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<p>In this study, we propose a scalable approach to deep kernel learning by integrating the structural advantages of deep learning with the flexibility of kernel methods. Our method employs a deep neural network (DNN) with linear activation functions and a scalable kernel design based on spectral combinations of relevant inputs. To further enhance scalability, we incorporate techniques such as local kernel interpolation, inducing points, and algebraic structures like Kronecker and Toeplitz matrices. These components enable efficient kernel computations, making them suitable for large-scale datasets. We jointly optimize the kernel and DNN parameters within a Gaussian process framework using marginal likelihood. This approach enables efficient training and inference. It achieves O(n) complexity for large datasets with n data points, and O(1) complexity for individual predictions. As a result, it overcomes the limitations of traditional Gaussian processes, which typically have O(n²) computational costs. Our method is evaluated on various regression tasks, including datasets from the UCI repository, facial patch directional detection, and handwritten digit magnitude extraction. Results demonstrate that the proposed approach outperforms conventional Gaussian processes and deep neural networks in accuracy without a significant increase in computational cost.</p>

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Efficient scalable deep kernels: unifying deep learning and nonparametric methods for large-scale data analysis

  • 期刊论文

  • 发表日期：

    2025年9月5日

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  • M. Hamidi,
  • P. Azhdari,
  • K. Fathi Vajargah

摘要

In this study, we propose a scalable approach to deep kernel learning by integrating the structural advantages of deep learning with the flexibility of kernel methods. Our method employs a deep neural network (DNN) with linear activation functions and a scalable kernel design based on spectral combinations of relevant inputs. To further enhance scalability, we incorporate techniques such as local kernel interpolation, inducing points, and algebraic structures like Kronecker and Toeplitz matrices. These components enable efficient kernel computations, making them suitable for large-scale datasets. We jointly optimize the kernel and DNN parameters within a Gaussian process framework using marginal likelihood. This approach enables efficient training and inference. It achieves O(n) complexity for large datasets with n data points, and O(1) complexity for individual predictions. As a result, it overcomes the limitations of traditional Gaussian processes, which typically have O(n²) computational costs. Our method is evaluated on various regression tasks, including datasets from the UCI repository, facial patch directional detection, and handwritten digit magnitude extraction. Results demonstrate that the proposed approach outperforms conventional Gaussian processes and deep neural networks in accuracy without a significant increase in computational cost.