Knot Selection in Sparse Gaussian Processes with a Variational Objective Function

• URL: http://arxiv.org/abs/2003.02729v2
• Date: Mon, 13 Apr 2020 23:26:43 GMT
• Title: Knot Selection in Sparse Gaussian Processes with a Variational Objective Function
• Abstract summary: We propose a one-at-a-time knot selection algorithm based on Bayesian optimization to select the number and locations of knots. We showcase the competitive performance of this method relative to simultaneous optimization of knots on three benchmark data sets, but at a fraction of the computational cost.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sparse, knot-based Gaussian processes have enjoyed considerable success as scalable approximations to full Gaussian processes. Certain sparse models can be derived through specific variational approximations to the true posterior, and knots can be selected to minimize the Kullback-Leibler divergence between the approximate and true posterior. While this has been a successful approach, simultaneous optimization of knots can be slow due to the number of parameters being optimized. Furthermore, there have been few proposed methods for selecting the number of knots, and no experimental results exist in the literature. We propose using a one-at-a-time knot selection algorithm based on Bayesian optimization to select the number and locations of knots. We showcase the competitive performance of this method relative to simultaneous optimization of knots on three benchmark data sets, but at a fraction of the computational cost.

Related papers

• Improving search efficiency via adaptive acquisition function selection in discrete black-box optimization [0.7734726150561088]
  In black-box optimization, it is important to identify promising solutions efficiently within a limited number of trials.<n>We propose a hybrid method that uses BOCS as the main search framework and generates alternative unevaluated points.<n>We show that its effectiveness comes from selecting points that promote search progress within Hamming-distance neighborhoods.
  arXiv  Detail & Related papers  (2026-05-11T17:03:01Z)
• Diff3R: Feed-forward 3D Gaussian Splatting with Uncertainty-aware Differentiable Optimization [76.38917994186733]
  Diff3R is a novel framework that bridges feed-forward prediction and test-time optimization.<n>We show that it can be seamlessly integrated into existing feed-forward 3DGS architectures for both pose-given and pose-free methods.
  arXiv  Detail & Related papers  (2026-04-01T15:40:20Z)
• Local Entropy Search over Descent Sequences for Bayesian Optimization [48.7994415668802]
  A practical alternative is to iteratively refine the neighborhood of an initial design using local optimization methods such as gradient descent.<n>We propose local entropy search (LES), a Bayesian optimization paradigm that explicitly targets the solutions reachable by the descent sequences.
  arXiv  Detail & Related papers  (2025-11-24T15:52:17Z)
• Zeroth-Order Methods for Stochastic Nonconvex Nonsmooth Composite Optimization [51.63258496873442]
  Previous works on composite optimization problem requires the major part to smoothness or some machine learning examples which excludes such two approximate smoothness points respectively.<n>In this work we propose two new algorithms for such problem.<n>We show that these algorithms are effective using numerical experiments.
  arXiv  Detail & Related papers  (2025-10-06T02:35:42Z)
• Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Exploration [2.984929040246293]
  novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. New algorithms retain the ease of implementation of the classical GP-UCB, but an additional exploration step facilitates their convergence.
  arXiv  Detail & Related papers  (2024-01-30T14:16:06Z)
• Adapting Newton's Method to Neural Networks through a Summary of Higher-Order Derivatives [0.0]
  We focus on the exact and explicit computation of projections of the Hessian and higher-order derivatives on well-chosen subspaces. We propose an optimization method exploiting tensors at order 2 and 3 with several interesting properties.
  arXiv  Detail & Related papers  (2023-12-06T20:24:05Z)
• Random Postprocessing for Combinatorial Bayesian Optimization [0.552480439325792]
  We numerically study the effect of a postprocessing method on Bayesian optimization. We find the postprocessing method significantly reduces the number of sequential steps to find the global optimum.
  arXiv  Detail & Related papers  (2023-09-06T08:59:34Z)
• Self-concordant Smoothing for Large-Scale Convex Composite Optimization [0.0]
  We introduce a notion of self-concordant smoothing for minimizing the sum of two convex functions, one of which is smooth and the other may be nonsmooth. We prove the convergence of two resulting algorithms: Prox-N-SCORE, a proximal Newton algorithm and Prox-GGN-SCORE, a proximal generalized Gauss-Newton algorithm.
  arXiv  Detail & Related papers  (2023-09-04T19:47:04Z)
• Accelerated First-Order Optimization under Nonlinear Constraints [73.2273449996098]
  We exploit between first-order algorithms for constrained optimization and non-smooth systems to design a new class of accelerated first-order algorithms. An important property of these algorithms is that constraints are expressed in terms of velocities instead of sparse variables.
  arXiv  Detail & Related papers  (2023-02-01T08:50:48Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• Tree ensemble kernels for Bayesian optimization with known constraints over mixed-feature spaces [54.58348769621782]
  Tree ensembles can be well-suited for black-box optimization tasks such as algorithm tuning and neural architecture search. Two well-known challenges in using tree ensembles for black-box optimization are (i) effectively quantifying model uncertainty for exploration and (ii) optimizing over the piece-wise constant acquisition function. Our framework performs as well as state-of-the-art methods for unconstrained black-box optimization over continuous/discrete features and outperforms competing methods for problems combining mixed-variable feature spaces and known input constraints.
  arXiv  Detail & Related papers  (2022-07-02T16:59:37Z)
• STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization [74.1615979057429]
  We investigate non-batch optimization problems where the objective is an expectation over smooth loss functions. Our work builds on the STORM algorithm, in conjunction with a novel approach to adaptively set the learning rate and momentum parameters.
  arXiv  Detail & Related papers  (2021-11-01T15:43:36Z)
• Improving the Quantum Approximate Optimization Algorithm with postselection [0.0]
  Combinatorial optimization is among the main applications envisioned for near-term and fault-tolerant quantum computers. We consider a well-studied quantum algorithm for optimization: the Quantum Approximate Optimization Algorithm (QAOA) applied to the MaxCut problem on 3-regular graphs. We derive theoretical upper and lower bounds showing that a constant (though small) increase of the fraction of satisfied edges is indeed achievable.
  arXiv  Detail & Related papers  (2020-11-10T22:17:50Z)
• Convergence of adaptive algorithms for weakly convex constrained optimization [59.36386973876765]
  We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
  arXiv  Detail & Related papers  (2020-06-11T17:43:19Z)
• Global Optimization of Gaussian processes [52.77024349608834]
  We propose a reduced-space formulation with trained Gaussian processes trained on few data points. The approach also leads to significantly smaller and computationally cheaper sub solver for lower bounding. In total, we reduce time convergence by orders of orders of the proposed method.
  arXiv  Detail & Related papers  (2020-05-21T20:59:11Z)
• Knot Selection in Sparse Gaussian Processes [0.0]
  We propose a one-at-a-time knot selection algorithm to select both the number and placement of knots. Our algorithm uses Bayesian optimization to efficiently propose knots that are likely to be good and largely avoids the pathologies encountered when using the marginal likelihood as the objective function.
  arXiv  Detail & Related papers  (2020-02-21T20:32:05Z)

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.