Data distributions and outliers in ML Python - Model Metrics & Evaluation

Metrics & Evaluation - Data distributions and outliers

Which metric matters for this concept and WHY

When working with data distributions and outliers, key metrics include mean, median, standard deviation, and interquartile range (IQR). These help us understand the center and spread of data.

Outliers are data points far from the main distribution. Metrics like Z-score or IQR-based fences help detect them.

Why? Because outliers can distort averages and affect model training. Using median and IQR is better when outliers exist, as they are less sensitive to extreme values.

Confusion matrix or equivalent visualization (ASCII)

Data distribution example (sorted values):

10, 12, 13, 14, 15, 16, 17, 18, 19, 100

Mean = (10+12+...+19+100)/10 = 23.4
Median = (15+16)/2 = 15.5

Outlier detection using IQR:
Q1 (25th percentile) = 13.25
Q3 (75th percentile) = 18.25
IQR = Q3 - Q1 = 5

Lower fence = Q1 - 1.5*IQR = 13.25 - 7.5 = 5.75
Upper fence = Q3 + 1.5*IQR = 18.25 + 7.5 = 25.75

Values outside fences are outliers. Here, 100 > 25.75, so 100 is an outlier.
    

Precision vs Recall (or equivalent tradeoff) with concrete examples

In outlier detection, there is a tradeoff between catching all outliers (high recall) and not labeling normal points as outliers (high precision).

High recall, low precision: Detects most outliers but may mark normal points wrongly. Good when missing outliers is costly, like fraud detection.

High precision, low recall: Only marks clear outliers, fewer false alarms but may miss some outliers. Useful when false alarms are costly, like quality control.

What "good" vs "bad" metric values look like for this use case

Good: Median close to center of data, IQR capturing most normal points, few outliers detected that make sense. For example, median=15.5, IQR=5, and only 1 outlier (100) detected.

Bad: Mean far from median due to outliers, IQR too small or too large, many false outliers detected or none detected when obvious outliers exist.

Metrics pitfalls (accuracy paradox, data leakage, overfitting indicators)

• Using mean alone: Mean is sensitive to outliers and can mislead about data center.
• Ignoring outliers: Outliers can skew model training and evaluation.
• Data leakage: Using future data to detect outliers can cause unrealistic results.
• Overfitting: Removing too many points as outliers may remove valid data, hurting model generalization.

Self-check

Your dataset has a mean of 50 and median of 20. The IQR is 10, but you see some points at 200 and 300. Is your data distribution likely affected by outliers? What metric should you trust more to understand the center?

Answer: Yes, the high mean compared to median suggests outliers are pulling the mean up. The median is more reliable here to understand the center.

Key Result

Median and IQR are robust metrics to understand data center and spread when outliers exist; detecting outliers helps avoid misleading model training.

Practice

1. What is an outlier in a data distribution?

easy

A. A data point that is very different from most other points

B. The average value of all data points

C. The most common value in the data

D. A data point exactly in the middle of the dataset

Solution

1. Step 1: Understand what an outlier means

   An outlier is a point that stands out because it is far from the rest of the data.

2. Step 2: Compare options to definition

   Only A data point that is very different from most other points describes a point very different from others, which matches the outlier definition.

3. Final Answer:

   A data point that is very different from most other points -> Option A

4. Quick Check:

   Outlier = Different point [OK]

Hint: Outliers are points far from the main group [OK]

Common Mistakes:

• Confusing outlier with average
• Thinking outlier is the most common value
• Mixing outlier with median

2. Which of the following Python code snippets correctly calculates the interquartile range (IQR) to detect outliers?

easy

A. iqr = q3 - q1 # where q1 and q3 are 25th and 75th percentiles

B. iqr = mean + std # mean and standard deviation

C. iqr = max(data) - min(data) # range of data

D. iqr = median(data) * 2 # double the median

Solution

1. Step 1: Recall the IQR formula

   IQR is the difference between the 75th percentile (Q3) and 25th percentile (Q1).

