asymptotic_partition_function

Compute the asymptotic approximation of the logarithm of the partition function,
using the iteration algorithm of mukherjee2016;textualBayesMallows.

internal

An implementation of the Bayesian version of the Mallows rank model
(Vitelli et al., Journal of Machine Learning Research, 2018 <https://jmlr.org/papers/v18/15-481.html>;
Crispino et al., Annals of Applied Statistics, 2019 <doi:10.1214/18-AOAS1203>;
Sorensen et al., R Journal, 2020 <doi:10.32614/RJ-2020-026>;
Stein, PhD Thesis, 2023 <https://eprints.lancs.ac.uk/id/eprint/195759>). Both Metropolis-Hastings
and sequential Monte Carlo algorithms for estimating the models are available. Cayley, footrule,
Hamming, Kendall, Spearman, and Ulam distances are supported in the models. The rank data to be
analyzed can be in the form of complete rankings, top-k rankings, partially missing rankings, as well
as consistent and inconsistent pairwise preferences. Several functions for plotting and studying the
posterior distributions of parameters are provided. The package also provides functions for estimating
the partition function (normalizing constant) of the Mallows rank model, both with the importance
sampling algorithm of Vitelli et al. and asymptotic approximation with the IPFP algorithm
(Mukherjee, Annals of Statistics, 2016 <doi:10.1214/15-AOS1389>).

Oystein Sorensen

BayesMallows

Bayesian Preference Learning with the Mallows Rank Model

Waldir Leoncio

Valeria Vitelli

Marta Crispino

Qinghua Liu

Cristina Mollica

Luca Tardella

Anja Stein

asymptotic_partition_function function

<dl><dt>alpha_vector</dt>
<dd>A numeric vector of alpha values.</dd>
<dt>n_items</dt>
<dd>Integer specifying the number of items.</dd>
<dt>metric</dt>
<dd>One of <code>"footrule"</code> and <code>"spearman"</code>.</dd>
<dt>K</dt>
<dd>Integer.</dd>
<dt>n_iterations</dt>
<dd>Integer specifying the number of iterations.</dd>
<dt>tol</dt>
<dd>Stopping criterion for algorithm. The previous matrix is subtracted
from the updated, and if the maximum absolute relative difference is below <code>tol</code>,
the iteration stops.</dd></dl>

Arguments

Asymptotic Approximation of Partition Function — asymptotic_partition_function

<dl>

<dt>alpha_vector</dt>
<dd>A numeric vector of alpha values.</dd>


<dt>n_items</dt>
<dd>Integer specifying the number of items.</dd>


<dt>metric</dt>
<dd>One of <code>"footrule"</code> and <code>"spearman"</code>.</dd>


<dt>K</dt>
<dd>Integer.</dd>


<dt>n_iterations</dt>
<dd>Integer specifying the number of iterations.</dd>


<dt>tol</dt>
<dd>Stopping criterion for algorithm. The previous matrix is subtracted
from the updated, and if the maximum absolute relative difference is below <code>tol</code>,
the iteration stops.</dd>

</dl>

Asymptotic Approximation of Partition Function

asymptotic_partition_function: Asymptotic Approximation of Partition Function

Description

Usage

Value

Arguments

References