Inferring the finest pattern of mutual independence from data
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929490925453312 |
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| author | Marrelec, G. Giron, A. |
| author_facet | Marrelec, G. Giron, A. |
| contents | For a random variable $X$, we are interested in the blind extraction of its finest mutual independence pattern $μ( X )$. We introduce a specific kind of independence that we call dichotomic. If $Δ( X )$ stands for the set of all patterns of dichotomic independence that hold for $X$, we show that $μ( X )$ can be obtained as the intersection of all elements of $Δ( X )$. We then propose a method to estimate $Δ( X )$ when the data are independent and identically (i.i.d.) realizations of a multivariate normal distribution. If $\hatΔ ( X )$ is the estimated set of valid patterns of dichotomic independence, we estimate $μ( X )$ as the intersection of all patterns of $\hatΔ ( X )$. The method is tested on simulated data, showing its advantages and limits. We also consider an application to a toy example as well as to experimental data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12984 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inferring the finest pattern of mutual independence from data Marrelec, G. Giron, A. Machine Learning Statistics Theory Methodology For a random variable $X$, we are interested in the blind extraction of its finest mutual independence pattern $μ( X )$. We introduce a specific kind of independence that we call dichotomic. If $Δ( X )$ stands for the set of all patterns of dichotomic independence that hold for $X$, we show that $μ( X )$ can be obtained as the intersection of all elements of $Δ( X )$. We then propose a method to estimate $Δ( X )$ when the data are independent and identically (i.i.d.) realizations of a multivariate normal distribution. If $\hatΔ ( X )$ is the estimated set of valid patterns of dichotomic independence, we estimate $μ( X )$ as the intersection of all patterns of $\hatΔ ( X )$. The method is tested on simulated data, showing its advantages and limits. We also consider an application to a toy example as well as to experimental data. |
| title | Inferring the finest pattern of mutual independence from data |
| topic | Machine Learning Statistics Theory Methodology |
| url | https://arxiv.org/abs/2306.12984 |