<\/title><\/p>\n<p><script src=\"CategoricalVariablesLinearScalingTrees_files\/jquery-1.11.3\/jquery.min.js\"><\/script><br \/>\n<meta name=\"viewport\" content=\"width=device-width, initial-scale=1\" \/>\n<link href=\"CategoricalVariablesLinearScalingTrees_files\/bootstrap-3.3.5\/css\/bootstrap.min.css\" rel=\"stylesheet\" \/>\n<script src=\"CategoricalVariablesLinearScalingTrees_files\/bootstrap-3.3.5\/js\/bootstrap.min.js\"><\/script><br \/>\n<script src=\"CategoricalVariablesLinearScalingTrees_files\/bootstrap-3.3.5\/shim\/html5shiv.min.js\"><\/script><br \/>\n<script src=\"CategoricalVariablesLinearScalingTrees_files\/bootstrap-3.3.5\/shim\/respond.min.js\"><\/script><br \/>\n<script src=\"CategoricalVariablesLinearScalingTrees_files\/navigation-1.1\/tabsets.js\"><\/script>\n<link href=\"CategoricalVariablesLinearScalingTrees_files\/highlightjs-9.12.0\/default.css\" rel=\"stylesheet\" \/>\n<script src=\"CategoricalVariablesLinearScalingTrees_files\/highlightjs-9.12.0\/highlight.js\"><\/script><\/p>\n<style type=\"text\/css\">code{white-space: pre;}<\/style>\n<style type=\"text\/css\">\n pre:not([class]) {\n background-color: white;\n }\n<\/style>\n<p><script type=\"text\/javascript\">\nif (window.hljs) {\n hljs.configure({languages: []});\n hljs.initHighlightingOnLoad();\n if (document.readyState && document.readyState === \"complete\") {\n window.setTimeout(function() { hljs.initHighlighting(); }, 0);\n }\n}\n<\/script><\/p>\n<style type=\"text\/css\">\nh1 {\n font-size: 34px;\n}\nh1.title {\n font-size: 38px;\n}\nh2 {\n font-size: 30px;\n}\nh3 {\n font-size: 24px;\n}\nh4 {\n font-size: 18px;\n}\nh5 {\n font-size: 16px;\n}\nh6 {\n font-size: 12px;\n}\n.table th:not([align]) {\n text-align: left;\n}\n<\/style>\n<p><\/head><\/p>\n<p><body><\/p>\n<style type = \"text\/css\">\n.main-container {\n max-width: 940px;\n margin-left: auto;\n margin-right: auto;\n}\ncode {\n color: inherit;\n background-color: rgba(0, 0, 0, 0.04);\n}\nimg {\n max-width:100%;\n height: auto;\n}\n.tabbed-pane {\n padding-top: 12px;\n}\nbutton.code-folding-btn:focus {\n outline: none;\n}\n<\/style>\n<div class=\"container-fluid main-container\">\n<p><br \/>\n<script>\n$(document).ready(function () {\n window.buildTabsets(\"TOC\");\n});\n<\/script><\/p>\n<p><\/p>\n<div class=\"fluid-row\" id=\"header\">\n<\/div>\n<p>I find it remarkable that very few of the current implementations of tree algorithms in R exploit an important \u201ctrick\u201d which was mentioned in the original seminal paper in 1984!<\/p>\n<blockquote>\n<p>\u201cFor a two-class problem, the search for the best categorical split can be reduced to M steps using the Gini criterion\u201d<\/p>\n<\/blockquote>\n<p>Breiman, L., Friedman, J., Olshen, R. and Stone, C. (1984). <em>Classification and Regression Trees<\/em> , Wadsworth International Group<\/p>\n<p>See also <a href=\"http:\/\/www.math.ccu.edu.tw\/~yshih\/papers\/spl.pdf\" class=\"uri\">http:\/\/www.math.ccu.edu.tw\/~yshih\/papers\/spl.pdf<\/a><\/p>\n<p>and p.\u00a011 in <a href=\"http:\/\/www.cs.ubbcluj.ro\/~csatol\/mestint\/pdfs\/Gehrke_Loh_DecTree.pdf\" class=\"uri\">http:\/\/www.cs.ubbcluj.ro\/~csatol\/mestint\/pdfs\/Gehrke_Loh_DecTree.pdf<\/a><\/p>\n<p>(The effect of dummifying categorical variables on performance is nicely elaborated upon in this post <a class=\"uri\" href=\"https:\/\/roamanalytics.com\/2016\/10\/28\/are-categorical-variables-getting-lost-in-your-random-forests\/\">Are categorical variables getting lost in your random forests?