{"action":"created","comment":{"url":"https://api.github.com/repos/apache/spark/pulls/comments/66714994","id":66714994,"diff_hunk":"@@ -685,6 +685,76 @@ The implementation matches the result from R's survival function\n </div>\n \n \n+## Isotonic regression\n+[Isotonic regression](http://en.wikipedia.org/wiki/Isotonic_regression)\n+belongs to the family of regression algorithms. Formally isotonic regression is a problem where\n+given a finite set of real numbers `$Y = {y_1, y_2, ..., y_n}$` representing observed responses\n+and `$X = {x_1, x_2, ..., x_n}$` the unknown response values to be fitted\n+finding a function that minimises\n+\n+`\\begin{equation}\n+  f(x) = \\sum_{i=1}^n w_i (y_i - x_i)^2\n+\\end{equation}`\n+\n+with respect to complete order subject to\n+`$x_1\\le x_2\\le ...\\le x_n$` where `$w_i$` are positive weights.\n+The resulting function is called isotonic regression and it is unique.\n+It can be viewed as least squares problem under order restriction.\n+Essentially isotonic regression is a\n+[monotonic function](http://en.wikipedia.org/wiki/Monotonic_function)\n+best fitting the original data points.\n+\n+In `spark.ml`, we implement a","path":"docs/ml-classification-regression.md","position":23,"original_position":23,"commit_id":"2e46416317356f8f8fa53457ba2318449a795218","original_commit_id":"2e46416317356f8f8fa53457ba2318449a795218","user":{"login":"jkbradley","id":5084283,"avatar_url":"https://avatars.githubusercontent.com/u/5084283?v=3","gravatar_id":"","url":"https://api.github.com/users/jkbradley","html_url":"https://github.com/jkbradley","followers_url":"https://api.github.com/users/jkbradley/followers","following_url":"https://api.github.com/users/jkbradley/following{/other_user}","gists_url":"https://api.github.com/users/jkbradley/gists{/gist_id}","starred_url":"https://api.github.com/users/jkbradley/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jkbradley/subscriptions","organizations_url":"https://api.github.com/users/jkbradley/orgs","repos_url":"https://api.github.com/users/jkbradley/repos","events_url":"https://api.github.com/users/jkbradley/events{/privacy}","received_events_url":"https://api.github.com/users/jkbradley/received_events","type":"User","site_admin":false},"body":"I'd avoid using ```spark.ml```.  It was useful when there were 2 active APIs, but the naming confuses people sometimes.  I'd just start with \"We implement...\"","created_at":"2016-06-12T02:32:32Z","updated_at":"2016-06-12T02:32:32Z","html_url":"https://github.com/apache/spark/pull/13381#discussion_r66714994","pull_request_url":"https://api.github.com/repos/apache/spark/pulls/13381","_links":{"self":{"href":"https://api.github.com/repos/apache/spark/pulls/comments/66714994"},"html":{"href":"https://github.com/apache/spark/pull/13381#discussion_r66714994"},"pull_request":{"href":"https://api.github.com/repos/apache/spark/pulls/13381"}}},"pull_request":{"url":"https://api.github.com/repos/apache/spark/pulls/13381","id":71807355,"html_url":"https://github.com/apache/spark/pull/13381","diff_url":"https://github.com/apache/spark/pull/13381.diff","patch_url":"https://github.com/apache/spark/pull/13381.patch","issue_url":"https://api.github.com/repos/apache/spark/issues/13381","number":13381,"state":"open","locked":false,"title":"[SPARK-15608][ml][examples][doc] add examples and documents of ml.isotonic regression","user":{"login":"WeichenXu123","id":19235986,"avatar_url":"https://avatars.githubusercontent.com/u/19235986?v=3","gravatar_id":"","url":"https://api.github.com/users/WeichenXu123","html_url":"https://github.com/WeichenXu123","followers_url":"https://api.github.com/users/WeichenXu123/followers","following_url":"https://api.github.com/users/WeichenXu123/following{/other_user}","gists_url":"https://api.github.com/users/WeichenXu123/gists{/gist_id}","starred_url":"https://api.github.com/users/WeichenXu123/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/WeichenXu123/subscriptions","organizations_url":"https://api.github.com/users/WeichenXu123/orgs","repos_url":"https://api.github.com/users/WeichenXu123/repos","events_url":"https://api.github.com/users/WeichenXu123/events{/privacy}","received_events_url":"https://api.github.com/users/WeichenXu123/received_events","type":"User","site_admin":false},"body":"## What changes were proposed in this pull request?