Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noise
Constructing valid prediction intervals rather than point estimates is a well-established approach for uncertainty quantification in the regression setting. Models equipped with this capacity output an interval of values in which the ground truth target will fall with some prespecified probability. This is an essential requirement in many real-world applications where simple point predictions' inability to convey the magnitude and frequency of errors renders them insufficient for high-stakes decisions. Quantile regression is a leading approach for obtaining such intervals via the empirical estimation of quantiles in the (non-parametric) distribution of outputs. This method is simple, computationally inexpensive, interpretable, assumption-free, and effective. However, it does require that the specific quantiles being learned are chosen a priori. This results in (a) intervals that are arbitrarily symmetric around the median which is sub-optimal for realistic skewed distributions, or (b) learning an excessive number of intervals. In this work, we propose Relaxed Quantile Regression (RQR), a direct alternative to quantile regression based interval construction that removes this arbitrary constraint whilst maintaining its strengths. We demonstrate that this added flexibility results in intervals with an improvement in desirable qualities (e.g. mean width) whilst retaining the essential coverage guarantees of quantile regression.
Code (1)
Tasks
PredictionPrediction Intervalsquantile regressionregressionUncertainty QuantificationvalidSimilar Papers 제목 키워드 기반
Regression Conformal Prediction under Bias
Uncertainty quantification is crucial to account for the imperfect predictions of machine learning algorithms for high-impact applications. Conformal prediction (CP) is a powerful framework for uncertainty quantification…
Computed Tomography (CT)Conformal PredictionCT ReconstructionPrediction+4Fast Conformal Prediction using Conditional Interquantile Intervals
We introduce Conformal Interquantile Regression (CIR), a conformal regression method that efficiently constructs near-minimal prediction intervals with guaranteed coverage. CIR leverages black-box machine learning models…
Computational EfficiencyImproved conformalized quantile regression
Conformalized quantile regression is a procedure that inherits the advantages of conformal prediction and quantile regression. That is, we use quantile regression to estimate the true conditional quantile and then apply …
Conformal PredictionPredictionPrediction Intervalsquantile regression+1Bayesian Multivariate Quantile Regression with alternative Time-varying Volatility Specifications
This article proposes a novel Bayesian multivariate quantile regression to forecast the tail behavior of energy commodities, where the homoskedasticity assumption is relaxed to allow for time-varying volatility. In parti…
quantile regressionregressionOptimal Adaptive Prediction Intervals for Electricity Load Forecasting in Distribution Systems via Reinforcement Learning
Prediction intervals offer an effective tool for quantifying the uncertainty of loads in distribution systems. The traditional central PIs cannot adapt well to skewed distributions, and their offline training fashion is …
Load ForecastingPrediction Intervalsquantile regressionReinforcement Learning (RL)