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QuEst: Enhancing Estimates of Quantile-Based Distributional Measures Using Model Predictions
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Proposes QuEst, a prediction-powered estimator for quantile-based distributional measures (CVaR, interval VaR, quantile segments) with closed-form variance-minimizing mixing weight, multidimensional CLT, and an optimized imputed-weighting extension (QuEst-Opt).
Problem
Hybrid inference combining small observed data with large model-imputed data has only covered means and single quantiles; estimating quantile-based distributional measures like CVaR, interval VaR, and multi-measure joint estimates with valid confidence intervals is not supported.
Approach
Extends prediction-powered inference to quantile-based distributional measures via an L-statistic representation, uses an estimator Q(λ) = λQ(imputed large) + (Q(observed) − λQ(imputed observed)), chooses λ in closed form to minimize asymptotic variance, and further optimizes a parameterized weighting function on imputed data (QuEst-Opt).
Key results
- On GeneExpression with only 100 observed examples, QuEst roughly halves both estimation error and interval width relative to observed-only estimation.
- In the toxicity red-teaming task, multivariate QuEst reduced 90% confidence region volume by 34% for univariate and 7% for multivariate relative to classical estimation on news summarization (univariate -34%, multivariate -7%).
- QuEst-Opt outperforms QuEst on synthetic heteroskedastic data, with the largest gains in the low observed-data regime.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use QuEst instead of classical univariate estimation | Estimating bottom-20% coherence, relevance, and consistency for Qwen2-7B-Instruct summaries · XSum | confidence-region volume: 1.57 e-2 -> 1.04e-2; -34% | Helped |
| Use multivariate QuEst instead of classical multivariate estimation | Estimating bottom-20% coherence, relevance, and consistency for Qwen2-7B-Instruct summaries · XSum | confidence-region volume: 5.55e-3 -> 5.17e-3; -7% | Helped |
| Use multivariate QuEst instead of classical multivariate estimation | Estimating bottom-20% coherence, relevance, and consistency for Qwen2-7B-Instruct summaries · XSum | MSE: 1.17e-2 -> 1.08e-2; -7% | Helped |
| Combine observed labels with imputed predictions using QuEst rather than using observed data alone | Estimating Interval-VaR and CVaR · PovertyMap, GeneExpression, OpinionQA | absolute estimation error: roughly a 50% reduction on GeneExpression with only 100 gold-standard examples | Helped |
| Select lambda adaptively rather than use the fixed-parameter PPI approach | Estimating the 0.75 quantile · GeneExpression, PovertyMap | estimation error | Helped |
| Select lambda adaptively rather than use the fixed-parameter PPI approach | Estimating the 0.75 quantile · GeneExpression, PovertyMap | confidence-interval width | No clear effect |
| Combine high-quality observed toxicity scores with cheaper imputed scores using QuEst | Estimating toxicity in the worst 25% of responses · Helpful/Harmless red-teaming split | absolute estimation error | Helped |
| Use QuEst for model selection rather than baseline estimates | Ranking candidate chatbots by worst-25% toxicity · Helpful/Harmless red-teaming split | rank correlation | Helped |
| Use QuEst-Opt with an optimized adaptive weighting function instead of QuEst | Estimating quantile-based distributional measures · Synthetic heteroskedastic datasets | estimation error | Helped |
| Use QuEst-Opt with an optimized adaptive weighting function instead of QuEst | Estimating quantile-based distributional measures · OpinionQA | estimation performance | No clear effect |
| Use QuEst-Opt with an optimized adaptive weighting function instead of QuEst | Estimating quantile-based distributional measures · GeneExpression | estimation performance | Helped |
Surprising findings
- Using only observed data becomes competitive with QuEst on PovertyMap and OpinionQA once about 1,000 observed examples are collected.
- The imputed-only estimate is markedly worse on GeneExpression and OpinionQA, so naive reliance on model predictions is harmful.
Limitations
- Theory relies on asymptotic regularity conditions; finite-sample validity only approximated via CLT and clipping lambda to [0,1].
- Gains depend on correlation between observed and imputed labels; little gain when imputations are weakly correlated.
- QuEst-Opt is evaluated mainly on synthetic data and shows only comparable or modest gains on real datasets.
Experimental setup
Datasets: PovertyMap GeneExpression OpinionQA Anthropic HH-RLHF red-teaming XSum
Benchmarks: PovertyMap GeneExpression OpinionQA red-teaming toxicity (HH-RLHF) XSum news summarization
Metrics: absolute estimation error confidence interval width confidence interval coverage rank correlation confidence region volume MSE
Baselines: classical observed-only estimator imputed-only estimator PPI
Builds on: prediction-powered inference L-statistics power-tuning
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