madeleineudell
commented
9 years ago Interesting. I'd call that a loss function rather than a regularization on unobserved entries. I'd say your observations take values in the set [image: S = \mathbb{R} \cup \mathrm{NA}] and that your loss function is a function $L: S \times \mathbb{R} \to \mathbb{R}$. Then $L(\mathrm{NA}, z)$ has some functional form and $L(a,z)$ has a different function form for $a \ne \mathrm{NA}$.
This happens frequently in a variety of settings (recommender systems come to mind): missing entries are not missing iid; rather, missingness tells you something about the unseen value. In the recommender system context, someone who didn't rate a movie probably didn't watch the movie (or rate it) because they didn't think they'd like the movie. And often, they're right.
Putting together an example illustrating how to deal with this would be super useful.
On Thu, Aug 20, 2015 at 11:23 AM, Alex Williams notifications@github.com wrote:
In many experimental contexts (RNA-sequencing is a good example), ground truth data that are below a detection threshold are not observed due to technical error. Thus, we have a data matrix A with many NA entries. However, we suspect many of these NA entries to be small, though not necessarily zero.
For each observed entry A_ij we have a loss function: L[A_ij, dot(x_i,y_j)]
Maybe for each unobserved entry we could add some regularization: R_a[dot(x_i,y_j)]
Where R_a is a function defined by the user... Perhaps R_a[z] = z^2 or R_a[z] = abs(z)
Aside: For the RNA sequencing application, something like R_a[z] = sqrt(z), z > 0 would be interesting (though not convex). Actually even something non-monotonic would be interesting for reasons I won't go into. These are probably too weird/specialized to include, but I would be curious.
— Reply to this email directly or view it on GitHub https://github.com/madeleineudell/LowRankModels.jl/issues/37.
Madeleine Udell Postdoctoral Fellow at the Center for the Mathematics of Information California Institute of Technology www.stanford.edu/~udell (415) 729-4115
ahwillia
In many experimental contexts (RNA-sequencing is a good example), ground truth data that are below a detection threshold are not observed due to technical error. Thus, we have a data matrix
Awith manyNAentries. However, we suspect many of theseNAentries to be small, though not necessarily zero.For each observed entry
A_ijwe have a loss function:L[A_ij, dot(x_i,y_j)]Maybe for each unobserved entry we could add some regularization:
R_a[dot(x_i,y_j)]Where
R_ais a function defined by the user... PerhapsR_a[z] = z^2orR_a[z] = abs(z)Aside: For the RNA sequencing application, something like
R_a[z] = sqrt(z), z > 0would be interesting (though not convex). Actually even something non-monotonic would be interesting for reasons I won't go into. These are probably too weird/specialized to include, but I would be curious.