<\/a>)<\/p>\n<p>This implies that instead of having to search <span class=\"math inline\">\$2^k-1\$<\/span> combinations of the <span class=\"math inline\">\$k\$<\/span> levels it is sufficient to try just <strong>k<\/strong> of them !<\/p>\n<p>The practical consequences of this exponential vs.\u00a0linear scaling are quite grave, especially with modern datasets that often contain lots of categorical variables with <strong>many<\/strong> (not rare to see <span class=\"math inline\">\$k> 1000\$<\/span>) levels.<\/p>\n<p>Of the popular packages that I tried, only <em>rpart<\/em>, <em>gbm<\/em> and <em>RWeka<\/em> avoid the \u201cexponential trap\u201d and pose (almost) no limit on the number of levels:<\/p>\n<pre class=\"r\"><code>#read in the Rossman data set from this kaggle competition:\r\n# https:\/\/www.kaggle.com\/c\/rossmann-store-sales\r\n#train = read.csv('H:\/kaggle\/Rossmann\/input\/train.csv.gz',as.is=T)\r\n\r\n# oh well, fake data serve to illustrate the point just as well:\r\nN=5*10^5\r\ntrain = cbind.data.frame(Sales= 0, Store=sample(1:1000,N,replace=TRUE))\r\ntrain$Sales = 0.1*train$Store +rnorm(N)\r\ntrain$Store = factor(train$Store)\r\n\r\ncat ("There are ", length(levels(train$Store)),"stores\/levels in this dataset.\\n")<\/code><\/pre>\n<pre><code>## There are 1000 stores\/levels in this dataset.<\/code><\/pre>\n<hr \/>\n<div id=\"libraries-that-fail-to-exploit-the-linear-search-strategy\" class=\"section level3\">\n<h3>Libraries that fail to exploit the linear search strategy:<\/h3>\n<div id=\"the-tree-package\" class=\"section level4\">\n<h4>The <em>tree<\/em> package<\/h4>\n<pre class=\"r\"><code>library(tree, quietly=TRUE)\r\ntry({fit = tree(Sales ~ Store, data = train)})<\/code><\/pre>\n<\/div>\n<div id=\"the-party-package\" class=\"section level4\">\n<h4>The <em>party<\/em> package<\/h4>\n<pre class=\"r\"><code>library(party, quietly=TRUE)\r\ntry({fit = ctree(Sales ~ Store, data = train)})\r\ndetach("package:party", unload=TRUE)<\/code><\/pre>\n<pre><code>## Warning: Error in matrix(0, nrow = mi, ncol = nl) : \r\n## invalid 'nrow' value (too large or NA)\r\n## In addition: Warning message:\r\n## In matrix(0, nrow = mi, ncol = nl) :\r\n## NAs introduced by coercion to integer range<\/code><\/pre>\n<\/div>\n<div id=\"the-partykit-package\" class=\"section level4\">\n<h4>The <em>partykit<\/em> package<\/h4>\n<pre class=\"r\"><code>library(partykit, quietly=TRUE)\r\ntry({fit = lmtree(Sales ~ Store, data = train)})\r\ndetach("package:partykit", unload=TRUE)<\/code><\/pre>\n<pre><code>## Warning: Error in matrix(0, nrow = mi, ncol = nl) : \r\n## invalid 'nrow' value (too large or NA)\r\n## In addition: Warning message:\r\n## In matrix(0, nrow = mi, ncol = nl) :\r\n## NAs introduced by coercion to integer range<\/code><\/pre>\n<\/div>\n<div id=\"the-randomforest-package\" class=\"section level4\">\n<h4>The <em>randomForest<\/em> package<\/h4>\n<pre class=\"r\"><code>library(randomForest, quietly=TRUE)\r\ntry({fit = randomForest(Sales ~ Store, data = train, ntree=1)})<\/code><\/pre>\n<pre><code>## Warning: Error in randomForest.default(m, y, ...) : \r\n## Can not handle categorical predictors with more than 53 categories.