MMAD

This function allows the user to maximize the target function \(f(\boldsymbol{\theta})\) using MM algorithm with AD technology.

The minorization-maximization (MM) algorithm is a powerful tool for maximizing nonconcave target function. However, for most existing MM algorithms, the surrogate function in the minorization step is constructed in a case-specific manner and requires manual programming. To address this limitation, we develop the R package MMAD, which systematically integrates the assembly--decomposition technology in the MM framework. This new package provides a comprehensive computational toolkit for one-stop inference of complex target functions, including function construction, evaluation, minorization and optimization via MM algorithm. By representing the target function through a hierarchical composition of assembly functions, we design a hierarchical algorithmic structure that supports both bottom-up operations (construction, evaluation) and top-down operation (minorization).

Jiaqi Gu

An R Package of Minorization-Maximization Algorithm via the
Assembly--Decomposition Technology

Xifen Huang

Jinfeng Xu

MMAD function

<dl><dt>Function_obj</dt>
<dd>An R list depicting the target function.</dd>
<dt>init</dt>
<dd>The initial value \(\boldsymbol{\theta}^{(0)}\) for iterative optimization.</dd>
<dt>tol</dt>
<dd>The tolerance for convergence detection (default: \(1\times 10^{-4}\)).</dd></dl>

Arguments

Minorization-Maximization Algorithm via the Assembly--Decomposition Technology — MMAD

<dl>

<dt>Function_obj</dt>
<dd>An R list depicting the target function.</dd>


<dt>init</dt>
<dd>The initial value \(\boldsymbol{\theta}^{(0)}\) for iterative optimization.</dd>


<dt>tol</dt>
<dd>The tolerance for convergence detection (default: \(1\times 10^{-4}\)).</dd>

</dl>

MMAD: Minorization-Maximization Algorithm via the Assembly--Decomposition Technology

Description

Usage

Value

Arguments