论文标题
将时间数据建模为具有随机过程扩散的连续函数
Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion
论文作者
论文摘要
时间序列等时间数据可以看作是基础函数的离散测量。要构建此类数据的生成模型，我们必须对控制它的随机过程进行建模。我们通过定义函数空间中的降解扩散模型来提出解决方案，这也使我们能够自然处理不规则采样的观测值。远期过程逐渐增加函数的噪声，保留其连续性，而学习的反向过程消除了噪声并返回作为新样本的功能。为此，我们定义了合适的噪声源，并引入了新颖的DeNoising和得分匹配模型。我们展示了如何将我们的方法用于多元概率的预测和归纳，以及如何将我们的模型解释为神经过程。
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.
