JavaVersion1. 7. 067Decision Boundaries for Deep Learning and other Machine Learning classifiers. By Takashi J. OZAKI, Ph. D. For a while at least several months since many people began to implement it with Python andor Theano, Py. Java Version 1.7.0_67' title='Java Version 1.7.0_67' />Learn. Ive given up practicing Deep Learning with R and Ive felt I was left alone much further away from advanced technologyBut now we have a great masterpiece h. H2. O framework in R. I believe h. 2o is the easiest way of applying Deep Learning technique to our own datasets because we dont have to even write any code scripts but only to specify some of its parameters. That is, using h. With using h. 2o on R, in principle we can implement Deep Belief Net, that is the original version of Deep Learning1. I know its already not the state of the art style of Deep Learning, but it must be helpful for understanding how Deep Learning works on actual datasets. G7Zlp.png' alt='Java Version 1.7.0_67' title='Java Version 1.7.0_67' />Please remember a previous post of this blog that argues about how decision boundaries tell us how each classifier works in terms of overfitting or generalization, if you already read this blog. Its much simple how to tell which overfits or well gets generalized with the given dataset generated by 4 sets of fixed 2. D normal distribution. My points are 1 if decision boundaries look well smoothed, theyre well generalized, 2 if they look too complicated, theyre overfitting, because underlying true distributions can be clearly divided into 4 quadrants with 2 perpendicular axes. Java Version 1.7.0_67' title='Java Version 1.7.0_67' />OK, lets run the same trial with Deep Learning of h. R in order to see how DL works on the given dataset. Datasets. Please get 3 datasets from my repository on Git. Hub simple XOR pattern, complex XOR pattern, and a grid dataset. Github Repo for the current post. 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Note that bug fixes are cumulative, that is, bug fixes in previous update versions are. Of course, feel free to clone it but any pull request will be rejected because this repository is not for software development. PGetting started with h. RFirst of all, H2. O itself requires Java Virtual Machine environment. Prior to installing h. Java SE SDK. Next, h. CRAN but available on Git. Hub. In order to install it, you have to add some arguments to run install. R. get. Optionrepos libraryh. C Program FilesRR 3. Your next step is to start H2. O and get a connection object named. H2. O,for example local. H2. O h. 2o. init. For H2. O package documentation, ask for help After starting H2. O, you can use the Web UI at http localhost 5. For more information visit http docs. At any rate, now you can run h. R. How h. 2o works on ROnce h. H2. O instance on Java. VM. In the case below nthreads argument was set to 1, that means all CPU cores must be used for the H2. O instance. If you want spare any cores, specify the number of cores you want to use for H2. O, e. g. 7 or 6. local. H2. O lt h. 2o. H2. O TRUE. H2. O is not running yet, starting it now. Note In case of errors look at the following log files. C UsersXXXApp. DataLocalTempRtmpghjv. Goh. 2oXXXwinstartedfromr. C UsersXXXApp. DataLocalTempRtmpghjv. Goh. 2oXXXwinstartedfromr. JavaTM SE Runtime Environment build 1. Java Hot. SpotTM6. Bit Server VM build 2. Successfully connected to http localhost 5. R is connected to H2. O cluster. H2. O cluster uptime 1 seconds 5. H2. O cluster version 2. H2. O cluster name H2. OstartedfromR. H2. O cluster total nodes 1. H2. O cluster total memory 7. GB. H2. O cluster total cores 8. H2. O cluster allowed cores 8. H2. O cluster healthy TRUENow you can run all functions of h. Then load the simple XOR pattern and the grid dataset. Data lt h. 2o. Filelocal. H2. O, path xorsimple. Vocaloid 4 Editor more. Datalt h. 2o. import. Filelocal. H2. O,pathpgrid. Were ready to draw various decision boundaries using h. Deep Learning. Lets go to the next step. Prior to trying Deep Learning, see the previous result. To compare a result of Deep Learning with ones of the other classifiers, please see the previous result. In the ones below, I ran decision tree, SVM with some sets of parameters, neural network with only a hidden layer, and random forest. Linearly inseparable and simple XOR pattern. As clearly seen, all of the classifiers showed decision boundaries well reflecting its true distribution. Linearly inseparable and complex XOR pattern. In contrast to the simple XOR pattern, the result showed a wide variety of decision boundaries. Decision tree, neural network and random forest estimated much more complicated boundaries than the true boundaries, although SVM with well generalized by specific parameters gave natural and well smoothed boundaries but classification accuracy was not good. Drawing decision boundaries with h. OK, lets run h. 2o. Deep Learning. Our primary interest here is what kind of set of tuning parameters shows what kind of decision boundaries. In h. 2o. deeplearning function, we can tune parameters arguments below activation Tanh, Rectifier and Maxout. We can also add With. Dropout to implement the dropout procedure. Of course larger epochs, more trained output you can get. Here we ignore it because the sample size is too small. Even if you want to implement the dropout procedure, we recommend to specify only 0. Baldi NIPS, 2. 01. For simplification, in this post I only tune activation and hidden. In particular about hidden, the number of hidden layers are fixed to 2 or 3 and the number of units are fixed to 5 or 1. Anyway we can run it as below. Data,classificationT. Tanh,hiddenc1. Data prd. T plotxors, 3, pch1. Tanh, 1. 0,1. 0 parnewT contourpx, py, arrayprd. FA script above is just an example please rewrite or adjust it to your environment. XOR pattern with 2 hidden layers. Rectifier. Maxout. Maxout failed to estimate a classification model correctly perhaps it was caused by too small sample size only 1. D. On the other hand, Tanh and Rectifier showed fairly good decision boundaries. XOR pattern with 2 hidden layers. Rectifier. In contrast to the result of the simple XOR pattern, Rectifier worked better than Tanh and its decision boundary is similar to the one of SVM well generalized version. Tanh looks overfitting. XOR pattern with 3 hidden layers. This is just a trial for evaluating an effect of the number of hidden layers. Prior to this trial, I think its number may affect a bit results of classification so, how was it Both of decision boundaries look getting more overfit than ones with 2 hidden layers, but seem to well classify samples. XOR pattern with 3 hidden layers. I feel like joking. Tanh looks almost never working. Rectifier classified well but seems less generalized although its decision boundary looks not so overfitting.