Density Estimation with Semidefinite Programming

The models of probability density functions are Gaussian or exponential distributions with polynomial correction terms. Using a maximum likelihood method, 'dsdp' computes parameters of Gaussian or exponential distributions together with degrees of polynomials by a grid search, and coefficient of polynomials by a variant of semidefinite programming. It adopts Akaike Information Criterion for model selection. See a vignette for a tutorial and more on our 'Github' repository < https://github.com/tsuchiya-lab/dsdp/>.

dsdp

The goal of dsdp is to estimate probability density functions from a data set using a maximum likelihood method. The models of density functions in use are familiar Gaussian or exponential distributions with polynomial correction terms. To find an optimal model, we adopt a grid search for parameters of base functions and degrees of polynomials, together with semidefinite programming for coefficients of polynomials, and then model selection is done by Akaike Information Criterion.

Installation

## Install from CRAN
install.packages(dsdp)

You can install the development version of dsdp from this repository:

## Install from github
devtools::install_github("tsuchiya-lab/dsdp")

To install from source codes, the user needs an appropriate compiler toolchain, for example, rtools in Windows, to build dsdp, along with devtools package.

Usage

Please refer to the tutorial and the reference in tsuchiya-lab.github.io/dsdp/.

Pdf version of articles are also available: A Tutorial for dsdp, Problem Formulations for dsdp.

Acknowledgements

This research was supported in part with Grant-in-Aid for Scientific Research(B) JP18H03206, JP21H03398 and Grant-in-Aid for Exploratory Research JP20K21792 from the Japan Society for the Promotion of Sciences.