Questions about loss and likelihood implementation

[michaelGuo1204]

Hi!

Your work on integrating spatial gradients and multiple tasks in ST data analysis is truly inspiring!

I'm opening this issue to for some tiny problems in GASTON framework. According to your article, a neural network is used to predict the expression (a_{i}) from spatial coordinates ((x,y)) via isodepth (d_i). In the methods section (lines 613-616) of the preprint, it states that "solving (10) is equivalent to learning the parameters of a single network...". My understanding is that this implies using the likelihood of (\mathbb{P}(a_{i,g}|h_{\theta'(d_{\theta}(x,y))})) as the training loss for the network. However, while reading the code, I noticed that the gaston.neural_net.train function uses a general MSE loss to evaluate the bias between the reconstructed expression profile and the ground truth GLM-PCs. Is this the intended behavior?

GASTON/src/gaston/neural_net.py

Line 167 in 08fdfc2

loss_function=torch.nn.MSELoss(reduction=loss_reduction)

Additionally, I observed that a linear regression, rather than a Poisson regression, is applied during segment regression. Does this mean that a simple linear regression is sufficient for handling the expression profiles?

GASTON/src/gaston/dp_related.py

Line 61 in 08fdfc2

:param opt_function: function to fit each segment (default is least squares for linear regression)

Looking forward to your response!

Best regards!
14 Dec 2024