Accelerating co-ordinate ascent updates for linear regression using DAAREM

Last updated: 2019-06-04

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Knit directory: daarem/analysis/

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A small script to illustrate application of the DAAREM method for computing maximum-likelihood estimates of mixture proportions in a mixture model.

Set up environment

Load some packages and function definitions used in the example below.

library(ggplot2)
library(cowplot)
library(daarem)
source("../code/misc.R")
source("../code/mixem.R")

Load data set

TO DO: Add text here.

load("../data/mixdata.RData")
n <- nrow(L)
m <- ncol(L)
cat(sprintf("Loaded %d x %d data matrix.\n",n,m))
# Loaded 100000 x 10 data matrix.

Set the initial estimate of the mixture proportions.

x0 <- rep(1/m,m)

Run basic EM updates

Compute maximum-likelihood estimates of the mixture proportions by running 200 iterations of the EM updates.

cat("Fitting mixture model with basic EM method.\n")
out <- system.time(fit1 <- mixem(L,x0,numiter = 200))
f1  <- mixobjective(L,fit1$x)
cat(sprintf("Computation took %0.2f seconds.\n",out["elapsed"]))
cat(sprintf("Log-likelihood at EM estimate is %0.12f.\n",f1))
# Fitting mixture model with basic EM method.
# Computation took 9.18 seconds.
# Log-likelihood at EM estimate is -59912.068371303445.

Run accelerated EM

Re-run the EM updates, this time using DAAREM to accelerate convergence toward the solution.

out <- system.time(fit2 <- mixdaarem(L,x0,numiter = 200))
f2  <- mixobjective(L,fit2$x)
cat(sprintf("Computation took %0.2f seconds.\n",out["elapsed"]))
cat(sprintf("Objective value at DAAREM estimate is %0.12f.\n",f2))
# Computation took 6.39 seconds.
# Objective value at DAAREM estimate is -59895.960056733769.

Plot improvement in solution over time