findWeiszfeldMedian: Find M-posterior using samples from subset posteriors

In Mposterior: Mposterior: R package for Robust and Scalable Bayes via a Median of Subset Posterior Measures

Description

Find M-posterior given list of samples from subset posteriors using Weiszfeld algorithm of Minsker et al. (2014).

Usage

findWeiszfeldMedian(subsetAtomsList, sigma = 0.1, maxit = 100,
  tol = 1e-10)

Arguments

subsetAtomsList	list of samples from subset posteriors; each element of the list must be a matrix
sigma	parameter of RBF kernel with form exp(- sigma || x - y ||^2)
maxit	maximum number of iterations estimating M-posterior
tol	tolerance for declaring convergence of Weiszfeld algorithm

Details

Samples from subset posteriors are represented as matrices, with the rows representing atoms and the columns indexing dimensions. Length of subsetAtomsList equals the number of subsets (and posteriors). M-posterior estimates the weights of its atoms given the atoms of subset posteriors using Weiszfeld algorithm as implemented in findWeiszfeldMedian; sigma controls the sensitivity of distance between subset posteriors.

Value

list containing Weiszfeld wts of subset posteriors, M-posterior atoms, and the estimation set-up

Author(s)

Sanvesh Srivastava [e-mail]

References

Minsker, S., Srivastava, S., Lin, L., and Dunson, D.B. (2014). Robust and Scalable Bayes via a Median of Subset Posterior Measures. http://arxiv.org/abs/1403.2660

Examples

set.seed(12345)
## list that contains subset posterior samples from 2-dim Gaussian density
subAtomList <- vector("list", 5)
subAtomList[[1]] <- cbind(rnorm(100, mean = 1),  rnorm(100, mean = 1))
subAtomList[[2]] <- cbind(rnorm(100, mean = -1),  rnorm(100, mean= -1))
subAtomList[[3]] <- cbind(rnorm(100, mean = -1),  rnorm(100, mean = 1))
subAtomList[[4]] <- cbind(rnorm(100, mean = 1),  rnorm(100, mean = -1))
subAtomList[[5]] <- cbind(rnorm(100, mean = 2),  rnorm(100, mean = 2))
library(Mposterior)
medPosterior <- findWeiszfeldMedian(subAtomList, sigma = 0.1, maxit = 100, tol = 1e-10)
medPosterior
summary(medPosterior)
plot(medPosterior)

Example output

Loading required package: Rcpp
## 
## Mposterior: R package for Robust and Scalable Bayes via a Median of Subset Posterior Measures
## (Version 0.1.2, built: 2014-06-01)
## Copyright (C) 2013-2019 Sanvesh Srivastava
Weiszfeld iteration: 10
Weiszfeld iteration: 20
Weiszfeld iteration: 30
Weiszfeld iteration: 40
Weiszfeld algorithm coverged at iteration: 48
Subset posteriors: 
  Subset Natoms WeiszfeldWts
1      1    100         0.34
2      2    100         0.14
3      3    100         0.16
4      4    100         0.19
5      5    100         0.17
M-posterior has 2 dimensions
RBF kernel with sigma= 0.1
Weiszfeld algorithm converged in 48 iterations
Subset posteriors: 
  Subset Natoms WeiszfeldWts
1      1    100         0.34
2      2    100         0.14
3      3    100         0.16
4      4    100         0.19
5      5    100         0.17
M-posterior has 2 dimensions
RBF kernel with sigma = 0.1
Weiszfeld algorithm converged in 48 iterations

Mposterior documentation built on May 29, 2017, 6:38 p.m.