In a regression tree (I am particularly interested in random forest regression, but it seems like this can be generalised to regression trees as a whole) a number of random variables is selected at a root node of the tree and the best variable split is selected in order to split the node into two daughter nodes. This continues until a set of criteria is fulfilled. My questions here are: How is the best variable split determined at each tree point in a regression tree? What are the criteria to stop?  As far as I understand the default for random forest regression is that the best variable split should produce lowest mean squared error (a mean squared error of what exactly?) and the stopping criteria are either mean squared error is lower than the entire dataset (somehow I don’t think that is entirely correct) or the resulting leaf size would contain less than 5 variables.   Once it is completed, the algorithm outputs an ensemble of trees. The prediction can then be made. My other question here is; How is the final prediction made at each leaf in a regression tree?  Of course the prediction is an average of the ensemble of the trees, but an average of what exactly? I think in the simplest case (called a constant estimate) it simply is the mean value of variables in that leaf averaged over all trees(?). Or is it a linear regression computed within that leaf averaged over an ensemble?
I am not an expert of random forest but I clearly understand that the key issue with random forest is the (random) tree generation. Can you explain me how the trees are generated? (i.e. What is the used distribution for tree generation?)  Thanks in advance !
How to batch watermark JPG files? I have around 15,000 JPG files that need to be watermarked. Is there any way to process these images en masse and add a watermark?  The images may be different sizes, I want the watermark placed in the center of the images. Proof for $e^z = \lim \limits_{x \rightarrow \infty} \left( 1 + \frac{z}{x} \right)^x$ Q1: Could someone provide a proof for this equation (please focus on this question):   $$e^z = \lim \limits_{x \rightarrow \infty} \left( 1 + \frac{z}{x} \right)^x$$  Q2: Is there any corelationn between above equation and the equation below (this would benefit me a lot because i at least know how to proove this one):  $$e = \lim \limits_{x \rightarrow \infty} \left( 1 + \frac{1}{x} \right)^x$$ When I am in texture mode one of my objects looks like it is in solid mode. The model is textured like all other models in the scene, but it doesn't look like it is in texture mode.  Screenshot will explain better:      What this model looks like. What all models should look like in texture mode. How do I delete Windows after an Ubuntu install? I downloaded Ubuntu 12.04 LTS to my Dell Dimension 4600 with Windows XP installed.  I now have a neat dual-boot system, but I want to get rid of the XP OS and keep Ubuntu as my only OS.  How do I do this? Number of isosceles triangle. In Clash of Clans there was an update on 9/16 adding a Tie-breaker into the wars, can anybody explain in detail how this mechanism works? In s08e03 we see Melisandre and Arya meet for the second time after Season 3 when Melisandre said to Arya back then:     "I see a darkness in you. And in that darkness, eyes staring back at me. Brown eyes, blue eyes, green eyes. Eyes you'll shut forever. We will meet again. "   I think Blue Eyes referred to the Night King and the White Walkers since we saw Arya killing the Night King in s08e03.   I also believe that Brown Eyes referred to Walder Frey who was also killed by Arya back in Season 6.    But where do the Green Eyes reffer to? I don't remember her executing any important character with green eyes. My guess is that:       they reffer to Cersei. Do you think that  the prophecy implies that she is going to bring her hateful enemy down somehow? Bash copy all files that don't match the given extensions When I import pictures from my camera in Shotwell, it also imports the video clips. This is somewhat annoying, as I would like to store my videos in another folder. I've tried to write a bash command to do this, but have not had success.  I need a command that meets the following requirements:   Locate all files in a directory structure that do not have an extension of .jpg, .png, .gif, or .xcf (case insensitive). Move all of these files into a target directory, regardless of whether the file names or directory paths contain spaces or special characters.   Any help would be appreciated!  EDIT: I'm using the default shell in Ubuntu, meaning that some commands are aliased, etc.  