In stephenslab/mixsqp: Sequential Quadratic Programming for Fast Maximum-Likelihood Estimation of Mixture Proportions

knitr::opts_chunk$set(collapse = TRUE,results = "hold",comment = "#",
                      fig.align = "center",eval = FALSE)

In this vignette, we illustrate the use of the sequential quadratic programming (SQP) algorithm implemented in mixsqp.

Environment set-up

Load the mixsqp package.

library(mixsqp)

Next, initialize the sequence of pseudorandom numbers.

set.seed(1)

Generate a small data set

We begin with a small example to show how mixsqp works.

L <- simulatemixdata(1000,20)$L
dim(L)

This call to simulatemixdata created an $n \times m$ conditional likelihood matrix for a mixture of zero-centered normals, with $n = 1000$ and $m = 20$. By default, simulatemixdata normalizes the rows of the likelihood matrix so that the maximum entry in each row is 1.

Fit mixture model

Now we fit the mixture model using the SQP algorithm:

fit.sqp <- mixsqp(L)

In this example, the SQP algorithm converged to a solution in a small number of iterations.

By default, mixsqp outputs information on its progress. It begins by summarizing the optimization problem and the algorithm settings used. (Since we did not change these settings in the mixsqp call, all the settings shown here are the default settings.)

After that, it outputs, at each iteration, information about the current solution, such as the value of the objective ("objective") and the number of nonzeros ("nnz").

The "max(rdual)" column shows the quantity used to assess convergence. It reports the maximum value of the "dual residual"; the SQP solver terminates when the maximum dual residual is less than conv.tol, which by default is $10^{-8}$. In this example, we see that the dual residual shrinks rapidly toward zero.

Another useful indicator of convergence is the "max.diff" column---it reports the maximum difference between the solution estimates at two successive iterations. We normally expect these differences to shrink as we approach the solution, which is precisely what we see in this example.

This information is also provided in the return value, which we can use, for example, to create a plot of the objective value at each iteration of the SQP algorithm:

numiter <- nrow(fit.sqp$progress)
plot(1:numiter,fit.sqp$progress$objective,type = "b",
     pch = 20,lwd = 2,xlab = "SQP iteration",
     ylab = "objective",xaxp = c(1,numiter,numiter - 1))

Session information

This next code chunk gives information about the computing environment used to generate the results contained in this vignette, including the version of R and the packages used.

sessionInfo()

stephenslab/mixsqp documentation built on Jan. 4, 2024, 1 a.m.