English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In recent years, it has become increasingly easy to obtain approximateposterior samples via efficient computation algorithms, such as those invariational Bayes. On the other hand, concerns exist on the accuracy ofuncertainty estimates, which make it tempting to consider exploiting theapproximate samples in canonical Markov chain Monte Carlo algorithms. A majortechnical barrier is that the approximate sample, when used as a proposal inMetropolis-Hastings steps, tends to have a low acceptance rate as the dimensionincreases. In this article, we propose a simple yet general solution named''graph-accelerated Markov Chain Monte Carlo''. We first build a graph witheach node location assigned to an approximate sample, then we run Markov chainMonte Carlo with random walks over the graph. In the first stage, we optimizethe choice of graph edges to enforce small differences in posteriordensity/probability between neighboring nodes, while encouraging edges tocorrespond to large distances in the parameter space. This optimized graphallows us to accelerate a canonical Markov transition kernel through mixingwith a large-jump Metropolis-Hastings step, when collecting Markov chainsamples at the second stage. Due to its simplicity, this acceleration can beapplied to most of the existing Markov chain Monte Carlo algorithms. Wetheoretically quantify the rate of acceptance as dimension increases, and showthe effects on improved mixing time. We demonstrate our approach throughimproved mixing performances for challenging sampling problems, such as thoseinvolving multiple modes, non-convex density contour, or large-dimension latentvariables.

Graph-accelerated Markov Chain Monte Carlo using Approximate Samples