Movatterモバイル変換

VBel

Variational Bayes for fast and accurate empirical likelihoodinference

About this package

This package allows you to run GVA on a data set in R and C++ forfaster computation (for 10,000 iterations of GVA: 40.23s for partial Rand cpp and 28.5s for purely cpp computation).

This package also allows you to run AEL on a data set in R and C++for faster computation (for 500 iterations of AEL: 0.2s for purely cppand 0.1s for R and cpp with pre-z calculation).

Pre-installationinstructions (Mac Users Only)

To install this package in Mac requires a Fortran compiler (throughits RcppEigen dependency). Chances are, your current Fortran compiler isnot up-to-date. To update your Fortran compiler, simply follow the stepshere:
 

1. In your Mac App Store, search “Xcode” and install.
   
2. Open Terminal application. Type in

xcode-select --install

     and follow the instructions.
     3. Click on the linkhere.Download the gfortan dmg file according to your MacOS version.
    4. Open the dmg file, run the gfortran installer, follow all theinstructions.

An alternative recommended method is to use the packet managerHomebrew:

  1. Check if you have homebrew with

$ brew doctor

     If you don’t have it installed, use the following code from theHomebrew webiste. Check the website that it hasn’t changed since. Itwill ask for your user password (you won’t see characters as you type).Follow the instructions.

/bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/HEAD/install.sh)"

     2. Install GFortran using gcc (contains GFortran).

brew install gcc

Installation

# Install the development version from GitHub:install.packages("devtools")devtools::install_github("jlimrasc/VBel")

Toy example

library(VBel)# -----------------------------# Generate toy variables# -----------------------------# Generating 30 data points from a simple linear-regression modelset.seed(1)x    <- runif(30, min = -5, max = 5)vari <- rnorm(30, mean = 0, sd = 1)y    <- 0.75 - x + varilam0 <- matrix(c(0,0), nrow = 2)th   <- matrix(c(0.8277, -1.0050), nrow = 2)z    <- cbind(x, y)# Specify moment condition functions for linear regression and its corresponding derivativeh    <- function(z, th) { xi     <- z[1] yi     <- z[2] h_zith <- c(yi - th[1] - th[2] * xi, xi*(yi - th[1] - th[2] * xi)) matrix(h_zith, nrow = 2)}delthh <- function(z, th) { xi <- z[1] matrix(c(-1, -xi, -xi, -xi^2), 2, 2)}# Specify derivative of log priordelth_logpi <- function(theta) { -0.0001 * mu0 }# Specify AEL constant and Newton-Rhapson iterationa         <- 0.00001AEL_iters <- 500# Specify initial values for GVA mean vector and Choleskyreslm <- lm(y ~ x)mu0   <- matrix(unname(reslm$coefficients),2,1)C0    <- unname(t(chol(vcov(reslm))))# Specify details for ADADELTA (Stochastic Gradient-Descent)SGD_iters <- 10000epsil     <- 10^-5rho       <- 0.9# -----------------------------# Excecute functions# -----------------------------ansAELRcpp <- compute_AEL(th, h, lam0, a, z, AEL_iters)resultGVA <-compute_GVA(mu, C0, h, delthh, delth_logpi, z, lam0, rho, epsil, a, SGD_iters, AEL_iters)diagnostic_plot(resultGVA) # Plot the results to check for convergence