Laplace Approximation for Bayesian Tensor Network Kernel Machines
TLDR
Introduces LA-TNKM, a novel Bayesian Tensor Network Kernel Machine using Laplace approximation for principled uncertainty estimation.
Key contributions
- Addresses the challenge of principled uncertainty estimation in scalable tensor network kernel machines.
- Introduces LA-TNKM, a Bayesian Tensor Network Kernel Machine using Laplace approximation.
- Enables principled uncertainty quantification for non-Gaussian tensor network models.
- Achieves performance comparable to or better than GPs and BNNs on regression tasks.
Why it matters
This paper addresses the critical lack of principled uncertainty estimates in scalable tensor network kernel machines. The proposed LA-TNKM offers a practical solution for robust decision-making, outperforming or matching GPs and BNNs. This is significant for applications needing reliable uncertainty quantification.
Original Abstract
Uncertainty estimation is essential for robust decision-making in the presence of ambiguous or out-of-distribution inputs. Gaussian Processes (GPs) are classical kernel-based models that offer principled uncertainty quantification and perform well on small- to medium-scale datasets. Alternatively, formulating the weight space learning problem under tensor network assumptions yields scalable tensor network kernel machines. However, these assumptions break Gaussianity, complicating standard probabilistic inference. This raises a fundamental question: how can tensor network kernel machines provide principled uncertainty estimates? We propose a novel Bayesian Tensor Network Kernel Machine (LA-TNKM) that employs a (linearized) Laplace approximation for Bayesian inference. A comprehensive set of numerical experiments shows that the proposed method consistently matches or surpasses Gaussian Processes and Bayesian Neural Networks (BNNs) across diverse UCI regression benchmarks, highlighting both its effectiveness and practical relevance.
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