AND joined_on_Tuesday
  THEN predict: CHURN

Too specific - won't generalize

Balanced Tree (Pruned):

IF contract < 12 months AND satisfaction < 3
  THEN predict: CHURN
ELSE IF contract >= 12 AND usage_drop > 50%
  THEN predict: CHURN  
ELSE predict: STAY

Just right - captures patterns without overfitting

Summary

  • Bias: Decision trees naturally have LOW BIAS (very flexible)
  • Variance: Decision trees naturally have HIGH VARIANCE (unstable)
  • Challenge: Controlling the high variance without increasing bias too much
  • Solution: Pruning, regularization, or using ensembles like Random Forests

The key insight: A single decision tree is like a very detailed but unreliable witness - it remembers everything about what it saw (low bias) but might tell a completely different story next time (high variance)!

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