Kernel-based Optimally Weighted Conformal Time-Series Prediction
Jonghyeok Lee, Chen Xu, Yao Xie
TL;DR
This paper introduces KOWCPI, a novel conformal prediction method for time-series that adapts kernel-based estimators with optimal weights, providing reliable and narrower prediction intervals under dependent data conditions.
Contribution
The paper develops a new conformal prediction approach for dependent time-series data, establishing theoretical coverage guarantees and demonstrating improved empirical performance.
Findings
KOWCPI achieves narrower confidence intervals with maintained coverage.
The method outperforms existing state-of-the-art techniques on real and synthetic data.
Theoretical guarantees are provided under strong mixing conditions.
Abstract
In this work, we present a novel conformal prediction method for time-series, which we call Kernel-based Optimally Weighted Conformal Prediction Intervals (KOWCPI). Specifically, KOWCPI adapts the classic Reweighted Nadaraya-Watson (RNW) estimator for quantile regression on dependent data and learns optimal data-adaptive weights. Theoretically, we tackle the challenge of establishing a conditional coverage guarantee for non-exchangeable data under strong mixing conditions on the non-conformity scores. We demonstrate the superior performance of KOWCPI on real and synthetic time-series data against state-of-the-art methods, where KOWCPI achieves narrower confidence intervals without losing coverage.
Peer Reviews
Decision·ICLR 2025 Poster
- Authors provide a conditional coverage guarantee (much more meaningful than marginal coverage guarantee) - Proofs are included and assumptions are clearly stated - Strong coverage and efficiency results on intervals
- Grammatical errors/typos scattered throughout - Notation is rather dense. More plain language accompanying the mathematical formalism would help the reader - Presentation of Algorithm 1 seems to be missing some pieces. In the required line should it be $(X_t, Y_t), t=1, 2, ..., T$? Variables $n, w$ are referenced but not explained earlier in the box. - Table 1 is a little bit confusing at first glance. Typically bold indicates "best" but in this case it only shows what the authors' method is
- This article applies the conformal prediction and the RNW method to establish a prediction interval. Therefore, the proposed method is independent of specific time series models and has a broader range of applications. - Instead of establishing prediction intervals using the quantiles $Q_{\alpha/2}$ and $Q_{1-\alpha/2}$. The method seeks a $\beta$ such that the distance between the quantiles $Q_{\alpha/2+\beta}$ and $Q_{1-\alpha/2+\beta}$ is minimized to form the prediction intervals. This ap
- The authors make a natural integration of the conformal prediction with the RNW method. However, the innovation of this approach is not particularly strong. The theoretical results primarily focus on the asymptotic accuracy of distribution estimation. - When the dependence in the time series is strong, the dimension of $\tilde{X}$ may be large. In this case, when the data is limited, kernel estimates may not yield reliable results. Also, large $w$ leads to a low convergence rate of coverage.
1. The paper is well-written and easy-to-follow. 2. The considered problem is important and well-motivated. 3. The proposed KOWCPI is efficient in various real datasets.
1. Regarding the experiments, the author only provides real datasets to demonstrate the efficiency of marginal and conditional coverage without offering information about dependency. However, I believe it would be beneficial to include additional synthetic experiments to explore different dependency structures and more comprehensively assess the scope and validity of the methods. 2. While a theoretical guarantee is provided, the bound heavily depends on the estimation of weights and the stron
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques