{"action":"created","issue":{"url":"https://api.github.com/repos/DiffusionMapsAcademics/pyDiffMap/issues/16","repository_url":"https://api.github.com/repos/DiffusionMapsAcademics/pyDiffMap","labels_url":"https://api.github.com/repos/DiffusionMapsAcademics/pyDiffMap/issues/16/labels{/name}","comments_url":"https://api.github.com/repos/DiffusionMapsAcademics/pyDiffMap/issues/16/comments","events_url":"https://api.github.com/repos/DiffusionMapsAcademics/pyDiffMap/issues/16/events","html_url":"https://github.com/DiffusionMapsAcademics/pyDiffMap/issues/16","id":298851065,"node_id":"MDU6SXNzdWUyOTg4NTEwNjU=","number":16,"title":"Move to using Transition rate matrix rather than Transition matrix","user":{"login":"ehthiede","id":15326830,"node_id":"MDQ6VXNlcjE1MzI2ODMw","avatar_url":"https://avatars2.githubusercontent.com/u/15326830?v=4","gravatar_id":"","url":"https://api.github.com/users/ehthiede","html_url":"https://github.com/ehthiede","followers_url":"https://api.github.com/users/ehthiede/followers","following_url":"https://api.github.com/users/ehthiede/following{/other_user}","gists_url":"https://api.github.com/users/ehthiede/gists{/gist_id}","starred_url":"https://api.github.com/users/ehthiede/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ehthiede/subscriptions","organizations_url":"https://api.github.com/users/ehthiede/orgs","repos_url":"https://api.github.com/users/ehthiede/repos","events_url":"https://api.github.com/users/ehthiede/events{/privacy}","received_events_url":"https://api.github.com/users/ehthiede/received_events","type":"User","site_admin":false},"labels":[{"id":739039836,"node_id":"MDU6TGFiZWw3MzkwMzk4MzY=","url":"https://api.github.com/repos/DiffusionMapsAcademics/pyDiffMap/labels/enhancement","name":"enhancement","color":"84b6eb","default":true},{"id":739039843,"node_id":"MDU6TGFiZWw3MzkwMzk4NDM=","url":"https://api.github.com/repos/DiffusionMapsAcademics/pyDiffMap/labels/question","name":"question","color":"cc317c","default":true}],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":3,"created_at":"2018-02-21T05:57:47Z","updated_at":"2018-10-15T23:03:52Z","closed_at":null,"author_association":"MEMBER","body":"I'm wondering if we should move from using the transition matrix in the code to the transition rate matrix $L = (P-I) / \\epsilon$ (modulo the appropriate scaling factor due to how we've defined the exponential).\r\n\r\nThis would have the following advantages.\r\n\r\n1. It would make the code more naturally compatibile with the variable bandwidth schemes\r\n2. The spectral gap of L will not go to zero as epsilon goes to zero, so I suspect the linear algebra will be better posed (although I've never seen this effect in practice)\r\n3.  L is more naturally interpretable for cases where alpha is not 0.5 or 1.\r\n4.  We don't have to do this weird scaling with the output eigenvalues every time we look at the eigenvalues, as that will automatically be done by the code\r\n\r\nI can't really think of any disadvantages, apart from slightly added complexity, and the fact that people seem to be slightly more comfortable with transition matrices than transition rate matrices.\r\n\r\nThoughts? "},"comment":{"url":"https://api.github.com/repos/DiffusionMapsAcademics/pyDiffMap/issues/comments/430043777","html_url":"https://github.com/DiffusionMapsAcademics/pyDiffMap/issues/16#issuecomment-430043777","issue_url":"https://api.github.com/repos/DiffusionMapsAcademics/pyDiffMap/issues/16","id":430043777,"node_id":"MDEyOklzc3VlQ29tbWVudDQzMDA0Mzc3Nw==","user":{"login":"ehthiede","id":15326830,"node_id":"MDQ6VXNlcjE1MzI2ODMw","avatar_url":"https://avatars2.githubusercontent.com/u/15326830?v=4","gravatar_id":"","url":"https://api.github.com/users/ehthiede","html_url":"https://github.com/ehthiede","followers_url":"https://api.github.com/users/ehthiede/followers","following_url":"https://api.github.com/users/ehthiede/following{/other_user}","gists_url":"https://api.github.com/users/ehthiede/gists{/gist_id}","starred_url":"https://api.github.com/users/ehthiede/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ehthiede/subscriptions","organizations_url":"https://api.github.com/users/ehthiede/orgs","repos_url":"https://api.github.com/users/ehthiede/repos","events_url":"https://api.github.com/users/ehthiede/events{/privacy}","received_events_url":"https://api.github.com/users/ehthiede/received_events","type":"User","site_admin":false},"created_at":"2018-10-15T23:03:52Z","updated_at":"2018-10-15T23:03:52Z","author_association":"MEMBER","body":"Reopened because I realized a workaround for the VBW case, so we can indeed discuss these issues separately."}}
{"actor":{"display_login":"ehthiede"}}