Basis Function Learning for Variable-Length and Continuous-Indexed Signals

Representing variable-length and continuous-indexed signals through a linear combination of basis functions poses a fundamental challenge in science and engineering. Current approaches resort to preprocessing steps, such as interpolation and extrapolation, to handle irregular and off-grid measurements, which compromise the physical nature of signals and degrade the representation performance. To address this challenge, rather than utilizing discrete vectors, we introduce a Bayesian functional representation model that capitalizes on the continuous nature and rich expressiveness of Gaussian processes to facilitate interpretable and effective basis function learning. Moreover, an analytical and efficient algorithm based on the variational inference framework is developed. Experimental results using real-life datasets demonstrate the superior performance of our proposed method.