Preconditioned Additive Gaussian Processes with Fourier Acceleration

• URL: http://arxiv.org/abs/2504.00480v1
• Date: Tue, 01 Apr 2025 07:14:06 GMT
• Title: Preconditioned Additive Gaussian Processes with Fourier Acceleration
• Authors: Theresa Wagner, Tianshi Xu, Franziska Nestler, Yuanzhe Xi, Martin Stoll,
• Abstract summary: We introduce a matrix-free method to achieve nearly linear complexity in the multiplication of kernel matrices and their derivatives.<n>To address high-dimensional problems, we propose an additive kernel approach.<n>Each sub- Kernel captures lower-order feature interactions, allowing for the efficient application of the NFFT method.
• Score: 2.292881746604941
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Gaussian processes (GPs) are crucial in machine learning for quantifying uncertainty in predictions. However, their associated covariance matrices, defined by kernel functions, are typically dense and large-scale, posing significant computational challenges. This paper introduces a matrix-free method that utilizes the Non-equispaced Fast Fourier Transform (NFFT) to achieve nearly linear complexity in the multiplication of kernel matrices and their derivatives with vectors for a predetermined accuracy level. To address high-dimensional problems, we propose an additive kernel approach. Each sub-kernel in this approach captures lower-order feature interactions, allowing for the efficient application of the NFFT method and potentially increasing accuracy across various real-world datasets. Additionally, we implement a preconditioning strategy that accelerates hyperparameter tuning, further improving the efficiency and effectiveness of GPs.

Related papers

• Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems [49.819436680336786]
  Gaussian process state-space models (GPSSMs) have emerged as a powerful framework for modeling dynamical systems.<n>We propose an efficient transformed Gaussian process state-space model (ETGPSSM) to address these limitations.<n>Our approach leverages a single shared Gaussian process (GP) combined with normalizing flows and Bayesian neural networks, enabling efficient modeling of complex, high-dimensional state transitions.
  arXiv  Detail & Related papers  (2025-03-24T03:19:45Z)
• A quantum gradient descent algorithm for optimizing Gaussian Process models [28.16587217223671]
  We propose a quantum gradient descent algorithm to optimize the Gaussian Process model.<n>Our algorithm achieves exponential speedup in computing the gradients of the log marginal likelihood.
  arXiv  Detail & Related papers  (2025-03-22T14:14:31Z)
• Sample-efficient Bayesian Optimisation Using Known Invariances [56.34916328814857]
  We show that vanilla and constrained BO algorithms are inefficient when optimising invariant objectives. We derive a bound on the maximum information gain of these invariant kernels. We use our method to design a current drive system for a nuclear fusion reactor, finding a high-performance solution.
  arXiv  Detail & Related papers  (2024-10-22T12:51:46Z)
• The Stochastic Conjugate Subgradient Algorithm For Kernel Support Vector Machines [1.738375118265695]
  This paper proposes an innovative method specifically designed for kernel support vector machines (SVMs) It not only achieves faster iteration per iteration but also exhibits enhanced convergence when compared to conventional SFO techniques. Our experimental results demonstrate that the proposed algorithm not only maintains but potentially exceeds the scalability of SFO methods.
  arXiv  Detail & Related papers  (2024-07-30T17:03:19Z)
• Variance-Reducing Couplings for Random Features [57.73648780299374]
  Random features (RFs) are a popular technique to scale up kernel methods in machine learning. We find couplings to improve RFs defined on both Euclidean and discrete input spaces. We reach surprising conclusions about the benefits and limitations of variance reduction as a paradigm.
  arXiv  Detail & Related papers  (2024-05-26T12:25:09Z)
• Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domains [13.56018270837999]
  We propose a simple method to extend neural operators to arbitrary domains. An efficient implementation* of such direct spectral evaluations is coupled with existing neural operator models. We demonstrate that the proposed method allows us to extend neural operators to arbitrary point distributions with significant gains in training speed over baselines.
  arXiv  Detail & Related papers  (2023-05-31T09:01:20Z)
• Linear Self-Attention Approximation via Trainable Feedforward Kernel [77.34726150561087]
  In pursuit of faster computation, Efficient Transformers demonstrate an impressive variety of approaches. We aim to expand the idea of trainable kernel methods to approximate the self-attention mechanism of the Transformer architecture.
  arXiv  Detail & Related papers  (2022-11-08T08:14:11Z)
• FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels [82.53569355337586]
  This work offers an efficient solution to temporal point processes inference using general parametric kernels with finite support. The method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG) Results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.
  arXiv  Detail & Related papers  (2022-10-10T12:35:02Z)
• Scalable Gaussian Process Hyperparameter Optimization via Coverage Regularization [0.0]
  We present a novel algorithm which estimates the smoothness and length-scale parameters in the Matern kernel in order to improve robustness of the resulting prediction uncertainties. We achieve improved UQ over leave-one-out likelihood while maintaining a high degree of scalability as demonstrated in numerical experiments.
  arXiv  Detail & Related papers  (2022-09-22T19:23:37Z)
• Automatic and effective discovery of quantum kernels [41.61572387137452]
  Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data.<n>We present an approach to this problem, which employs optimization techniques, similar to those used in neural architecture search and AutoML.<n>The results obtained by testing our approach on a high-energy physics problem demonstrate that, in the best-case scenario, we can either match or improve testing accuracy with respect to the manual design approach.
  arXiv  Detail & Related papers  (2022-09-22T16:42:14Z)
• Reducing the Variance of Gaussian Process Hyperparameter Optimization with Preconditioning [54.01682318834995]
  Preconditioning is a highly effective step for any iterative method involving matrix-vector multiplication. We prove that preconditioning has an additional benefit that has been previously unexplored. It simultaneously can reduce variance at essentially negligible cost.
  arXiv  Detail & Related papers  (2021-07-01T06:43:11Z)
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition [54.07797071198249]
  We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
  arXiv  Detail & Related papers  (2021-06-10T18:17:57Z)
• The Fast Kernel Transform [21.001203328543006]
  We propose the Fast Kernel Transform (FKT), a general algorithm to compute matrix-vector multiplications for datasets in moderate dimensions with quasilinear complexity. The FKT is easily applied to a broad class of kernels, including Gaussian, Matern, and Rational Quadratic covariance functions and physically motivated Green's functions. We illustrate the efficacy and versatility of the FKT by providing timing and accuracy benchmarks and by applying it to scale the neighborhood embedding (t-SNE) and Gaussian processes to large real-world data sets.
  arXiv  Detail & Related papers  (2021-06-08T16:15:47Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• Certified and fast computations with shallow covariance kernels [0.0]
  We introduce and analyze a new and certified algorithm for the low-rank approximation of a parameterized family of covariance operators. The proposed algorithm provides the basis of a fast sampling procedure for parameter dependent random fields.
  arXiv  Detail & Related papers  (2020-01-24T20:28:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.