EDIT 2: I've attempted this myself (not the copy part, just the listing of files part). I turned on extglob and ran the following command:  $ ls -R /path | awk '   /:$/&amp;&amp;f{s=$0;f=0}   /:$/&amp;&amp;!f{sub(/:$/,"");s=$0;f=1;next}   NF&amp;&amp;f{ print s"/"$0 }'   This lists everything. I tried using grep on the end of it, but haven't the foggiest idea of how to get it to not match a pattern I give it. The extglob switch didn't help much with grep, even though it does help with other commands. I want to search for all .conf files in /etc/. I tried grep -r *.conf /etc, but the result isn't right. What am I doing wrong? iOS: How to change app language programmatically WITHOUT restarting the app? Setting page numbering on Word I have a word document. The first four pages are title and index. After that, the “Chapter 1” starts. I want page numbers to begin from the “Chapter 1” onwards only. The first 4 pages should not have any page number.  How do I achieve this? Concatenate multiple files with two blank lines as delimiter? I'm trying to join Markdown files with two newlines between each file.   I've tried using the following command:  paste -sd '\n\n' file1.md file2.md   This joins the files with a newline, but not two newlines, as I need.   What command can I use to join an arbitrary number of files with two \n characters between each join? What's the difference between Google Chrome and/or Chromium? What are the advantages/disadvantages to each? I used Google Chrome in Windows, and am now using Chromium in Ubuntu.  Is there any difference to the two programs?  What are the advantages and disadvantages to each program?  Which one seems better? Elements order in a "for (… in …)" loop Does the "for…in" loop in Javascript loop through the hashtables/elements in the order they are declared? Is there a browser which doesn't do it in order? The object I wish to use will be declared once and will never be modified.  Suppose I have:  var myObject = { A: "Hello", B: "World" };   And I further use them in:  for (var item in myObject) alert(item + " : " + myObject[item]);   Can I expect 'A : "Hello"' to always come before 'B : "World"' in most decent browsers? Why does US Robotics destroy Lanning's house? Shortly after the death of Dr. Lanning, Detective Spooner travels to the doctor's house to look for clues.  While he is searching the house a demolition bot (which had been programmed to demolish the house the next day) goes on a rampage and destroys the house with Detective Spooner in it.   The house is fully furnished and appears to be in good condition. Why would US Robotics want to destroy the house with everything in it? Why not sell the house and everything inside? Highly unbalanced test data set and balanced training data in classification I have a training set with about 3000 positive instances and 3000 negative instances. But my test data set is pretty much un-balanced. The positive set only has 50 instances and negative has 1500 instances.This causes the precision very low. Are there any approaches to solve this problem? I use SVM to build classifier. Is there a fast way to get to the bottom of the Death Star? In Tiny Death Star, you can get to the top of your tower by tapping on the top of the screen while avoiding the "Add Level" button. However, the only way I can find to go to the bottom of the tower is to wait for someone to want an elevator ride, and tap on the button to give them that ride. Is there any other hot-spot for getting to the bottom of your Death Star? Could not load 'vboxdrv' after upgrade to Ubuntu 16.04 (and I want to keep secure boot) I upgrade from Ubuntu 15.10 to 16.04 and since then VirtualBox 5.0.18 isn't starting my VMs anymore. It complains that 'vboxdrv' isn't loaded. So I try to load it and get the following error:  $ sudo modprobe vboxdrv modprobe: ERROR: could not insert 'vboxdrv': Required key not available   I believe it is related to secure boot which I use and which I want to continue using. Actually with Ubuntu 15.10 secure boot and VirtualBox were working just fine.  Also I tried $ sudo apt-get --reinstall install virtualbox-dkms which built the kernel module successfully but didn't solve this issue.  Any idea how to get vboxdrv loaded while keeping secure boot enabled?  Update 2: Also I tried executing sudo mokutil --disable-validation. When executing this command, during the next boot I get prompted to disable secure boot, add a key or hash from disk. Since I don't want to disable secure boot, it seems that this doesn't solve my issue either. Also I want to keep UEFI activated for a parallel Windows installation.  Note: If you don't mind disabling secure boot, see  instead. SQL Server - copy stored procedures from one db to another What are the C++ coding and file organization guidelines you suggest for people who have to deal with lots of interdependent classes spread over several source and header files?  I have this situation in my project and solving class definition related errors crossing over several header files has become quite a headache.