var_nvd

This function computes the Fréchet variance around a specified network from
an observed sample of network-valued random variables according to a
specified distance. In most cases, the user is willing to compute the sample
variance, in which case the Fréchet variance has to be evaluated w.r.t. the
sample Fréchet mean. In this case, it is important that the user indicates
the same distance as the one (s)he used to separately compute the sample
Fréchet mean. This function can also be used as is as the function to be
minimized in order to find the Fréchet mean for a given distance.

A flexible statistical framework for network-valued data analysis.
It leverages the complexity of the space of distributions on graphs by using
the permutation framework for inference as implemented in the 'flipr' package.
Currently, only the two-sample testing problem is covered and generalization
to k samples and regression will be added in the future as well. It is a
4-step procedure where the user chooses a suitable representation of the
networks, a suitable metric to embed the representation into a metric space,
one or more test statistics to target specific aspects of the distributions
to be compared and a formula to compute the permutation p-value. Two types
of inference are provided: a global test answering whether there is a
difference between the distributions that generated the two samples and a
local test for localizing differences on the network structure. The latter
is assumed to be shared by all networks of both samples. References: Lovato,
I., Pini, A., Stamm, A., Vantini, S. (2020) "Model-free two-sample test for
network-valued data" <doi:10.1016/j.csda.2019.106896>; Lovato, I., Pini, A.,
Stamm, A., Taquet, M., Vantini, S. (2021) "Multiscale null hypothesis
testing for network-valued data: Analysis of brain networks of patients with
autism" <doi:10.1111/rssc.12463>.

Aymeric Stamm

nevada

Network-Valued Data Analysis

Ilenia Lovato

Alessia Pini

Simone Vantini

var_nvd function

<dl><dt>x</dt>
<dd>An <code>nvd</code> object listing a sample of networks.</dd>
<dt>x0</dt>
<dd>A network already in matrix representation around which to
calculate variance (usually the Fréchet mean but not necessarily). Note
that the chosen matrix representation is extracted from this parameter.</dd>
<dt>weights</dt>
<dd>A numeric vector specifying weights for each observation
(default: equally weighted).</dd>
<dt>distance</dt>
<dd>A string specifying the distance to be used. Possible choices
are: hamming, frobenius, spectral or root-euclidean. Default is frobenius.
When the Fréchet mean is used as <code>x0</code> parameter, the distance should
match the one used to compute the mean. This is not currently checked.</dd></dl>

Arguments

Fréchet Variance of Network-Valued Data Around a Given Network — var_nvd

<dl>

<dt>x</dt>
<dd>An <code>nvd</code> object listing a sample of networks.</dd>


<dt>x0</dt>
<dd>A network already in matrix representation around which to
calculate variance (usually the Fréchet mean but not necessarily). Note
that the chosen matrix representation is extracted from this parameter.</dd>


<dt>weights</dt>
<dd>A numeric vector specifying weights for each observation
(default: equally weighted).</dd>


<dt>distance</dt>
<dd>A string specifying the distance to be used. Possible choices
are: hamming, frobenius, spectral or root-euclidean. Default is frobenius.
When the Fréchet mean is used as <code>x0</code> parameter, the distance should
match the one used to compute the mean. This is not currently checked.</dd>

</dl>

var_nvd: Fréchet Variance of Network-Valued Data Around a Given Network

Description

Usage

Value

Arguments

Examples