We present coarse-to-fine autoregressive networks (C2FAR), a method for modeling the probability distribution of univariate, numeric random variables. C2FAR generates a hierarchical, coarse-to-fine discretization of a variable autoregressively; progressively finer intervals of support are generated from a sequence of binned distributions, where each distribution is conditioned on previously-generated coarser intervals. Unlike prior (flat) binned distributions, C2FAR can represent values with exponentially higher precision, for only a linear increase in complexity. We use C2FAR for probabilistic forecasting via a recurrent neural network, thus modeling time series autoregressively in both space and time. C2FAR is the first method to simultaneously handle discrete and continuous series of arbitrary scale and distribution shape. This flexibility enables a variety of time series use cases, including anomaly detection, interpolation, and compression. C2FAR achieves improvements over the state-of-the-art on several benchmark forecasting datasets.

我们提出了粗细自回归网络（C2FAR），一种对单变量数值随机变量的概率分布建模的方法。C2FAR通过渐进细化的离散化来进行变量的层次化自回归生成，可以以指数级别的精度表示值，并且具有更高的灵活性，可以同时处理离散和连续的任意尺度和分布形状的时间序列，实现了在多个基准预测数据集上的改进。

C2FAR：精确概率预测的粗糙到精细自回归网络