{"id":72,"date":"2005-05-06T10:37:06","date_gmt":"2005-05-06T16:37:06","guid":{"rendered":"\/?p=72"},"modified":"2005-05-06T10:37:12","modified_gmt":"2005-05-06T16:37:12","slug":"dont-mix-the-solution-and-the-problem","status":"publish","type":"post","link":"https:\/\/hunch.net\/?p=72","title":{"rendered":"Don&#8217;t mix the solution into the problem"},"content":{"rendered":"<p>A common defect of many pieces of research is defining the problem in terms of the solution.  Here are some examples in learning:<\/p>\n<ol>\n<li>&#8220;The learning problem is finding a good seperating hyperplane.&#8221;<\/li>\n<li>&#8220;The goal of learning is to minimize <em>(y-p)<sup>2<\/sup> + C w<sup>2<\/sup><\/em> where <em>y<\/em> = the observation, <em>p<\/em> = the prediction and <em>w<\/em> = a parameter vector.&#8221;<\/li>\n<li>Defining the <a href=\"https:\/\/hunch.net\/index.php?p=11\">loss<\/a> function to be the one that your algorithm optimizes rather than the one imposed by the world.<\/li>\n<\/ol>\n<p>The fundamental reason why this is a defect is that it creates artificial boundaries to problem solution.  Artificial boundaries lead to the possibility of being blind-sided.  For example, someone committing (1) or (2) above might find themselves themselves surprised to find a decision tree working well on a problem.  Example (3) might result in someone else solving a learning problem better for real world purposes, even if it&#8217;s worse with respect to the algorithm optimization.  This defect should be avoided so as to not artificially limit your learning kungfu.<\/p>\n<p>The way to avoid this defect while still limiting the scope of investigation to something you can manage is to be explicit.<\/p>\n<ol>\n<li>Admit what the real world-imposed learning problem is.  For example &#8220;The problem is to find a classifier minimizing error rate&#8221;.<\/li>\n<li>Be explicit about where the problem ends and the solution begins.  For example &#8220;We use a support vector machine with a l<sub>2<\/sub> loss to train a classifier. We use the l<sub>2<\/sub> loss because it is an upper bound on the error rate which is computationally tractable to optimize.&#8221;<\/li>\n<li>Finish the solution. For example &#8220;The error rate on our test set was 0.34.&#8221;<\/li>\n<\/ol>\n<p>It is important to note that this is not a critique about any particular <em>method<\/em> for solving learning problems, but rather about the process of thinking about learning problems.  Eliminating this thinking-bug will leave people more capable of appreciating and using different approaches to solve the real learning problem.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A common defect of many pieces of research is defining the problem in terms of the solution. Here are some examples in learning: &#8220;The learning problem is finding a good seperating hyperplane.&#8221; &#8220;The goal of learning is to minimize (y-p)2 + C w2 where y = the observation, p = the prediction and w = &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/hunch.net\/?p=72\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Don&#8217;t mix the solution into the problem&#8221;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-72","post","type-post","status-publish","format-standard","hentry","category-general"],"_links":{"self":[{"href":"https:\/\/hunch.net\/index.php?rest_route=\/wp\/v2\/posts\/72","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hunch.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hunch.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hunch.net\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/hunch.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=72"}],"version-history":[{"count":0,"href":"https:\/\/hunch.net\/index.php?rest_route=\/wp\/v2\/posts\/72\/revisions"}],"wp:attachment":[{"href":"https:\/\/hunch.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=72"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hunch.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=72"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hunch.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=72"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}