· Xiaojing Yang · Explainability and Responsible AI · 4 min read
中文Statistical Reliability: Bias, Variance, Bootstrap, and Attribution Uncertainty
Attribution scores are estimates. This note separates estimator bias, sampling variance, training randomness, evaluation uncertainty, and bootstrap confidence intervals.
Core idea
A ranking without uncertainty is fragile. Training-data attribution should report not only scores, but also the sources of uncertainty behind those scores.
This note is part of my series Training Data Attribution for NLP and LLM Research. The series is written as both a research notebook and an interview preparation path: each article should help me explain the idea clearly, connect it to my thesis, and identify what would become future PhD work.
Guiding question: How reliable is an attribution score?
Intuition
If one data group ranks first in one seed and fourth in another, the story is unstable. If a score changes after resampling the test set, the evaluation target may be noisy. If Monte Carlo Shapley uses too few samples, the estimator itself may have high variance.
In NLP and LLM research, this matters because model behaviour is deeply shaped by data mixture. A model may be fluent because of broad web text, domain-accurate because of specialised documents, safer because of curated instruction data, or biased because of repeated patterns in a subset of the corpus. Training-data attribution gives us language for asking these questions systematically instead of only saying “the data matters”.
Formal lens
Important uncertainty sources include estimator bias, estimator variance, random initialization and training order, test-set sampling uncertainty, metric noise, and data preprocessing uncertainty. Bootstrap confidence intervals can quantify uncertainty over evaluation examples, but they do not automatically capture training randomness unless the resampling design includes it.
The important discipline is to define the attribution setup before interpreting the score:
| Design choice | Question to answer |
|---|---|
| Attribution unit | What receives credit: source, group, document, example, or token? |
| Utility function | Which behaviour is being explained: quality, terminology, style, factuality, or safety? |
| Intervention | Are we adding, deleting, reweighting, correcting, or retraining? |
| Estimator | Is the score exact, sampled, gradient-based, surrogate-based, or heuristic? |
| Uncertainty | How stable is the score across seeds, samples, metrics, and evaluation sets? |
NLP / LLM example
For an MT attribution table, I would report scores over multiple seeds, include confidence intervals for metrics or deltas, and compare against random baselines. If a group’s interval overlaps zero or changes sign across seeds, I would avoid strong claims.
This is why I do not want to treat attribution as a generic interpretability topic. For my profile, the natural connection is multilingual and domain-specific NLP: low-resource settings, technical terminology, written-standard variation, and evaluation beyond one headline metric.
Connection to my thesis
In my thesis narrative, training-data attribution is useful because it turns a vague data question into an experimental design:
- define interpretable data units;
- define the model behaviour to explain;
- compare controlled data coalitions or interventions;
- estimate contribution;
- report uncertainty and limitations;
- decide what evidence is strong enough to support a causal-style claim.
That structure helps me avoid overclaiming. A score is not automatically a causal explanation. It is a measurement produced by a specific setup.
What I have done, understand, and would extend
| Level | Status |
|---|---|
| Already completed / thesis-ready | Group-level attribution, coalition thinking, metric-based utilities, cautious interpretation, random baselines, bootstrap-style reliability checks. |
| I understand but may not fully implement yet | Instance-level gradient attribution, influence functions, TracIn, Monte Carlo Shapley, surrogate/datamodel approximations. |
| Strong PhD extension | Hierarchical attribution, intervention-based validation, factuality/style-specific utilities, scalable attribution for LLM data mixtures. |
Interview answer
My bootstrap confidence intervals measure uncertainty in the evaluated score or attribution estimate under a specific resampling scheme. They do not magically prove causality. I would use them to communicate reliability, compare against random baselines, and identify which conclusions are stable enough to discuss.
References and reading path
- Lloyd Shapley, A Value for n-Person Games.
- Ghorbani and Zou, Data Shapley: Equitable Valuation of Data for Machine Learning.
- Koh and Liang, Understanding Black-box Predictions via Influence Functions.
- Pruthi et al., Estimating Training Data Influence by Tracing Gradient Descent.
- Ilyas et al., Datamodels: Predicting Predictions from Training Data.
- Rei et al., COMET: A Neural Framework for MT Evaluation.