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snehamitra / SCARlink

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can you explain this loss function #5

Closed BenxiaHu closed 6 months ago

BenxiaHu commented 6 months ago

Hello, SCARlink looks great to predict gene expression and identify cell-type-specific enhancers.

I just read your SCARlink paper. I am a little confused about the loss function. Would you like to explain it?

image

Best,

snehamitra commented 6 months ago

Hi, is your question about the hyperparameter $\alpha$? It is the weight associated with l2 regularization of the regression coefficient vector $\mathbf{w}$. We tune the value of $\alpha$ during cross validation to obtain the best fit of the model. We use l2 regularization to shrink the weights of tiles that that are not putative enhancers. Also, the first part of the loss function is the Poisson loss.

BenxiaHu commented 6 months ago

my question is the formula: can you explain each term?

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snehamitra commented 6 months ago

The first two terms correspond to Poisson loss and the last term corresponds to l2-regularization. I linked the terms to some relevant pages but you can look up more resources online.

BenxiaHu commented 6 months ago

thanks. Xi W+e is the predicted gene expression. Yi log(Xi W+e) looks a little confused. Would you like to explain Yi log(Xi * W+e)?

snehamitra commented 6 months ago

It is derived from the likelihood function of the Poisson distribution. https://web.stanford.edu/class/archive/stats/stats200/stats200.1172/Lecture27.pdf

Closing this thread since it is not related to the implementation of SCARlink.

BenxiaHu commented 5 months ago

hello,

image

I am still confused this model: x and y are normliazed values, not count. why are they applied to poisson distribution?