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Transductive Conformal Inference with Adaptive Scores: Theory and Applications

Q: How does adaptive scoring improve performance in transductive settings

Adaptive scoring improves performance in transductive settings by allowing the scores to be tailored to the specific characteristics of the data, particularly in cases where there is a domain shift between different sets of data. In the context provided, adaptive scores are generated using transfer learning techniques that leverage information from both a training sample and a calibration/test sample. This approach enables the creation of more accurate and reliable non-conformity scores, which are essential for constructing prediction intervals or detecting novelties. By incorporating information from both the training and test/calibration samples in an exchangeable manner, adaptive scoring can capture nuances in the data distribution that may not be evident when using traditional non-adaptive scoring methods. This adaptability leads to improved model performance, especially when dealing with complex datasets or situations where there is variability between different subsets of data.

Q: What are the implications of considering FDP over FDR in multiple testing scenarios

In multiple testing scenarios, considering False Discovery Proportion (FDP) over False Discovery Rate (FDR) has important implications for controlling errors while conducting hypothesis tests. FDP provides a scale-invariant measure that accounts for both the number of false discoveries and the total number of declared positives/negatives. By focusing on FDP instead of FDR, practitioners can better assess and control error rates across various scales without being influenced by sample size differences. The use of FDP allows researchers to evaluate error proportions more accurately across different subsets or levels within their analysis. It offers a robust way to quantify errors while accounting for variations in dataset sizes or complexities inherent in large-scale machine learning applications. Additionally, uniform bounds on FDP provide practitioners with consistent measures of error control that are applicable across various decision thresholds or parameter settings.

Q: How can uniform error bounds benefit practitioners dealing with sensitive data

Uniform error bounds offer significant benefits to practitioners dealing with sensitive data by providing consistent guarantees on error rates regardless of specific parameters chosen during analysis. These bounds ensure that error probabilities remain controlled at desired levels throughout decision-making processes involving sensitive information. For instance, when handling sensitive healthcare or financial data where accuracy and reliability are paramount, having uniform error bounds adds an extra layer of confidence in results obtained from predictive models or hypothesis tests. Practitioners can rely on these bounds to make informed decisions based on statistically sound principles while maintaining strict control over potential errors. Moreover, uniform error bounds help mitigate risks associated with making incorrect conclusions based on incomplete or biased analyses when working with sensitive datasets. By ensuring consistency and reliability in error rate controls across all stages of analysis, practitioners can uphold high standards of accuracy and accountability in their work involving sensitive information.

Core Concepts

Conformal inference provides distribution-free guarantees for machine learning tasks, with a focus on transductive settings and adaptive scores.

Abstract

The content discusses the theory and applications of transductive conformal inference with adaptive scores. It covers the joint distribution of conformal p-values, concentration inequalities, and error proportion bounds for prediction intervals and novelty detection. Theoretical results are illustrated through numerical experiments in regression and anomaly detection scenarios.

Abstract:

Conformal inference offers distribution-free guarantees for machine learning.
Transductive setting involves decisions on new points using conformal p-values.
Joint distribution of p-values follows a P´olya urn model.
Concentration inequality for empirical distribution function is established.

Introduction:

Conformal inference aims at sharp uncertainty quantification for machine learning algorithms.
Non-conformity scores are crucial in the construction of prediction intervals.
Motivating tasks include prediction intervals and novelty detection based on two-class classification.

Contributions:

New results presented for joint distribution of conformal p-values.
Concentration inequality derived for empirical distribution function.
Application cases demonstrated in interval prediction and novelty detection tasks.

Data Extraction:

"The central property of these scores is that they are an exchangeable family of random variables."
"The link to the two above tasks is as follows: for (PI), the prediction interval C(α) for Yn+i with coverage probability (1 − α) is obtained by inverting the inequality pi > α w.r.t. Yn+i."

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Stats

"The central property of these scores is that they are an exchangeable family of random variables."
"The link to the two above tasks is as follows: for (PI), the prediction interval C(α) for Yn+i with coverage probability (1 − α) is obtained by inverting the inequality pi > α w.r.t. Yn+i."

Quotes

"The central property of these scores is that they are an exchangeable family of random variables."
"The link to the two above tasks is as follows: for (PI), the prediction interval C(α) for Yn+i with coverage probability (1 − α) is obtained by inverting the inequality pi > α w.r.t. Yn+i."

Key Insights Distilled From

Transductive conformal inference with adaptive scores

by Ulysse Gazin... at arxiv.org 03-20-2024

https://arxiv.org/pdf/2310.18108.pdf

Transductive conformal inference with adaptive scores

Deeper Inquiries

How does adaptive scoring improve performance in transductive settings

Adaptive scoring improves performance in transductive settings by allowing the scores to be tailored to the specific characteristics of the data, particularly in cases where there is a domain shift between different sets of data. In the context provided, adaptive scores are generated using transfer learning techniques that leverage information from both a training sample and a calibration/test sample. This approach enables the creation of more accurate and reliable non-conformity scores, which are essential for constructing prediction intervals or detecting novelties.
By incorporating information from both the training and test/calibration samples in an exchangeable manner, adaptive scoring can capture nuances in the data distribution that may not be evident when using traditional non-adaptive scoring methods. This adaptability leads to improved model performance, especially when dealing with complex datasets or situations where there is variability between different subsets of data.

What are the implications of considering FDP over FDR in multiple testing scenarios

In multiple testing scenarios, considering False Discovery Proportion (FDP) over False Discovery Rate (FDR) has important implications for controlling errors while conducting hypothesis tests. FDP provides a scale-invariant measure that accounts for both the number of false discoveries and the total number of declared positives/negatives. By focusing on FDP instead of FDR, practitioners can better assess and control error rates across various scales without being influenced by sample size differences.
The use of FDP allows researchers to evaluate error proportions more accurately across different subsets or levels within their analysis. It offers a robust way to quantify errors while accounting for variations in dataset sizes or complexities inherent in large-scale machine learning applications. Additionally, uniform bounds on FDP provide practitioners with consistent measures of error control that are applicable across various decision thresholds or parameter settings.

How can uniform error bounds benefit practitioners dealing with sensitive data

Uniform error bounds offer significant benefits to practitioners dealing with sensitive data by providing consistent guarantees on error rates regardless of specific parameters chosen during analysis. These bounds ensure that error probabilities remain controlled at desired levels throughout decision-making processes involving sensitive information.
For instance, when handling sensitive healthcare or financial data where accuracy and reliability are paramount, having uniform error bounds adds an extra layer of confidence in results obtained from predictive models or hypothesis tests. Practitioners can rely on these bounds to make informed decisions based on statistically sound principles while maintaining strict control over potential errors.
Moreover, uniform error bounds help mitigate risks associated with making incorrect conclusions based on incomplete or biased analyses when working with sensitive datasets. By ensuring consistency and reliability in error rate controls across all stages of analysis, practitioners can uphold high standards of accuracy and accountability in their work involving sensitive information.