UC Riverside

Modal regression is a more robust regression model when compared with traditional linear regressions. For a long time, modal regression has been studied from a kernel density estimation perspective which has the problem of the "curse of dimensionality". In this paper, Random Forest-based quantile regression is utilized to model the unique global mode of the conditional distribution to provide a more flexible solution to modal regression. The asymptotic property of the mode estimator was proved theoretically, and the performances of the mode estimator were examined through a set of low-dimensional and high-dimensional simulations. To provide prediction intervals along with the modal estimator, a new cross-validation-based conformal prediction interval, named Bonferroni correction-based Cross Validation prediction interval (BCV conformal prediction interval), is proposed to generate a more consistent and shorter prediction interval when compared with the commonly used split conformal prediction interval. The validity of the proposed conformal prediction interval has also been confirmed through the set of synthetic data analyses. The performance of the proposed Modal Random Forest algorithm and the BCV conformal prediction interval on benchmark data is also compared with the other modal regression models.