title: Random Forest by R package party overfits on random data
body: <p>I am working on Random Forest classification.</p>
  
  <p>I found that cforest in "party" package usually performs better than "randomForest".<br />
  However, it seemed that cforest easily overfitted.</p>
  
  <h2>A toy example</h2>
  
  <p>Here is a random data set that includes response of binary factor and 10 numerical variables generated from rnorm().</p>
  
  <pre><code># Sorry for redundant preparation.
  data &lt;- data.frame(response=rnorm(100))
  data$response &lt;- factor(data$response &lt; 0)
  data &lt;- cbind(data, matrix(rnorm(1000), ncol=10))
  colnames(data)[-1] &lt;- paste("V",1:10,sep="")
  </code></pre>
  
  <p>Perform cforest, employing unbiased parameter set (maybe recommended).</p>
  
  <pre><code>cf &lt;- cforest(response ~ ., data=data, controls=cforest_unbiased())
  table(predict(cf), data$response)
  #       FALSE TRUE
  # FALSE    45    7
  # TRUE      6   42
  </code></pre>
  
  <p>Fairly good prediction performance on <em>meaningless</em> data.</p>
  
  <p>On the other hand, randomForest goes honestly.</p>
  
  <pre><code>rf &lt;- randomForest(response ~., data=data)
  table(predict(rf),data$response)
  #       FALSE TRUE
  # FALSE    25   27
  # TRUE     26   22
  </code></pre>
  
  <p>Where these differences come from?<br />
  I am afraid that I am using cforest in a wrong way.</p>
  
  <p>Let me put some extra observations in cforest:</p>
  
  <ol>
  <li>The number of variables did not much affect the result.</li>
  <li>Variable importance values (computed by varimp(cf)) were rather low, compared to those using some realistic explanatory variables.</li>
  <li>AUC of ROC curve was nearly 1.</li>
  </ol>
  
  <p>I would appreciate your advices.</p>
  
  <h2>Additional note</h2>
  
  <p>Some wondered why a training data set was applied to the predict().<br />
  I did not prepare any test data set because the prediction was done for OOB samples, which was not true for cforest.<br />
  <em>c.f.</em> <a href="http://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm" rel="noreferrer">http://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm</a></p>