6 accepted papers
The Hilbert-space Gaussian process (HGP) approach offers a hyperparameter-independent basis function approximation for speeding up Gaussian process (GP) inference by projecting the GP onto $M$ basis functions. These properties result in a favorable data-independent $\mathcal{O}(M^3)$ computational c…
In this paper we establish a new connection between Tensor Network (TN)-constrained kernel machines and Gaussian Processes (GPs). We prove that the outputs of Canonical Polyadic Decomposition (CPD) and Tensor Train (TT)-constrained kernel machines converge in the limit of large ranks to the same GP…
For the first time, this position paper introduces a fundamental link between tensor networks (TNs) and Green AI, highlighting their synergistic potential to enhance both the inclusivity and sustainability of AI research. We argue that TNs are valuable for Green AI due to their strong mathematical b…
In the context of kernel machines, polynomial and Fourier features are commonly used to provide a nonlinear extension to linear models by mapping the data to a higher-dimensional space. Unless one considers the dual formulation of the learning problem, which renders exact large-scale learning unfeas…
Kernel machines are one of the most studied family of methods in machine learning. In the exact setting, training requires to instantiate the kernel matrix, thereby prohibiting their application to large-sampled data. One popular kernel approximation strategy which allows to tackle large-sampled dat…
Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can decrease exponentially in the number of basis functions. Howev…