Accurate estimation of output quantiles is crucial in many use cases, where it is desired to model the range of possibility. Modeling target distribution at arbitrary quantile levels and at arbitrary input attribute levels are important to offer a comprehensive picture of the data, and requires the quantile function to be expressive enough. The quantile function describing the target distribution using quantile levels is critical for quantile regression. Although various parametric forms for the distributions (that the quantile function specifies) can be adopted, an everlasting problem is selecting the most appropriate one that can properly approximate the data distributions. In this paper, we propose a non-parametric and data-driven approach, Neural Spline Search (NSS), to represent the observed data distribution without parametric assumptions. NSS is flexible and expressive for modeling data distributions by transforming the inputs with a series of monotonic spline regressions guided by symbolic operators. We demonstrate that NSS outperforms previous methods on synthetic, real-world regression and time-series forecasting tasks.
翻译:对产出孔径的精确估计在许多使用案例中至关重要,在这些情况下,它希望对可能性的范围进行模型。在任意的孔径水平和任意输入属性水平上进行目标分布模型,对于提供数据的全面图象十分重要,要求量化函数足够表达。使用孔径水平描述目标分布的孔径函数对于四分位回归至关重要。尽管分布的各种参数形式(量化函数所指定的参数)可以被采用,但一个永恒的问题是在选择能够适当接近数据分布的最适当方法。在本文件中,我们提出一种非参数和数据驱动的方法,即神经线搜索(NSS),在不作参数假设的情况下代表所观察到的数据分布。NSS对于通过由象征性操作者指导的一系列单立式螺纹曲线回归来转换输入的模型数据分布具有灵活性和明确性。我们证明NSS在合成、真实世界回归和时间序列预测任务方面比以往的方法要差。