Sliced Kernelized Stein Discrepancy

• URL: http://arxiv.org/abs/2006.16531v3
• Date: Wed, 17 Mar 2021 09:54:48 GMT
• Title: Sliced Kernelized Stein Discrepancy
• Authors: Wenbo Gong, Yingzhen Li, Jos\'e Miguel Hern\'andez-Lobato
• Abstract summary: Kernelized Stein discrepancy (KSD) is extensively used in goodness-of-fit tests and model learning. We propose the sliced Stein discrepancy and its scalable and kernelized variants, which employ kernel-based test functions defined on the optimal one-dimensional projections. For model learning, we show its advantages over existing Stein discrepancy baselines by training independent component analysis models with different discrepancies.
• Score: 17.159499204595527
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Kernelized Stein discrepancy (KSD), though being extensively used in goodness-of-fit tests and model learning, suffers from the curse-of-dimensionality. We address this issue by proposing the sliced Stein discrepancy and its scalable and kernelized variants, which employ kernel-based test functions defined on the optimal one-dimensional projections. When applied to goodness-of-fit tests, extensive experiments show the proposed discrepancy significantly outperforms KSD and various baselines in high dimensions. For model learning, we show its advantages over existing Stein discrepancy baselines by training independent component analysis models with different discrepancies. We further propose a novel particle inference method called sliced Stein variational gradient descent (S-SVGD) which alleviates the mode-collapse issue of SVGD in training variational autoencoders.

Related papers

• SteinDreamer: Variance Reduction for Text-to-3D Score Distillation via Stein Identity [70.32101198891465]
  We show that gradient estimation in score distillation is inherent to high variance. We propose a more general solution to reduce variance for score distillation, termed Stein Score Distillation (SSD) We demonstrate that SteinDreamer achieves faster convergence than existing methods due to more stable gradient updates.
  arXiv  Detail & Related papers  (2023-12-31T23:04:25Z)
• Augmented Message Passing Stein Variational Gradient Descent [3.5788754401889014]
  We study the isotropy property of finite particles during the convergence process. All particles tend to cluster around the particle center within a certain range. Our algorithm achieves satisfactory accuracy and overcomes the variance collapse problem in various benchmark problems.
  arXiv  Detail & Related papers  (2023-05-18T01:13:04Z)
• A kernel Stein test of goodness of fit for sequential models [19.8408003104988]
  The proposed measure is an instance of the kernel Stein discrepancy (KSD), which has been used to construct goodness-of-fit tests for unnormalized densities. We extend the KSD to the variable-dimension setting by identifying appropriate Stein operators, and propose a novel KSD goodness-of-fit test. Our test is shown to perform well in practice on discrete sequential data benchmarks.
  arXiv  Detail & Related papers  (2022-10-19T17:30:15Z)
• Grassmann Stein Variational Gradient Descent [3.644031721554146]
  Stein variational gradient descent (SVGD) is a deterministic particle inference algorithm that provides an efficient alternative to Markov chain Monte Carlo. Recent developments have advocated projecting both the score function and the data onto real lines to sidestep this issue. We propose Grassmann Stein variational gradient descent (GSVGD) as an alternative approach, which permits projections onto arbitrary dimensional subspaces.
  arXiv  Detail & Related papers  (2022-02-07T15:36:03Z)
• Scaling Structured Inference with Randomization [64.18063627155128]
  We propose a family of dynamic programming (RDP) randomized for scaling structured models to tens of thousands of latent states. Our method is widely applicable to classical DP-based inference. It is also compatible with automatic differentiation so can be integrated with neural networks seamlessly.
  arXiv  Detail & Related papers  (2021-12-07T11:26:41Z)
• Generalised Kernel Stein Discrepancy(GKSD): A Unifying Approach for Non-parametric Goodness-of-fit Testing [5.885020100736158]
  Non-parametric goodness-of-fit testing procedures based on kernel Stein discrepancies (KSD) are promising approaches to validate general unnormalised distributions. We propose a unifying framework, the generalised kernel Stein discrepancy (GKSD), to theoretically compare and interpret different Stein operators in performing the KSD-based goodness-of-fit tests.
  arXiv  Detail & Related papers  (2021-06-23T00:44:31Z)
• On Stein Variational Neural Network Ensembles [8.178886940116035]
  In this work, we study different Stein variational gradient descent (SVGD) methods operating in the weight space, function space, and in a hybrid setting. We find that SVGD using functional and hybrid kernels can overcome the limitations of deep ensembles.
  arXiv  Detail & Related papers  (2021-06-20T21:52:46Z)
• Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descent [80.73580820014242]
  We focus on the problem of efficient sampling and learning of probability densities by incorporating symmetries in probabilistic models. We first introduce Equivariant Stein Variational Gradient Descent algorithm -- an equivariant sampling method based on Stein's identity for sampling from densities with symmetries. We propose new ways of improving and scaling up training of energy based models.
  arXiv  Detail & Related papers  (2021-06-15T01:35:17Z)
• Kernel Stein Generative Modeling [68.03537693810972]
  Gradient Langevin Dynamics (SGLD) demonstrates impressive results with energy-based models on high-dimensional and complex data distributions. Stein Variational Gradient Descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate a given distribution. We propose noise conditional kernel SVGD (NCK-SVGD), that works in tandem with the recently introduced Noise Conditional Score Network estimator.
  arXiv  Detail & Related papers  (2020-07-06T21:26:04Z)
• Stein Variational Inference for Discrete Distributions [70.19352762933259]
  We propose a simple yet general framework that transforms discrete distributions to equivalent piecewise continuous distributions. Our method outperforms traditional algorithms such as Gibbs sampling and discontinuous Hamiltonian Monte Carlo. We demonstrate that our method provides a promising tool for learning ensembles of binarized neural network (BNN) In addition, such transform can be straightforwardly employed in gradient-free kernelized Stein discrepancy to perform goodness-of-fit (GOF) test on discrete distributions.
  arXiv  Detail & Related papers  (2020-03-01T22:45:41Z)
• A Kernel Stein Test for Comparing Latent Variable Models [48.32146056855925]
  We propose a kernel-based nonparametric test of relative goodness of fit, where the goal is to compare two models, both of which may have unobserved latent variables. We show that our test significantly outperforms the relative Maximum Mean Discrepancy test, which is based on samples from the models and does not exploit the latent structure.
  arXiv  Detail & Related papers  (2019-07-01T07:46:16Z)

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.