Distributed, partially collapsed MCMC for Bayesian Nonparametrics

• URL: http://arxiv.org/abs/2001.05591v3
• Date: Wed, 4 Mar 2020 13:57:15 GMT
• Title: Distributed, partially collapsed MCMC for Bayesian Nonparametrics
• Authors: Avinava Dubey, Michael Minyi Zhang, Eric P. Xing, Sinead A. Williamson
• Abstract summary: We exploit the fact that completely random measures, which commonly used models like the Dirichlet process and the beta-Bernoulli process can be expressed as, are decomposable into independent sub-measures. We use this decomposition to partition the latent measure into a finite measure containing only instantiated components, and an infinite measure containing all other components. The resulting hybrid algorithm can be applied to allow scalable inference without sacrificing convergence guarantees.
• Score: 68.5279360794418
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used models like the Dirichlet process and the beta-Bernoulli process can be expressed as, are decomposable into independent sub-measures. We use this decomposition to partition the latent measure into a finite measure containing only instantiated components, and an infinite measure containing all other components. We then select different inference algorithms for the two components: uncollapsed samplers mix well on the finite measure, while collapsed samplers mix well on the infinite, sparsely occupied tail. The resulting hybrid algorithm can be applied to a wide class of models, and can be easily distributed to allow scalable inference without sacrificing asymptotic convergence guarantees.

Related papers

• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional general score-mismatched diffusion samplers. We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions. This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• Total Uncertainty Quantification in Inverse PDE Solutions Obtained with Reduced-Order Deep Learning Surrogate Models [50.90868087591973]
  We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models. We test the proposed framework by comparing it with the iterative ensemble smoother and deep ensembling methods for a non-linear diffusion equation.
  arXiv  Detail & Related papers  (2024-08-20T19:06:02Z)
• Fast Semisupervised Unmixing Using Nonconvex Optimization [80.11512905623417]
  We introduce a novel convex convex model for semi/library-based unmixing. We demonstrate the efficacy of Alternating Methods of sparse unsupervised unmixing.
  arXiv  Detail & Related papers  (2024-01-23T10:07:41Z)
• Bayesian Pseudo-Coresets via Contrastive Divergence [5.479797073162603]
  We introduce a novel approach for constructing pseudo-coresets by utilizing contrastive divergence. It eliminates the need for approximations in the pseudo-coreset construction process. We conduct extensive experiments on multiple datasets, demonstrating its superiority over existing BPC techniques.
  arXiv  Detail & Related papers  (2023-03-20T17:13:50Z)
• On counterfactual inference with unobserved confounding [36.18241676876348]
  Given an observational study with $n$ independent but heterogeneous units, our goal is to learn the counterfactual distribution for each unit. We introduce a convex objective that pools all $n$ samples to jointly learn all $n$ parameter vectors. We derive sufficient conditions for compactly supported distributions to satisfy the logarithmic Sobolev inequality.
  arXiv  Detail & Related papers  (2022-11-14T04:14:37Z)
• Sampling from Arbitrary Functions via PSD Models [55.41644538483948]
  We take a two-step approach by first modeling the probability distribution and then sampling from that model. We show that these models can approximate a large class of densities concisely using few evaluations, and present a simple algorithm to effectively sample from these models.
  arXiv  Detail & Related papers  (2021-10-20T12:25:22Z)
• Self-regularizing Property of Nonparametric Maximum Likelihood Estimator in Mixture Models [39.27013036481509]
  We introduce the nonparametric maximum likelihood (NPMLE) model for general Gaussian mixtures. We show that with high probability the NPMLE based on a sample size has $O(log n)$ atoms (mass points) Notably, any mixture is statistically in from a finite one with $Olog selection.
  arXiv  Detail & Related papers  (2020-08-19T03:39:13Z)
• Slice Sampling for General Completely Random Measures [74.24975039689893]
  We present a novel Markov chain Monte Carlo algorithm for posterior inference that adaptively sets the truncation level using auxiliary slice variables. The efficacy of the proposed algorithm is evaluated on several popular nonparametric models.
  arXiv  Detail & Related papers  (2020-06-24T17:53:53Z)
• Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors [8.11978827493967]
  We propose an approach using parallel runs of MCMC, variational, or mode-based inference to hit as many modes as possible. We present theoretical consistency with an example where the stacked inference process approximates the true data. We demonstrate practical implementation in several model families.
  arXiv  Detail & Related papers  (2020-06-22T15:26:59Z)
• Fast Learning in Reproducing Kernel Krein Spaces via Signed Measures [31.986482149142503]
  We cast this question as a distribution view by introducing the emphsigned measure A series of non-PD kernels can be associated with the linear combination of specific finite Borel measures. Specifically, this solution is also computationally implementable in practice to scale non-PD kernels in large sample cases.
  arXiv  Detail & Related papers  (2020-05-30T12:10:35Z)

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.