Gradient Descent for gene degradation

Question

[keren.danan]

Hey, I am trying to create a model of gene degradation specifacally in zebrafish embryo of maternal genes. After trying linear regression that did not lead to good results, my supervisor suggested to use gradient descent model with 5 parameters:

1. x0 - inital expression
2. t1- time the degradation starts
3. t2-time the degradation ends -> expression is 0
4. s1 - slope between t0-t1
5. s2 - slope between t1-t2

My data looks like this: for each gene, I have RNA expression in each stage starting from 3h->12h.

I don't have any experience creating a model using gradient descent and have to implement in R. the problem is not to create a function but how to create my parameters, since they would be the same for each sample (if I calculate for each gene the five ones with linear regression)

Any experience or idea? thanks

Answer 1

[Alex Reynolds]

You could modify the data frame in this post, replacing the columns of X with your genes (rows) and parameters (columns):

https://www.ocf.berkeley.edu/~janastas/stochastic-gradient-descent-in-r.html

As far as creating those rows goes, you need to look at your data and pull out expression values at time zero (3h) to time "9" (12h) for each gene. Then you simply calculate those parameters for each gene, based on how you define degradation start and end. Make your model from observed parameters.