AI Glossary / Governance, ethics and safety / Intermediate
Independence
Definition
Independence, in probability, means that knowing one event or variable does not change the probability information about another. In AI fairness, the same mathematical idea is applied to a model's output and a sensitive group attribute. For a binary decision, independence requires equal positive-decision rates across the groups being compared, a condition also called demographic or statistical parity.
What it means
The word has several uses. This entry explains statistical independence and its governance application. It is different from organisational independence, such as having an evaluator who is separate from a development team, and from an AI system operating autonomously.
For two events A and B, independence means P(A and B) = P(A) × P(B). When P(B) is positive, it also means P(A given B) = P(A). Learning that B occurred does not alter the probability assigned to A.
In fairness assessment, replace these abstract events with a decision and group membership. The criterion concerns the distribution of outputs, not simply whether the model directly receives a sensitive field. Removing that field does not establish independence if other inputs preserve related information.
How it works
Identify the variables and population under discussion. Independence is always a relationship between specified quantities under a specified distribution; a statement that “the model is independent” is incomplete.
For binary decisions, calculate the positive-decision rate in each group and compare it with the overall rate. For richer scores, independence concerns the full conditional distributions, not only equal averages. Sample estimates require uncertainty and representativeness checks.
Conditional independence adds another piece of information. Two variables can be independent within levels of a third variable while remaining dependent overall, or the reverse. In fairness terminology, separation conditions on the reference outcome, whereas independence does not. State explicitly which relationship is being assessed so that a technically correct measure is not mistaken for a different requirement.
Three practical examples
1. An analyst models two separately generated random draws as independent when the mechanism supports that assumption; multiplying their probabilities then gives the joint probability.
2. A fairness review checks whether a classifier selects the same proportion of cases in each relevant group, assessing independence of the binary decision from that group attribute.
3. A data scientist checks whether repeated observations from the same user can reasonably be treated as independent before interpreting an evaluation's uncertainty.
Think of it this way
Think of drawing a card from each of two separately shuffled packs. Information about the first draw need not change the probabilities for the second when the draws are genuinely separate.
The analogy is limited because real datasets often share people, conditions, or processes. Merely storing observations in different rows or files does not make them independent. For fairness, the analogy illustrates the mathematical relationship only; it does not establish whether equal output distributions fully address the social concern.
Worked example
Consider an invented dataset containing 200 cases in group A and 100 in group B. A binary classifier selects 60 from A and 30 from B. Both selection rates are 30%, and the overall rate is 90/300 = 30%.
Treating this table as the distribution for the exercise, P(selected and A) is 60/300 = 0.20. The product P(selected) × P(A) is 0.30 × 200/300 = 0.20, matching the joint probability. The table satisfies independence of this binary selection and the two-group attribute.
Now change B's selected count to 15. Its rate becomes 15%, while A remains at 30%. The relationship is no longer independent in the table.
Neither version tells us whether selections were accurate, accessible, or beneficial. Nor does exact equality in this finite table prove equality in a future population. Those questions require additional evidence beyond the arithmetic.
Illustrative case study
Fictional case: Oakmere Services evaluates an AI triage model. A supplier says the model is independent of a group attribute because that column was removed before training. The evaluation team asks for a more precise claim.
It compares outputs by group and finds unequal selection rates in the test data. The team investigates proxies, sampling, and the meaning of the selected criterion rather than assuming deletion of a column settled the issue.
The case illustrates the distinction between an input choice and an output relationship. It does not show that every observed difference is unjustified or that parity alone would make the service fair. The appropriate response depends on the task and consequences.
Common misconceptions and mistakes
Independence is not the same as mutual exclusivity. Two events that cannot occur together and each have positive probability are not independent: observing one rules out the other.
Zero correlation also does not generally prove independence; it rules out a particular linear association, while other relationships may remain.
Equal average scores do not necessarily mean equal score distributions. Likewise, independence at one level of aggregation may hide relationships within subgroups. Finally, statistical independence does not establish causal independence or prove that a decision process satisfies every relevant fairness concern.
Business use
Businesses should ask what a claim of independence actually refers to: inputs, outputs, observations, organisational roles, or a causal relationship. These are materially different claims requiring different evidence.
For fairness reporting, identify the decision, groups, population, period, and measure. Explain why that criterion matters and report its limitations alongside other relevant outcomes. For analytical work, examine whether shared users or conditions undermine assumptions about independent observations. Clear terminology prevents a reassuring word from standing in for the specific property the organization needs to understand.
People also ask
Does removing a sensitive input ensure independence?
No. Other inputs may carry related information, so the output relationship still needs assessment.
Is independence the same as uncorrelatedness?
No. Independence generally implies zero covariance when the relevant moments exist, but zero correlation does not generally imply independence.
Does demographic parity prove complete fairness?
No. It is one distributional criterion and does not assess every error, individual situation, or consequence.
Check your understanding
Two groups each receive positive decisions at a rate of 30%. What does that establish in the observed binary-decision table?
Answer: It establishes equal selection rates, the independence criterion for that table. It does not by itself establish accurate decisions, causal neutrality, or future population parity.
Related terms
- Conditional independence
- Demographic parity
- Correlation
- Probability
- separation
- sufficiency
- proxy variable
- independent evaluation
Learn next
Study conditional independence and fairness metrics next. Write a claim of independence using named variables, then identify the population and evidence required to test it. Compare that statement with any organisational meaning of the same word.
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Sources
NIST CSRC Glossary, Independent: https://csrc.nist.gov/glossary/term/independent
Barocas, Hardt, and Narayanan, Fairness and Machine Learning, Classification: https://fairmlbook.org/classification.html
Fairlearn, Common fairness metrics: https://fairlearn.org/main/user_guide/assessment/common_fairness_metrics.html
Primary explanations were read. The supplied AIMA glossary link did not expose the term during retrieval. Statistical and fairness senses are distinguished explicitly; examples and calculations are original.
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