Learning Causally-Generated Stationary Time Series
This work addresses the need for better causal time series models in fields like signal processing, though it appears incremental as it builds on a previous acausal variant.
The authors tackled the problem of modeling causal, spectrally complex dynamical phenomena by introducing the Causal Gaussian Process Convolution Model (CGPCM), a doubly nonparametric generative model, and developed enhanced variational inference schemes that significantly improved statistical accuracy.
We present the Causal Gaussian Process Convolution Model (CGPCM), a doubly nonparametric model for causal, spectrally complex dynamical phenomena. The CGPCM is a generative model in which white noise is passed through a causal, nonparametric-window moving-average filter, a construction that we show to be equivalent to a Gaussian process with a nonparametric kernel that is biased towards causally-generated signals. We develop enhanced variational inference and learning schemes for the CGPCM and its previous acausal variant, the GPCM (Tobar et al., 2015b), that significantly improve statistical accuracy. These modelling and inferential contributions are demonstrated on a range of synthetic and real-world signals.