<\/code><\/pre>\n<\/div>\n<div id=\"base-lm-runs-out-of-memory\" class=\"section level4\">\n<h4>base <em>lm<\/em> runs out of memory<\/h4>\n<pre class=\"r\"><code>try({fit0 = lm(Sales ~ Store, data = train)})<\/code><\/pre>\n<pre><code>## Warning: Cannot allocate vector of size...<\/code><\/pre>\n<hr \/>\n<\/div>\n<\/div>\n<div id=\"libraries-that-shine\" class=\"section level3\">\n<h3>Libraries that shine:<\/h3>\n<div id=\"the-rpart-package\" class=\"section level4\">\n<h4>The <em>rpart<\/em> package<\/h4>\n<pre class=\"r\"><code>library(rpart, quietly=TRUE)\r\nfit = rpart(Sales ~ Store, data = train)<\/code><\/pre>\n<\/div>\n<div id=\"the-gbm-package\" class=\"section level4\">\n<h4>The <em>gbm<\/em> package<\/h4>\n<p>Well, almost. At least the max number of levels is very high (1024):<\/p>\n<pre class=\"r\"><code>library(gbm, quietly=TRUE)\r\nfit = gbm(Sales ~ Store, data = train, interaction.depth = 8, n.trees=1)<\/code><\/pre>\n<pre><code>## Distribution not specified, assuming gaussian ...<\/code><\/pre>\n<p>(Not clear to me why there is a limit at all)<\/p>\n<\/div>\n<div id=\"the-rweka-package\" class=\"section level4\">\n<h4>The <em>RWeka<\/em> package<\/h4>\n<pre class=\"r\"><code>library(RWeka, quietly=TRUE)\r\n#handles only classification problems:\r\ntrain$Sales2 = train$Sales > mean(train$Sales)\r\nfit = J48(Sales2 ~ Store, data = train)<\/code><\/pre>\n<\/div>\n<div id=\"the-h2o-package\" class=\"section level4\">\n<h4>The <em>h2o<\/em> package<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<p><script><\/p>\n<p>\/\/ add bootstrap table styles to pandoc tables\nfunction bootstrapStylePandocTables() {\n $('tr.header').parent('thead').parent('table').addClass('table table-condensed');\n}\n$(document).ready(function () {\n bootstrapStylePandocTables();\n});<\/p>\n<p><\/script><\/p>\n<p><br \/>\n<script>\n (function () {\n var script = document.createElement(\"script\");\n script.type = \"text\/javascript\";\n script.src = \"https:\/\/mathjax.rstudio.com\/latest\/MathJax.js?config=TeX-AMS-MML_HTMLorMML\";\n document.getElementsByTagName(\"head\")[0].appendChild(script);\n })();\n<\/script><\/p>\n<p><\/body><br \/>\n<\/html><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I find it remarkable that very few of the current implementations of tree algorithms in R exploit an important \u201ctrick\u201d which was mentioned in the original seminal paper in 1984! \u201cFor a two-class problem, the search for the best categorical split can be reduced to M steps using the Gini criterion\u201d Breiman, L., Friedman, J., … <a href=\"https:\/\/blog.hwr-berlin.de\/codeandstats\/categorical-variables-in-trees-i\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Categorical Variables in Trees I<\/span><\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-40","post","type-post","status-publish","format-standard","hentry","category-r"],"yoast_head":"\n<title>Categorical Variables in Trees I - 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{"id":40,"date":"2016-03-08T15:29:29","date_gmt":"2016-03-08T14:29:29","guid":{"rendered":"http:\/\/blog.hwr-berlin.de\/codeandstats\/?p=40"},"modified":"2018-11-18T16:16:59","modified_gmt":"2018-11-18T15:16:59","slug":"categorical-variables-in-trees-i","status":"publish","type":"post","link":"https:\/\/blog.hwr-berlin.de\/codeandstats\/categorical-variables-in-trees-i\/","title":{"rendered":"Categorical Variables in Trees I"},"content":{"rendered":"

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