Function_construction

This function allows the user to create the target function in an interactive manner. Here, the target function is expressed as
$$	f(\boldsymbol{\theta})=f_J(\theta_{1},\ldots,\theta_{p},f_1,\ldots,f_{J-1}),$$
where<ul>
<li>$f_1$ is a function of $\theta_{1},\ldots,\theta_{p}$;</li>
<li>$f_j$ is a function of $\theta_{1},\ldots,\theta_{p},f_1,\ldots,f_{j-1}$, for $j=2,\ldots,J$;</li>
<li>$f_1,\ldots,f_J$ belongs to the bank of assembly functions.</li>
</ul>Here, user can input the function by<ol>
<li>inputting the dimensionality $p$;</li>
<li>for $j=1,\ldots,J$;<ol>
<li>selecting which assembly function $f_j$ belongs to;</li>
<li>inputting the indexes of coefficients or existing functions included as arguments of $f_j$;</li>
<li>inputting the coefficients.</li>
</ol></li>
</ol>

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

Function_construction: Function Construction

Description

Usage

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