Generative Particle Variational Inference via Estimation of Functional Gradients

• URL: http://arxiv.org/abs/2103.01291v1
• Date: Mon, 1 Mar 2021 20:29:41 GMT
• Title: Generative Particle Variational Inference via Estimation of Functional Gradients
• Authors: Neale Ratzlaff, Qinxun Bai, Li Fuxin, Wei Xu
• Abstract summary: This work proposes a new method for learning to approximately sample from the posterior distribution. Our generative ParVI (GPVI) approach maintains the performance of ParVI methods while offering the flexibility of a generative sampler.
• Score: 15.370890881254066
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recently, particle-based variational inference (ParVI) methods have gained interest because they directly minimize the Kullback-Leibler divergence and do not suffer from approximation errors from the evidence-based lower bound. However, many ParVI approaches do not allow arbitrary sampling from the posterior, and the few that do allow such sampling suffer from suboptimality. This work proposes a new method for learning to approximately sample from the posterior distribution. We construct a neural sampler that is trained with the functional gradient of the KL-divergence between the empirical sampling distribution and the target distribution, assuming the gradient resides within a reproducing kernel Hilbert space. Our generative ParVI (GPVI) approach maintains the asymptotic performance of ParVI methods while offering the flexibility of a generative sampler. Through carefully constructed experiments, we show that GPVI outperforms previous generative ParVI methods such as amortized SVGD, and is competitive with ParVI as well as gold-standard approaches like Hamiltonian Monte Carlo for fitting both exactly known and intractable target distributions.

Related papers

• Functional Gradient Flows for Constrained Sampling [29.631753643887237]
  We propose a new functional gradient ParVI method for constrained sampling, called constrained functional gradient flow (CFG) We also present novel numerical strategies to handle the boundary integral term arising from the domain constraints.
  arXiv  Detail & Related papers  (2024-10-30T16:20:48Z)
• Semi-Implicit Functional Gradient Flow [30.32233517392456]
  We propose a functional gradient ParVI method that uses perturbed particles as the approximation family. The corresponding functional gradient flow, which can be estimated via denoising score matching, exhibits strong theoretical convergence guarantee.
  arXiv  Detail & Related papers  (2024-10-23T15:00:30Z)
• Particle Semi-Implicit Variational Inference [2.555222031881788]
  Semi-implicit variational inference (SIVI) enriches the expressiveness of variational families by utilizing a kernel and a mixing distribution. Existing SIVI methods parameterize the mixing distribution using implicit distributions, leading to intractable variational densities. We propose a novel method for SIVI called Particle Variational Inference (PVI) which employs empirical measures to approximate the optimal mixing distributions.
  arXiv  Detail & Related papers  (2024-06-30T10:21:41Z)
• Score-based Source Separation with Applications to Digital Communication Signals [72.6570125649502]
  We propose a new method for separating superimposed sources using diffusion-based generative models. Motivated by applications in radio-frequency (RF) systems, we are interested in sources with underlying discrete nature. Our method can be viewed as a multi-source extension to the recently proposed score distillation sampling scheme.
  arXiv  Detail & Related papers  (2023-06-26T04:12:40Z)
• Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers [90.45898746733397]
  We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. We show that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current gradient.
  arXiv  Detail & Related papers  (2023-03-06T18:59:19Z)
• Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates [1.90365714903665]
  We introduce a suite of new particle-based methods for scalable Bayesian inference based on coin betting. We demonstrate comparable performance to other ParVI algorithms with no need to tune a learning rate.
  arXiv  Detail & Related papers  (2023-01-26T18:32:21Z)
• Generalised Gaussian Process Latent Variable Models (GPLVM) with Stochastic Variational Inference [9.468270453795409]
  We study the doubly formulation of the BayesianVM model amenable with minibatch training. We show how this framework is compatible with different latent variable formulations and perform experiments to compare a suite of models. We demonstrate how we can train in the presence of massively missing data and obtain high-fidelity reconstructions.
  arXiv  Detail & Related papers  (2022-02-25T21:21:51Z)
• Minibatch vs Local SGD with Shuffling: Tight Convergence Bounds and Beyond [63.59034509960994]
  We study shuffling-based variants: minibatch and local Random Reshuffling, which draw gradients without replacement. For smooth functions satisfying the Polyak-Lojasiewicz condition, we obtain convergence bounds which show that these shuffling-based variants converge faster than their with-replacement counterparts. We propose an algorithmic modification called synchronized shuffling that leads to convergence rates faster than our lower bounds in near-homogeneous settings.
  arXiv  Detail & Related papers  (2021-10-20T02:25:25Z)
• Loss function based second-order Jensen inequality and its application to particle variational inference [112.58907653042317]
  Particle variational inference (PVI) uses an ensemble of models as an empirical approximation for the posterior distribution. PVI iteratively updates each model with a repulsion force to ensure the diversity of the optimized models. We derive a novel generalization error bound and show that it can be reduced by enhancing the diversity of models.
  arXiv  Detail & Related papers  (2021-06-09T12:13:51Z)
• Efficient Semi-Implicit Variational Inference [65.07058307271329]
  We propose an efficient and scalable semi-implicit extrapolational (SIVI) Our method maps SIVI's evidence to a rigorous inference of lower gradient values.
  arXiv  Detail & Related papers  (2021-01-15T11:39:09Z)
• 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)

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.