{"action":"created","issue":{"url":"https://api.github.com/repos/madeleineudell/LowRankModels.jl/issues/37","labels_url":"https://api.github.com/repos/madeleineudell/LowRankModels.jl/issues/37/labels{/name}","comments_url":"https://api.github.com/repos/madeleineudell/LowRankModels.jl/issues/37/comments","events_url":"https://api.github.com/repos/madeleineudell/LowRankModels.jl/issues/37/events","html_url":"https://github.com/madeleineudell/LowRankModels.jl/issues/37","id":102201300,"number":37,"title":"Penalties/regularization of imputed values","user":{"login":"ahwillia","id":636625,"avatar_url":"https://avatars.githubusercontent.com/u/636625?v=3","gravatar_id":"","url":"https://api.github.com/users/ahwillia","html_url":"https://github.com/ahwillia","followers_url":"https://api.github.com/users/ahwillia/followers","following_url":"https://api.github.com/users/ahwillia/following{/other_user}","gists_url":"https://api.github.com/users/ahwillia/gists{/gist_id}","starred_url":"https://api.github.com/users/ahwillia/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ahwillia/subscriptions","organizations_url":"https://api.github.com/users/ahwillia/orgs","repos_url":"https://api.github.com/users/ahwillia/repos","events_url":"https://api.github.com/users/ahwillia/events{/privacy}","received_events_url":"https://api.github.com/users/ahwillia/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"milestone":null,"comments":4,"created_at":"2015-08-20T18:23:53Z","updated_at":"2015-09-04T19:03:16Z","closed_at":null,"body":"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.\r\n\r\nFor each observed entry `A_ij` we have a loss function: `L[A_ij, dot(x_i,y_j)]`\r\n\r\nMaybe for each unobserved entry we could add some regularization: `R_a[dot(x_i,y_j)]`\r\n\r\nWhere `R_a` is a function defined by the user... Perhaps `R_a[z] = z^2` or `R_a[z] = abs(z)`\r\n\r\n**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."},"comment":{"url":"https://api.github.com/repos/madeleineudell/LowRankModels.jl/issues/comments/137823564","html_url":"https://github.com/madeleineudell/LowRankModels.jl/issues/37#issuecomment-137823564","issue_url":"https://api.github.com/repos/madeleineudell/LowRankModels.jl/issues/37","id":137823564,"user":{"login":"ahwillia","id":636625,"avatar_url":"https://avatars.githubusercontent.com/u/636625?v=3","gravatar_id":"","url":"https://api.github.com/users/ahwillia","html_url":"https://github.com/ahwillia","followers_url":"https://api.github.com/users/ahwillia/followers","following_url":"https://api.github.com/users/ahwillia/following{/other_user}","gists_url":"https://api.github.com/users/ahwillia/gists{/gist_id}","starred_url":"https://api.github.com/users/ahwillia/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ahwillia/subscriptions","organizations_url":"https://api.github.com/users/ahwillia/orgs","repos_url":"https://api.github.com/users/ahwillia/repos","events_url":"https://api.github.com/users/ahwillia/events{/privacy}","received_events_url":"https://api.github.com/users/ahwillia/received_events","type":"User","site_admin":false},"created_at":"2015-09-04T19:03:16Z","updated_at":"2015-09-04T19:03:16Z","body":"Very nice! Much cleaner than what I suggested. I think it would be nice to put it into the codebase, but that call is above my paygrade."}}