Model-free two-sample test for network-valued data

Lovato, Ilenia; Pini, Alessia; Stamm, Aymeric; Vantini, Simone

doi:10.1016/j.csda.2019.106896

Cited by 6 publications

(8 citation statements)

References 53 publications

(66 reference statements)

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“…In particular, in this work, we will use the flexible non‐parametric permutation framework for two‐sample testing with populations of networks proposed by Lovato et al. (2020). The second issue lies in the complexity of any procedure for controlling the FWER.…”

Section: Local Inference For Network‐valued Datamentioning

confidence: 99%

“…In this case, the σ ‐algebra generated by the partition coincides with the partition itself and the local testing procedure boils down to performing a global test as in Lovato et al. (2020). On the other hand, one could think of assigning each vertex to its own element of the partition.…”

Section: Control Of the Family‐wise Error Ratementioning

confidence: 99%

“…For this purpose, we use the approach proposed in Lovato et al. (2020). In summary, it is a model‐free two‐sample test for network‐valued data based on a flexible permutation framework that achieves consistency and finite‐sample exactness without making any distributional assumption on the compared probability distributions.…”

Section: Control Of the Family‐wise Error Ratementioning

confidence: 99%

“…Further details can be found in Lovato et al. (2020). Finally, we define adjusted p ‐values for the intra‐ and inter‐hypothesis tests given by Equations () and () as follows:

p_{i} : = max_{A \in σ false(frakturV false) : V_{i} \in A} p_{A}^{normalintra}, p_{A}^{normalfull} p_{italicij} : = max_{A \in σ false(frakturV false) : V_{i}, V_{j} \in A} p_{A}^{normalinter}, p_{A}^{normalfull} .

The CMTP is summarized in the Web‐based supporting materials.…”

Section: Control Of the Family‐wise Error Ratementioning

confidence: 99%

“…(2017) provide a suitable test statistic along with its asymptotic distribution. The other two works propose non‐parametric testing procedures: either via a flexible generative probabilistic model for the data with subsequent Bayesian inference (Durante et al., 2017) or via model‐free permutation inference (Lovato et al., 2020). The interested reader can find a thorough review of statistical inference for network‐valued data in the latter.…”

Section: Introductionmentioning

confidence: 99%

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Multiscale Null Hypothesis Testing for Network-valued Data: Analysis of Brain Networks of Patients with Autism

Lovato

Pini

Stamm

et al. 2021

Journal of the Royal Statistical Society Series C: Applied Statistics

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Networks are a natural way of representing the human brain for studying its structure and function and, as such, have been extensively used. In this framework, case–control studies for understanding autism pertain to comparing samples of healthy and autistic brain networks. In order to understand the biological mechanisms involved in the pathology, it is key to localize the differences on the brain network. Motivated by this question, we hereby propose a general non‐parametric finite‐sample exact statistical framework that allows to test for differences in connectivity within and between prespecified areas inside the brain network, with strong control of the family‐wise error rate. We demonstrate unprecedented ability to differentiate children with non‐syndromic autism from children with both autism and tuberous sclerosis complex using electroencephalography data. The implementation of the method is available in the R package nevada.

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Section: Local Inference For Network‐valued Datamentioning

confidence: 99%

Section: Control Of the Family‐wise Error Ratementioning

confidence: 99%

Section: Control Of the Family‐wise Error Ratementioning

confidence: 99%

“…Further details can be found in Lovato et al. (2020). Finally, we define adjusted p ‐values for the intra‐ and inter‐hypothesis tests given by Equations () and () as follows:

p_{i} : = max_{A \in σ false(frakturV false) : V_{i} \in A} p_{A}^{normalintra}, p_{A}^{normalfull} p_{italicij} : = max_{A \in σ false(frakturV false) : V_{i}, V_{j} \in A} p_{A}^{normalinter}, p_{A}^{normalfull} .

The CMTP is summarized in the Web‐based supporting materials.…”

Section: Control Of the Family‐wise Error Ratementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multiscale Null Hypothesis Testing for Network-valued Data: Analysis of Brain Networks of Patients with Autism

Lovato

Pini

Stamm

et al. 2021

Journal of the Royal Statistical Society Series C: Applied Statistics

Self Cite

View full text Add to dashboard Cite

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Assessing portfolio diversification via two-sample graph kernel inference. A case study on the influence of ESG screening

Gudmundarson,

Peters

2024

PLoS ONE

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In this work we seek to enhance the frameworks practitioners in asset management and wealth management may adopt to asses how different screening rules may influence the diversification benefits of portfolios. The problem arises naturally in the area of Environmental, Social, and Governance (ESG) based investing practices as practitioners often need to select subsets of the total available assets based on some ESG screening rule. Once a screening rule is identified, one constructs a dynamic portfolio which is usually compared with another dynamic portfolio to check if it satisfies or outperforms the risk and return profile set by the company. Our study proposes a novel method that tackles the problem of comparing diversification benefits of portfolios constructed under different screening rules. Each screening rule produces a sequence of graphs, where the nodes are assets and edges are partial correlations. To compare the diversification benefits of screening rules, we propose to compare the obtained graph sequences. The method proposed is based on a machine learning hypothesis testing framework called the kernel two-sample test whose objective is to determine whether the graphs come from the same distribution. If they come from the same distribution, then the risk and return profiles should be the same. The fact that the sample data points are graphs means that one needs to use graph testing frameworks. The problem is natural for kernel two-sample testing as one can use so-called graph kernels to work with samples of graphs. The null hypothesis of the two-sample graph kernel test is that the graph sequences were generated from the same distribution, while the alternative is that the distributions are different. A failure to reject the null hypothesis would indicate that ESG screening does not affect diversification while rejection would indicate that ESG screening does have an effect. The article describes the graph kernel two-sample testing framework, and further provides a brief overview of different graph kernels. We then demonstrate the power of the graph two-sample testing framework under different realistic scenarios. Finally, the proposed methodology is applied to data within the SnP500 to demonstrate the workflow one can use in asset management to test for structural differences in diversification of portfolios under different ESG screening rules.

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Differentially Describing Groups of Graphs

Coupette

Dalleiger

Vreeken

2022

AAAI

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How does neural connectivity in autistic children differ from neural connectivity in healthy children or autistic youths? What patterns in global trade networks are shared across classes of goods, and how do these patterns change over time? Answering questions like these requires us to differentially describe groups of graphs: Given a set of graphs and a partition of these graphs into groups, discover what graphs in one group have in common, how they systematically differ from graphs in other groups, and how multiple groups of graphs are related. We refer to this task as graph group analysis, which seeks to describe similarities and differences between graph groups by means of statistically significant subgraphs. To perform graph group analysis, we introduce Gragra, which uses maximum entropy modeling to identify a non-redundant set of subgraphs with statistically significant associations to one or more graph groups. Through an extensive set of experiments on a wide range of synthetic and real-world graph groups, we confirm that Gragra works well in practice.

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Model-free two-sample test for network-valued data

Cited by 6 publications

References 53 publications

Multiscale Null Hypothesis Testing for Network-valued Data: Analysis of Brain Networks of Patients with Autism

Multiscale Null Hypothesis Testing for Network-valued Data: Analysis of Brain Networks of Patients with Autism

Assessing portfolio diversification via two-sample graph kernel inference. A case study on the influence of ESG screening

Differentially Describing Groups of Graphs

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