Cellular deconvolution intuition

Question

[Aspire]

Cellular deconvolution yields the proportion of cell types from bulk tissue.

After estimating the proportion of each cell type, why cannot one multiply the total expression by the proportion to get the expression by cell type?

Unsupervised (reference free) deconvolution yields the proportion without relying on a reference profile. How this is possible?

Could you provide a simple intuition to think about deconvolution that could explain these?

[Aspire]

The crude way I think about deconvolution is : Total expression * proportion = Cell-type expression. Given the total expression, and a typical cell-type expression, one estimates the proportion. However, if it were correct then (1) one could simply multiply the total expression by the proportion to get the cell-type expression (2) it would not be possible to estimate both the proportion and the cell-type expression in an "unsupervised" way. So that way of thinking must be wrong.

Answer 1

[dariober]

It would help if you gave your question more background and some references for the statements you make.

Anyway, a while ago I looked into quadratic programming for addressing the deconvolution problem. I found quadratic programming to be a really nice technique so for my own reference I wrote this tutorial see if it helps (pdf is here)...

Answer 2

[Aspire]

I have crossposted this question at another forum, where it has received a very generous answer.

https://stats.stackexchange.com/questions/521654/cellular-deconvolution-intuition/522087#522087

Note: reason for crossposting was to set a "bounty" on the answer (pay with reputation scores for an answer), which is available only at the linked forum.