approx_sb: lower bound of a vector of probabilities that sum to one

In zhenkewu/lotR: Latent class analysis with Observed Trees in R (lotR)

lower bound of a vector of probabilities that sum to one

Description

the lower bound is based on the best set of local variational parameters which comprise of logit of the stick-breaking form of the supplied vector

Usage

approx_sb(x)

Arguments

x	a vector of probabilities that sum to one

Value

approximation to a vector of probabilities

References

• Jaakkola, Tommi S., and Michael I. Jordan. "Bayesian parameter estimation via variational methods." Statistics and Computing 10.1 (2000): 25-37. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.399.9368&rep=rep1&type=pdf

• Titsias M(2016). One-vs-each approximation to softmax for scalable estimation of probabilities. Advances in Neural Information Processing Systems. https://papers.nips.cc/paper/6468-one-vs-each-approximation-to-softmax-for-scalable-estimation-of-probabilities.pdf

See Also

Other VI functions: g_fun.vec(), g_fun0(), g_fun(), lower_bd()

Examples

# based on Tsiatis 2016 NeuroIPS
approx <- function(x){
  res = rep(NA,length=length(x))
  for (i in 1:length(res)){
    curr_v <- x[i] - x[-i]
    res[i]  = prod(expit(curr_v))
  }
  res
}

tau = rep(0.25,4)
barplot(rbind(tau,approx_sb(tau),approx(tau)),beside=TRUE,
        legend.text=c("truth","sb + quad (lotR)","1 vs other + quad"),
        main="truth 1")

tau = c(0.5,0.3,0.15,0.05)
barplot(rbind(tau,approx_sb(tau),approx(tau)),beside=TRUE,
        legend.text=c("truth","sb + quad (lotR)","1 vs other + quad"),
        main="truth 2")

zhenkewu/lotR documentation built on April 24, 2022, 2:36 a.m.