Independent and identically distributed

As explained in Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI

The IID principle is the assumption that observations are independently sampled and follow the same probability distribution.

IID means observations are sampled independently and follow the same probability distribution. Each observation neither influences nor carries information about the next, and every observation comes from the same kind of data-generating process. section 2.1.1

For tabular modeling, IID data supports random sampling and randomly creating cross-validation folds. The assumption does not fit grouped, repeated, hierarchical, or time-dependent data, where related observations can share information. section 2.1.1

Coin flips and grouped sales

Repeated flips of the same coin provide an IID dataset: each result is independent, and heads or tails follow the same Bernoulli distribution. Sales from multiple stores are non-IID when observations from one store are correlated, while school classes can share distinctive characteristics. section 2.1.1

Figure 2.1 Comparison of IID and non--IID data sequences. The left chart shows IID data, while the right chart illustrates non-IID data, highlighting the sequential correlation patterns.

Compare an IID sequence with a non-IID sequence to see how sequential correlation breaks the independence assumption. section 2.1.1

How Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI covers it

How deep it goes

Defines independence and identical distribution, gives examples, and stops short of formal mathematical derivation.

Examples

Uses repeated coin flips, multi-store sales, school classes, and a visual comparison of IID and non-IID sequences.

What you can do after

Evaluate whether tabular observations justify random sampling and randomly constructed cross-validation folds.

How it connects

Connects IID assumptions with cross-validation, Bernoulli distributions, grouped data, repeated measures, and time series analysis.

liveBookmanning.com

Read Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI on liveBook Get the book at manning.com

Also explained in

• 

  liveBookmanning.com
  Causal AIIndependent and identically distributed data are observations that are mutually independent and share the same probability distribution.
• 

  liveBookmanning.com
  Experimentation for EngineersThe iid assumption states that measurements are independent of one another and drawn from the same probability distribution.

Compare how 3 books explain independent and identically distributed →

Related concepts

• posterior probabilityuses · A posterior probability or distribution expresses the probability assigned to an event, hypothesis, or unknown quantity conditional on observed evidence and prior information.

This explainer was generated by Manning's knowledge graph from the text of Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI. The section links point to the parts of the book it draws on.