#ai #machinelearning #uncertainty #quantification
In this MLBoost seminar, we hosted Chen Xu who presented his work on conformal prediction for time series.
Here are the links to his papers:
https://arxiv.org/abs/2403.03850
https://arxiv.org/abs/2212.03463
https://arxiv.org/abs/2010.09107
Conformal prediction for multi-dimensional time series by ellipsoidal sets
Conformal prediction (CP) has been a popular method for uncertainty quantification because it is distribution-free, model-agnostic, and theoretically sound. For forecasting problems in supervised learning, most CP methods focus on building prediction intervals for univariate responses. In this work, we develop a sequential CP method called 𝙼𝚞𝚕𝚝𝚒𝙳𝚒𝚖𝚂𝙿𝙲𝙸 that builds prediction regions for a multivariate response, especially in the context of multivariate time series, which are not exchangeable. Theoretically, we estimate finite-sample high-probability bounds on the conditional coverage gap. Empirically, we demonstrate that 𝙼𝚞𝚕𝚝𝚒𝙳𝚒𝚖𝚂𝙿𝙲𝙸 maintains valid coverage on a wide range of multivariate time series while producing smaller prediction regions than CP and non-CP baselines.
Sequential Predictive Conformal Inference for Time Series
We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the \textit{sequential predictive conformal inference} (\texttt{SPCI}). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to adaptively re-estimate the conditional quantile of non-conformity scores (e.g., prediction residuals), upon exploiting the temporal dependence among them. More precisely, we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of \texttt{SPCI} compared to other existing methods under the desired empirical coverage.
Conformal prediction for time series
We develop a general framework for constructing distribution-free prediction intervals for time series. Theoretically, we establish explicit bounds on conditional and marginal coverage gaps of estimated prediction intervals, which asymptotically converge to zero under additional assumptions. We obtain similar bounds on the size of set differences between oracle and estimated prediction intervals. Methodologically, we introduce a computationally efficient algorithm called \texttt{EnbPI} that wraps around ensemble predictors, which is closely related to conformal prediction (CP) but does not require data exchangeability. \texttt{EnbPI} avoids data-splitting and is computationally efficient by avoiding retraining and thus scalable to sequentially producing prediction intervals. We perform extensive simulation and real-data analyses to demonstrate its effectiveness compared with existing methods. We also discuss the extension of \texttt{EnbPI} on various other applications.