\r\n\r\nadd ml doc for ml isotonic regression\r\nadd scala example for ml isotonic regression\r\nadd java example for ml isotonic regression\r\nadd python example for ml isotonic regression\r\n\r\nmodify scala example for mllib isotonic regression\r\nmodify java example for mllib isotonic regression\r\nmodify python example for mllib isotonic regression\r\n\r\nadd data/mllib/sample_isotonic_regression_libsvm_data.txt\r\ndelete data/mllib/sample_isotonic_regression_data.txt\r\n## How was this patch tested?\r\n\r\nN/A\r\n\r\n\r\n","created_at":"2016-05-28T17:28:53Z","updated_at":"2016-06-12T02:32:33Z","closed_at":null,"merged_at":null,"merge_commit_sha":"19f2e98bc27d3d24e637c4b2a77b28f7b6355fc2","assignee":null,"milestone":null,"commits_url":"https://api.github.com/repos/apache/spark/pulls/13381/commits","review_comments_url":"https://api.github.com/repos/apache/spark/pulls/13381/comments","review_comment_url":"https://api.github.com/repos/apache/spark/pulls/comments{/number}","comments_url":"https://api.github.com/repos/apache/spark/issues/13381/comments","statuses_url":"https://api.github.com/repos/apache/spark/statuses/2e46416317356f8f8fa53457ba2318449a795218","head":{"label":"WeichenXu123:add_isotonic_regression_doc","ref":"add_isotonic_regression_doc","sha":"2e46416317356f8f8fa53457ba2318449a795218","user":{"login":"WeichenXu123","id":19235986,"avatar_url":"https://avatars.githubusercontent.com/u/19235986?v=3","gravatar_id":"","url":"https://api.github.com/users/WeichenXu123","html_url":"https://github.com/WeichenXu123","followers_url":"https://api.github.com/users/WeichenXu123/followers","following_url":"https://api.github.com/users/WeichenXu123/following{/other_user}","gists_url":"https://api.github.com/users/WeichenXu123/gists{/gist_id}","starred_url":"https://api.github.com/users/WeichenXu123/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/WeichenXu123/subscriptions","organizations_url":"https://api.github.com/users/WeichenXu123/orgs","repos_url":"https://api.github.com/users/WeichenXu123/repos","events_url":"https://api.github.com/users/WeichenXu123/events{/privacy}","received_events_url":"https://api.github.com/users/WeichenXu123/received_events","type":"User","site_admin":false},"repo":{"id":58255485,"name":"spark","full_name":"WeichenXu123/spark","owner":{"login":"WeichenXu123","id":19235986,"avatar_url":"https://avatars.githubusercontent.com/u/19235986?v=3","gravatar_id":"","url":"https://api.github.com/users/WeichenXu123","html_url":"https://github.com/WeichenXu123","followers_url":"https://api.github.com/users/WeichenXu123/followers","following_url":"https://api.github.com/users/WeichenXu123/following{/other_user}","gists_url":"https://api.github.com/users/WeichenXu123/gists{/gist_id}","starred_url":"https://api.github.com/users/WeichenXu123/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/WeichenXu123/subscriptions","organizations_url":"https://api.github.com/users/WeichenXu123/orgs","repos_url":"https://api.github.com/users/WeichenXu123/repos","events_url":"https://api.github.com/users/WeichenXu123/events{/privacy}","received_events_url":"https://api.github.com/users/WeichenXu123/received_events","type":"User","site_admin":false},"private":false,"html_url":"https://github.com/WeichenXu123/spark","description":"Mirror 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