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Stable Conformal Prediction Sets
Machine Learning · Submitted 19 Dec 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We demonstrate that our proposed confidence set does not lose any coverage guarantees while avoiding the need for data splitting as currently done in the literature.
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The abstract, sentence by sentence
When one observes a sequence of variables $(x_1, y_1), \ldots, (x_n, y_n)$, Conformal Prediction (CP) is a methodology that allows to estimate a confidence set for $y_{n+1}$ given $x_{n+1}$ by merely assuming that the distribution of the data is exchangeable. CP sets have guaranteed coverage for any finite population size $n$. While appealing, the computation of such a set turns out to be infeasible in general, e.g. when the unknown variable $y_{n+1}$ is continuous. The bottleneck is that it is based on a procedure that readjusts a prediction model on data where we replace the unknown target by all its possible values in order to select the most probable one. This requires computing an infinite number of models, which often makes it intractable. In this paper, we combine CP techniques with classical algorithmic stability bounds to derive a prediction set computable with a single model fit. We demonstrate that our proposed confidence set does not lose any coverage guarantees while avoiding the need for data splitting as currently done in the literature. We provide some numerical experiments to illustrate the tightness of our estimation when the sample size is sufficiently large, on both synthetic and real datasets.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | When one observes a sequence of variables $(x_1, y_1), \ldots, (x_n, y_n)$, Conformal Prediction (CP) is a methodology that allows to estimate a confidence set for $y_{n+1}$ given $x_{n+1}$ by merely assuming that the distribution of the data is exchangeable. | background 1.00 | 0.05 | 0.03 | asserted 0.99 |
| s1 | CP sets have guaranteed coverage for any finite population size $n$. | background 0.98 | 0.07 | 0.05 | asserted 1.00 |
| s2 | While appealing, the computation of such a set turns out to be infeasible in general, e.g. when the unknown variable $y_{n+1}$ is continuous. | background 0.59 | 0.15 | 0.02 | asserted 0.98 |
| s3 | The bottleneck is that it is based on a procedure that readjusts a prediction model on data where we replace the unknown target by all its possible values in order to select the most probable one. | background 0.86 | 0.10 | 0.03 | asserted 1.00 |
| s4 | This requires computing an infinite number of models, which often makes it intractable. | background 0.89 | 0.08 | 0.03 | asserted 0.78 |
| s5 | In this paper, we combine CP techniques with classical algorithmic stability bounds to derive a prediction set computable with a single model fit. | contribution 0.77 | 0.95 | 0.60 | asserted 1.00 |
| s6 | We demonstrate that our proposed confidence set does not lose any coverage guarantees while avoiding the need for data splitting as currently done in the literature. | result 0.83 | 0.93 | 0.55 | asserted 1.00 |
| s7 | We provide some numerical experiments to illustrate the tightness of our estimation when the sample size is sufficiently large, on both synthetic and real datasets. | contribution 0.42 | 0.96 | 0.07 | asserted 0.90 |
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The paper
Original abstract
When one observes a sequence of variables $(x_1, y_1), \ldots, (x_n, y_n)$, Conformal Prediction (CP) is a methodology that allows to estimate a confidence set for $y_{n+1}$ given $x_{n+1}$ by merely assuming that the distribution of the data is exchangeable. CP sets have guaranteed coverage for any finite population size $n$. While appealing, the computation of such a set turns out to be infeasible in general, e.g. when the unknown variable $y_{n+1}$ is continuous. The bottleneck is that it is based on a procedure that readjusts a prediction model on data where we replace the unknown target by all its possible values in order to select the most probable one. This requires computing an infinite number of models, which often makes it intractable. In this paper, we combine CP techniques with classical algorithmic stability bounds to derive a prediction set computable with a single model fit. We demonstrate that our proposed confidence set does not lose any coverage guarantees while avoiding the need for data splitting as currently done in the literature. We provide some numerical experiments to illustrate the tightness of our estimation when the sample size is sufficiently large, on both synthetic and real datasets.
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What this paper does with the arXiv papers it cites
What it cites · 1 sentence without a confident label
Uses the method or tool of 1 paper
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To define an oracle prediction set as reference, we follow in [ref] and assume that the unavailable target variable $y_n+1$ is observed by the algorithm.
Root-finding Approaches for Computing Conformal Prediction Set · Numerical Experiments · 0.89
Compares with 2 papers
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An important point is that, by using the stability bound, the coverage guarantee of the interpolated conformal set is preserved without the need of the expensive symmetrization proposed in [ref] .
Root-finding Approaches for Computing Conformal Prediction Set · Batch Approximation · 0.80
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Considering the leave-one-out score function, our proposal is therefore an alternative to the approximations via influence function used in [ref] when an exact computation [ref] would be unusable or too costly.
Approximating Full Conformal Prediction at Scale via Influence Functions · Batch Approximation · 0.99
Cites as background 3 papers
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Conformal prediction technique has been applied for designing uncertainty sets in active learning [ref] , anomaly detection [ref] , few shot learning [ref] , time series [ref] , robust optimization [ref] or to infer the performance guarantee for statistical learning algorithms [ref] .
Validity, consonant plausibility measures, and conformal prediction · Introduction · 0.96
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Conformal prediction technique has been applied for designing uncertainty sets in active learning [ref] , anomaly detection [ref] , few shot learning [ref] , time series [ref] , robust optimization [ref] or to infer the performance guarantee for statistical learning algorithms [ref] .
Making learning more transparent using conformalized performance prediction · Introduction · 0.96
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Conformal prediction technique has been applied for designing uncertainty sets in active learning [ref] , anomaly detection [ref] , few shot learning [ref] , time series [ref] , robust optimization [ref] or to infer the performance guarantee for statistical learning algorithms [ref] .
Testing for Outliers with Conformal p-values · Introduction · 0.96
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