{
  "id": 4317,
  "title": "Invertibility",
  "url": "/competitions/cause-effect-pairs/discussion/4317",
  "author_name": "",
  "post_date": "2013-04-15T08:47:34.847Z",
  "votes": null,
  "comment_count": 8,
  "views": 2699,
  "content": "<p>I'm not a statistician so having trouble understanding invertibility. I have understood about inverse of matrices but to see if a matrix has an inverse, it has to be a square matrix. Is it something simple like the data types?</p>",
  "messages": [
    {
      "id": "22829",
      "postDate": "04/15/2013 08:47:34",
      "content": "<p>I'm not a statistician so having trouble understanding invertibility. I have understood about inverse of matrices but to see if a matrix has an inverse, it has to be a square matrix. Is it something simple like the data types?</p>",
      "rawMarkdown": "",
      "votes": null
    },
    {
      "id": "22871",
      "postDate": "04/16/2013 00:37:04",
      "content": "I take &quot;invertible&quot; to mean that the underlying function passes the vertical line test. Is this too simplistic?",
      "rawMarkdown": "",
      "votes": null
    },
    {
      "id": "22872",
      "postDate": "04/16/2013 00:45:09",
      "content": "<p>I listed papers that might be useful on that page:</p>\r\n<p>http://www.causality.inf.ethz.ch/cause-effect.php?page=help</p>",
      "rawMarkdown": "",
      "votes": null
    },
    {
      "id": "22873",
      "postDate": "04/16/2013 00:48:11",
      "content": "<p>FP: That's how I've been interpreting it, but it can still be argued, I think, that we never know with certainty what the &quot;underlying function&quot; is.</p>",
      "rawMarkdown": "",
      "votes": null
    },
    {
      "id": "22885",
      "postDate": "04/16/2013 07:18:54",
      "content": "<p>thanks&nbsp; - I now have something to Google - vertical line test.</p>\r\n<p>Isabelle - none of those papers are useful to me because they are for experts and I can't try out the software because it's all in Matlab.</p>",
      "rawMarkdown": "",
      "votes": null
    },
    {
      "id": "22919",
      "postDate": "04/16/2013 21:32:22",
      "content": "<p>I think by vertical line test you simply check whether one value on axis A maps to multiple values on axis B.</p>\r\n<p>If there is such a case, you can not express B as a function of A.</p>",
      "rawMarkdown": "",
      "votes": null
    },
    {
      "id": "23062",
      "postDate": "04/18/2013 13:08:13",
      "content": "<p>VLT is for deciding function. &nbsp;HLT is for deciding invertible (one-to-one)</p>",
      "rawMarkdown": "",
      "votes": null
    },
    {
      "id": "23154",
      "postDate": "04/19/2013 11:51:34",
      "content": "Oop- your right Domcastro. Thanks for correcting.",
      "rawMarkdown": "",
      "votes": null
    },
    {
      "id": "23167",
      "postDate": "04/19/2013 14:02:14",
      "content": "<p>Ah - not me!</p>",
      "rawMarkdown": "",
      "votes": null
    }
  ],
  "comments": [
    {
      "id": 22871,
      "author_name": "feloniouspunk",
      "author_url": "",
      "post_date": "04/16/2013 00:37:04",
      "content": "I take &quot;invertible&quot; to mean that the underlying function passes the vertical line test. Is this too simplistic?",
      "votes": null,
      "replies": []
    },
    {
      "id": 22872,
      "author_name": "iguyon",
      "author_url": "",
      "post_date": "04/16/2013 00:45:09",
      "content": "<p>I listed papers that might be useful on that page:</p>\r\n<p>http://www.causality.inf.ethz.ch/cause-effect.php?page=help</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 22873,
      "author_name": "bcragin",
      "author_url": "",
      "post_date": "04/16/2013 00:48:11",
      "content": "<p>FP: That's how I've been interpreting it, but it can still be argued, I think, that we never know with certainty what the &quot;underlying function&quot; is.</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 22885,
      "author_name": "domcastro",
      "author_url": "",
      "post_date": "04/16/2013 07:18:54",
      "content": "<p>thanks&nbsp; - I now have something to Google - vertical line test.</p>\r\n<p>Isabelle - none of those papers are useful to me because they are for experts and I can't try out the software because it's all in Matlab.</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 22919,
      "author_name": "ogh27316",
      "author_url": "",
      "post_date": "04/16/2013 21:32:22",
      "content": "<p>I think by vertical line test you simply check whether one value on axis A maps to multiple values on axis B.</p>\r\n<p>If there is such a case, you can not express B as a function of A.</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 23062,
      "author_name": "markdebonis",
      "author_url": "",
      "post_date": "04/18/2013 13:08:13",
      "content": "<p>VLT is for deciding function. &nbsp;HLT is for deciding invertible (one-to-one)</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 23154,
      "author_name": "feloniouspunk",
      "author_url": "",
      "post_date": "04/19/2013 11:51:34",
      "content": "Oop- your right Domcastro. Thanks for correcting.",
      "votes": null,
      "replies": []
    },
    {
      "id": 23167,
      "author_name": "domcastro",
      "author_url": "",
      "post_date": "04/19/2013 14:02:14",
      "content": "<p>Ah - not me!</p>",
      "votes": null,
      "replies": []
    }
  ],
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