2. Step 2: Match code to formula

   iqr = q3 - q1 # where q1 and q3 are 25th and 75th percentiles correctly subtracts q1 from q3. Other options use unrelated statistics.

3. Final Answer:

   iqr = q3 - q1 # where q1 and q3 are 25th and 75th percentiles -> Option A

4. Quick Check:

   IQR = Q3 - Q1 [OK]

Hint: IQR = Q3 minus Q1, not mean or median [OK]

Common Mistakes:

• Using mean or median instead of percentiles
• Confusing IQR with full data range
• Mixing standard deviation with IQR

3. Given the data points [5, 7, 8, 9, 10, 100], which value is most likely an outlier based on the IQR method?

medium

A. 7

B. 100

C. 10

D. 5

Solution

1. Step 1: Calculate Q1 and Q3

   Sorted data: [5,7,8,9,10,100]. Q1 (25th percentile) ≈ 7, Q3 (75th percentile) ≈ 9.5.

2. Step 2: Compute IQR and check outliers

   IQR = 9.5 - 7 = 2.5. Outliers are points below Q1 - 1.5*IQR = 7 - 3.75 = 3.25 or above Q3 + 1.5*IQR = 9.5 + 3.75 = 13.25. Only 100 is above 13.25, so it is an outlier.

3. Final Answer:

   100 -> Option B

4. Quick Check:

   100 > 13.25 means outlier [OK]

Hint: Outliers lie beyond Q1-1.5*IQR or Q3+1.5*IQR [OK]

Common Mistakes:

• Ignoring the large gap and picking smallest value
• Confusing max value as normal
• Not calculating IQR correctly

4. You have this Python code to detect outliers but it gives wrong results:

import numpy as np
q1 = np.percentile(data, 25)
q3 = np.percentile(data, 75)
iqr = q1 - q3
lower_bound = q1 - 1.5 * iqr
upper_bound = q3 + 1.5 * iqr
outliers = [x for x in data if x < lower_bound or x > upper_bound]

What is the error?

medium

A. Percentiles should be 50 and 100, not 25 and 75

B. Outlier condition should use 'and' instead of 'or'

C. IQR calculation is reversed; should be q3 - q1

D. Bounds calculation should add 1.5 to q1 and q3 directly

Solution

1. Step 1: Check IQR calculation

   IQR is the difference between Q3 and Q1, so it must be q3 - q1, not q1 - q3.

2. Step 2: Verify other parts

   Percentiles 25 and 75 are correct. Outlier condition uses 'or' correctly. Bounds use multiplication correctly.

3. Final Answer:

   IQR calculation is reversed; should be q3 - q1 -> Option C

4. Quick Check:

   IQR = Q3 - Q1, not reversed [OK]

Hint: IQR = Q3 minus Q1, watch subtraction order [OK]

Common Mistakes:

• Swapping q1 and q3 in IQR calculation
• Using wrong percentile values
• Confusing 'or' with 'and' in conditions

5. You have a dataset with many outliers skewing the mean. Which method is best to reduce outlier impact before training a machine learning model?

hard

A. Ignore outliers and train directly

B. Replace all values with the mean

C. Use the maximum value as the central measure

D. Remove data points outside 1.5 times the IQR range

Solution

1. Step 1: Understand outlier impact on mean

   Outliers can pull the mean away from the center, causing bias in training.

2. Step 2: Choose method to reduce outlier effect

   Removing points outside 1.5*IQR is a common way to remove outliers. Replacing with mean or ignoring outliers keeps bias. Using max value is not a central measure.

3. Final Answer:

   Remove data points outside 1.5 times the IQR range -> Option D

4. Quick Check:

   Remove outliers using IQR method [OK]

Hint: Cut off points beyond 1.5*IQR to reduce outliers [OK]

Common Mistakes:

• Replacing all data with mean loses information
• Using max value as center is wrong
• Ignoring outliers causes model bias