# Sequential Quadratic Programming for Fast Maximum-Likelihood Estimation of Mixture Proportions

Provides an optimization method based on sequential quadratic programming (SQP) for maximum likelihood estimation of the mixture proportions in a finite mixture model where the component densities are known. The algorithm is expected to obtain solutions that are at least as accurate as the state-of-the-art MOSEK interior-point solver (called by function "KWDual" in the 'REBayes' package), and they are expected to arrive at solutions more quickly when the number of samples is large and the number of mixture components is not too large. This implements the "mix-SQP" algorithm, with some improvements, described in Y. Kim, P. Carbonetto, M. Stephens & M. Anitescu (2020) .

The mixsqp R package provides algorithms based on sequential quadratic programming for maximum likelihood estimation of the mixture proportions in a finite mixture model where the component densities are known. The SQP algorithm is expected to obtain solutions that are at least as accurate as the state-of-the-art MOSEK interior-point solver (called via the "KWDual" function in the REBayes package), and is expected to compute these solutions much more quickly in large data sets.

For more details on the SQP algorithm, please see our paper on arXiv.

See also the Julia implementation, which, at time of writing, is faster than the R implementation, particularly for large data sets.

If you find a bug, or you have a question or feedback on our work, please post an issue.

## Citing this work

If you find the mixsqp package or any of the source code in this repository useful for your work, please cite:

Anitescu. A fast algorithm for maximum likelihood estimation of mixture proportions using sequential quadratic programming. arXiv:1806.01412.

Copyright (c) 2017-2018, Youngseok Kim, Peter Carbonetto, Matthew Stephens and Mihai Anitescu.

All source code and software in this repository are made available under the terms of the MIT license. See file LICENSE for the full text of the license.

## Quick Start

Install mixsqp from CRAN:

For more detailed installation instructions, see the "Setup" section below.

Once you have installed the package, load the package in R:

Next, run the small example provided with the mixsqp function:

For a more detailed illustration of the SQP algorithm applied to the problem of computing maximum-likelihood estimates for a mixture model, read through the introductory vignette.

To learn more, visit the package website, or view the "mixsqp" help page:

## Setup

To install mixsqp from CRAN, in R run:

Alternatively, to install the latest version of the mixsqp package from GitHub, use devtools:

This command should automatically install all required packages if they are not installed already.

If you have cloned the repository locally, you can install the package with the install_local function from devtools. Assuming your working directory contains the mixsqp repository, run this code to install the package:

• Compiling the mixsqp package from source will require a C++ compiler setup that is appropriate for the the R installed on your computer. For details, refer to the CRAN documentation. For Mac computers, see these notes.

• To use the (optional) alternative solver, "mixkwdual", which is mostly useful for comparisons of the different optimization methods, you will need to install the REBayes package. The REBayes package, in turn, requires the Rmosek package. Refer to the MOSEK documentation for instructions on installing the Rmosek package. Once you have followed these steps, you can run this example to verify that Rmosek is correctly installed. Installation of the REBayes package also allows you to build the vignette and view it locally:

## Developer notes

### Testing the package

To install and test the mixsqp R package, run the following commands in the shell:

Note that these commands require that the dependencies have already been installed. See the DESCRIPTION file for details.

### Updating the C++ source and documentation

When any changes are made to roxygen2 markup or to the C++ code in the src directory, simply run devtools::document() to update the RcppExports.cpp, the NAMESPACE file, and the package documentation files in the man directory.

### Updating the pkgdown site

Run this line of R code to build the website (make sure you have an Internet connection while running the code):

### Other developer notes

Add file pre-commit to .git/hooks in the git repository to prevent commits that don't include a change to the package version.

## Credits

The mixsqp R package was developed by Youngseok Kim and Peter Carbonetto at the University of Chicago, with contributions from Matthew Stephens and Mihai Anitescu.

# Reference manual

install.packages("mixsqp")

0.3-43 by Peter Carbonetto, 8 months ago

https://github.com/stephenslab/mixsqp

Report a bug at https://github.com/stephenslab/mixsqp/issues

Browse source code at https://github.com/cran/mixsqp

Authors: Youngseok Kim [aut] , Peter Carbonetto [aut, cre] , Mihai Anitescu [aut] , Matthew Stephens [aut] , Jason Willwerscheid [ctb] , Jean Morrison [ctb]

Documentation:   PDF Manual

Task views: Optimization and Mathematical Programming