Bayesian Learning from Sequential Data using Gaussian Processes with Signature Covariances
This work addresses the challenge of handling sequences of varying lengths in time series analysis, though it appears incremental by combining existing techniques like GPs, signatures, and LSTMs/GRUs.
The paper tackles the problem of learning from sequential data by developing a Bayesian approach using Gaussian processes with signature kernels as covariance functions, and it benchmarks the resulting models on multivariate time series classification datasets, achieving competitive performance.
We develop a Bayesian approach to learning from sequential data by using Gaussian processes (GPs) with so-called signature kernels as covariance functions. This allows to make sequences of different length comparable and to rely on strong theoretical results from stochastic analysis. Signatures capture sequential structure with tensors that can scale unfavourably in sequence length and state space dimension. To deal with this, we introduce a sparse variational approach with inducing tensors. We then combine the resulting GP with LSTMs and GRUs to build larger models that leverage the strengths of each of these approaches and benchmark the resulting GPs on multivariate time series (TS) classification datasets. Code available at https://github.com/tgcsaba/GPSig.