2023-04-25

This is Marco's daily open-notebook.

Today is 2023.04.25

Changes to implement in the model

We made a mistake in the variance covariance matrix. In fact, we should have a product between the values of the covariances matrices and not a sum. For example, if I take two species that have 0 correlation and one molecule. Does having that molecule in one of the species give me any additional information about the presence of that molecule in the other species ? Other than the average presence $\mu$ NO we can't have any other information !

We thus have $cov(\epsilon_c, \epsilon_{c'}) = \prod_t \prod_{f=1}^{F_t} \sigma_{tf}(\tau_t(c), \tau_t(c')^{\alpha_{tf}})$

Furthermore, in order to reduce the variance covariance matrix, we first assume that a lot of molecules and a lot of species share no correlation. This, in theory, would allow us to split the data before creating the cov matrix of molecules and the cov matrix of species. This would imply to assume that some molecules and some species share 0 covariance.

Todo today

Doing

Done

Todo tomorrow