Conformalized Kernel Ridge Regression

Burnaev, Evgeny; Nazarov, Ivan

doi:10.1109/icmla.2016.0017

Cited by 39 publications

(34 citation statements)

References 28 publications

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“…Our work is closely related to the literature on randomization inference via permutations (Fisher, 1935;Rubin, 1984;Romano, 1990;Lehmann and Romano, 2005) and conformal inference (Vovk et al, 2005(Vovk et al, , 2009; Lei et al, 2013;Vovk, 2013;Lei and Wasserman, 2014;Burnaev and Vovk, 2014;Balasubramanian et al, 2014;Lei et al, 2015Lei et al, , 2017. These papers typically exploit the i.i.d assumption to obtain the exchangeability condition under all permutations and establish model-free validity of procedures that randomize the data for general algorithms.…”

Section: Introductionmentioning

confidence: 93%

Exact and robust conformal inference methods for predictive machine learning with dependent data

Chernozhukov

Wüthrich

Zhu

2018

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We extend conformal inference to general settings that allow for time series data. Our proposal is developed as a randomization method and accounts for potential serial dependence by including block structures in the permutation scheme such that the latter forms a group. As a result, the proposed method retains the exact, model-free validity when the data are i.i.d. or more generally exchangeable, similar to usual conformal inference methods. When exchangeability fails, as is the case for common time series data, the proposed approach is approximately valid under weak assumptions on the conformity score.

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Section: Introductionmentioning

confidence: 93%

Exact and robust conformal inference methods for predictive machine learning with dependent data

Chernozhukov

Wüthrich

Zhu

2018

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“…Because of the problems that high dimensions pose for linear regression, we also explore the use of ridge regression (Table 3). The parametric intervals here are derived in a similar fashion to those for ordinary linear regression (Burnaev & Vovk, 2014). For all methods we used ridge regression tuning parameter λ = 10, which gives nearly optimal prediction bands in the ideal setting (Setting A).…”

Section: Comparisons To Parametric Intervals From Linear Regressionmentioning

confidence: 99%

Distribution-Free Predictive Inference for Regression

Lei

G’Sell

Rinaldo

et al. 2018

Journal of the American Statistical Association

509

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We develop a general framework for distribution-free predictive inference in regression, using conformal inference. The proposed methodology allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preserves the consistency properties of the original estimator under standard assumptions, while guaranteeing finite-sample marginal coverage even when these assumptions do not hold. We analyze and compare, both empirically and theoretically, the two major variants of our conformal framework: full conformal inference and split conformal inference, along with a related jackknife method. These methods offer different tradeoffs between statistical accuracy (length of resulting prediction intervals) and computational efficiency. As extensions, we develop a method for constructing valid in-sample prediction intervals called rank-one-out conformal inference, which has essentially the same computational efficiency as split conformal inference. We also describe an extension of our procedures for producing prediction bands with locally varying length, in order to adapt to heteroskedascity in the data. Finally, we propose a model-free notion of variable importance, called leave-one-covariate-out or LOCO inference. Accompanying this paper is an R package conformalInference that implements all of the proposals we have introduced. In the spirit of reproducibility, all of our empirical results can also be easily (re)generated using this package.

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“…As a dependence measure we use a simple Pearson correlation, or more complex non-linear measures like mutual information; 2. For each group of parameters we use anomaly detection algorithms to detect anomalies: -The most typical anomaly detection algorithms are based on manifold modeling approaches [31]- [34]; yet another approach could be to construct a surrogate model [35]- [39] in order to approximate dependencies between the observed parameters and then detect anomalies based on a predictive error with a non-parametric confidence measure [40], [41] as the diagnostic indicator; -In a linear case we can use the low rank linear PCA reconstruction error [42] as the diagnostic timeseries; -Observations with errors, exceeding 90%-95% empirical quantile, are considered as anomalies. 3.…”

Section: Event Matchingmentioning

confidence: 99%