用拉普拉斯近似实现张量网络核机器的可信不确定性估计
Laplace Approximation for Bayesian Tensor Network Kernel Machines
- 基于张量网络假设，结合线性化拉普拉斯近似进行贝叶斯推断
- 在多个UCI回归数据集上表现优于或媲美高斯过程和贝叶斯神经网络
- 适合需要可靠置信度估计的中小型机器学习任务
不确定性估计对处理模糊或分布外输入的鲁棒决策至关重要。高斯过程（GPs）是经典的基于核的模型，能提供严谨的不确定性量化，在小到中等规模数据集上表现良好。相比之下，基于张量网络假设的权重空间学习可构建可扩展的张量网络核机器，但该假设破坏了高斯性，使标准概率推断复杂化。这引出一个核心问题：如何让张量网络核机器提供严谨的不确定性估计？本文提出一种新的贝叶斯张量网络核机器（LA-TNKM），采用（线性化）拉普拉斯近似进行贝叶斯推断。大量数值实验表明，所提方法在多种UCI回归基准上始终匹配或超越高斯过程与贝叶斯神经网络，凸显其有效性与实际应用价值。
原文摘要 · Abstract (English)
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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