Invariant Priors for Bayesian Quadrature

• URL: http://arxiv.org/abs/2112.01578v1
• Date: Thu, 2 Dec 2021 19:42:04 GMT
• Title: Invariant Priors for Bayesian Quadrature
• Abstract summary: We explore priors that encode invariance of the integrand under a set of transformations in the input domain. We show initial results on superior performance in comparison to standard Bayesian quadrature on several synthetic and one real world application.
• Score: 8.185918509343818
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian quadrature (BQ) is a model-based numerical integration method that is able to increase sample efficiency by encoding and leveraging known structure of the integration task at hand. In this paper, we explore priors that encode invariance of the integrand under a set of bijective transformations in the input domain, in particular some unitary transformations, such as rotations, axis-flips, or point symmetries. We show initial results on superior performance in comparison to standard Bayesian quadrature on several synthetic and one real world application.

Related papers

• WUSH: Near-Optimal Adaptive Transforms for LLM Quantization [52.77441224845925]
  Quantization to low bitwidth is a standard approach for deploying large language models.<n>A few extreme weights and activations stretch the dynamic range and reduce the effective resolution of the quantizer.<n>We derive, for the first time, closed-form optimal linear blockwise transforms for joint weight-activation quantization.
  arXiv  Detail & Related papers  (2025-11-30T16:17:34Z)
• Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problems [8.115032818930457]
  We propose a novel framework for solving inverse problems by a Monte Carlo sampling algorithm.<n>We show that the method achieves competitive performance in terms of reconstruction quality.
  arXiv  Detail & Related papers  (2025-11-15T15:27:31Z)
• Variational Autoencoders for Efficient Simulation-Based Inference [0.3495246564946556]
  We present a generative modeling approach based on the variational inference framework for likelihood-free simulation-based inference. We demonstrate the efficacy of these models on well-established benchmark problems, achieving results comparable to flow-based approaches.
  arXiv  Detail & Related papers  (2024-11-21T12:24:13Z)
• Relative Representations: Topological and Geometric Perspectives [53.88896255693922]
  Relative representations are an established approach to zero-shot model stitching. We introduce a normalization procedure in the relative transformation, resulting in invariance to non-isotropic rescalings and permutations. Second, we propose to deploy topological densification when fine-tuning relative representations, a topological regularization loss encouraging clustering within classes.
  arXiv  Detail & Related papers  (2024-09-17T08:09:22Z)
• Variable Substitution and Bilinear Programming for Aligning Partially Overlapping Point Sets [48.1015832267945]
  This research presents a method to meet requirements through the minimization objective function of the RPM algorithm. A branch-and-bound (BnB) algorithm is devised, which solely branches over the parameters, thereby boosting convergence rate. Empirical evaluations demonstrate better robustness of the proposed methodology against non-rigid deformation, positional noise, and outliers, when compared with prevailing state-of-the-art transformations.
  arXiv  Detail & Related papers  (2024-05-14T13:28:57Z)
• Manifold Gaussian Variational Bayes on the Precision Matrix [70.44024861252554]
  We propose an optimization algorithm for Variational Inference (VI) in complex models. We develop an efficient algorithm for Gaussian Variational Inference whose updates satisfy the positive definite constraint on the variational covariance matrix. Due to its black-box nature, MGVBP stands as a ready-to-use solution for VI in complex models.
  arXiv  Detail & Related papers  (2022-10-26T10:12:31Z)
• A Variational Approach for Joint Image Recovery and Feature Extraction Based on Spatially-Varying Generalised Gaussian Models [13.952521992627847]
  The joint problem of reconstruction / extraction optimisation is a challenging task in image processing. It consists in performing, in a joint manner, the restoration of an image and the extraction of the image.
  arXiv  Detail & Related papers  (2022-09-03T09:10:23Z)
• Equivariant Mesh Attention Networks [10.517110532297021]
  We present an attention-based architecture for mesh data that is provably equivariant to all transformations mentioned above. Our results confirm that our proposed architecture is equivariant, and therefore robust, to these local/global transformations.
  arXiv  Detail & Related papers  (2022-05-21T19:53:14Z)
• Topographic VAEs learn Equivariant Capsules [84.33745072274942]
  We introduce the Topographic VAE: a novel method for efficiently training deep generative models with topographically organized latent variables. We show that such a model indeed learns to organize its activations according to salient characteristics such as digit class, width, and style on MNIST. We demonstrate approximate equivariance to complex transformations, expanding upon the capabilities of existing group equivariant neural networks.
  arXiv  Detail & Related papers  (2021-09-03T09:25:57Z)
• 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)
• Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes [3.564709604457361]
  "Projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to be inferred jointly with the GP parameters. We extend the proposed framework to multi-fidelity models using GPs including the scenarios of training multiple outputs together. The benefits of our proposed framework, are illustrated on the computationally challenging three-dimensional aerodynamic optimization of a last-stage blade for an industrial gas turbine.
  arXiv  Detail & Related papers  (2020-08-05T22:28:53Z)
• Asymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants [94.46276668068327]
  In [1], an ensemble of randomly projected linear discriminants is used to classify datasets. We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator. We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
  arXiv  Detail & Related papers  (2020-04-17T12:47:04Z)

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.