##### How to interpret decision tree results in r

When we reach a leaf we will find the prediction usually it is a simple statistic of the dataset the leaf represents, like the most common value from the available classes. Contrary to linear or polynomial regression which are global models the predictive formula is supposed to hold in the entire data spacetrees try to partition the data space into small enough parts where we can apply a simple different model on each part.

One of the most comprehensible non-parametric methods is k-nearest-neighbors: find the points which are most similar to you, and do what, on average, they do. Trees get around both problems: leaves correspond to regions of the input space a neighborhoodbut one where the responses are similar, as well as the inputs being nearby; and their size can vary arbitrarily.

Prediction trees are adaptive nearest-neighbor methods. Regression Trees like say linear regression, outputs an expected value given a certain output. Notice that the leaf values represent the log of the price, since that was the way we represented the formula in the tree function. We can compare the predictions with the dataset darker is more expensive which seem to capture the global price trend:. The tree fitting function has a number of controls settings which limit how much it will grow each node has to contain a certain number of points, and adding a node has to reduce the error by at least a certain amount.

The default for the latter, min. We can prune the tree to prevent overfitting. The next function prune.

The argument newdata accepts new input for making the prune decision. If new data is not given, the method uses the original dataset from which the tree model was built.

This package can also do K-fold cross-validation using cv. Random forests are an ensemble learning method for classification and regression that operate by constructing a multitude of decision trees at training time and outputting the class that is the mode of the classes output by individual trees â€” Wikipedia. Check the manual for options and available tools.

We can also tune the structure, ie, finding the best hyperparameters of the method via grid search:. Conditional inference trees estimate a regression relationship by binary recursive partitioning in a conditional inference framework. Roughly, the algorithm works as follows: 1 Test the global null hypothesis of independence between any of the input variables and the response which may be multivariate as well.

Stop if this hypothesis cannot be rejected. Otherwise select the input variable with strongest association to the resonse. This association is measured by a p-value corresponding to a test for the partial null hypothesis of a single input variable and the response. Regression Trees Regression Trees like say linear regression, outputs an expected value given a certain output. Median Mean 3rd Qu.

Also, we can include all the variables, not only the latitude and longitude: tree. Classification Trees Classification trees output the predicted class for a given sample. Length" "Petal. Width" "Sepal. Length" Number of terminal nodes: 6 Residual mean deviance: 0. Width" Number of terminal nodes: 4 Residual mean deviance: 0. Package rpart This package is faster than tree. Width Fitted party: [1] root [2] Petal.

### Motivating Problem

Random Forests Random forests are an ensemble learning method for classification and regression that operate by constructing a multitude of decision trees at training time and outputting the class that is the mode of the classes output by individual trees â€” Wikipedia Check the manual for options and available tools. Width, "versicolor" We can extract a given tree or get some information about the ensemble.Let's imagine you are playing a game of Twenty Questions.

At each turn, you may ask a yes-or-no question, and your opponent must answer truthfully. How do you find out the secret in the fewest number of questions? It should be obvious some questions are better than others.

For example, asking "Can it fly? Intuitively, you want each question to significantly narrow down the space of possibly secrets, eventually leading to your answer. That is the basic idea behind decision trees. At each point, you consider a set of questions that can partition your data set.

You choose the question that provides the best split and again find the best questions for the partitions. You stop once all the points you are considering are of the same class. Then the task of classication is easy. You can simply grab a point, and chuck it down the tree. The questions will guide it to its appropriate class. Since this tutorial is in R, I highly recommend you take a look at our Introduction to R or Intermediate R course, depending on your level of advancement.

In this tutorial, you will learn about the different types of decision treesthe advantages and disadvantagesand how to implement these yourself in R.

Decision tree is a type of supervised learning algorithm that can be used in both regression and classification problems. It works for both categorical and continuous input and output variables. Root Node represents the entire population or sample. It further gets divided into two or more homogeneous sets. When you remove sub-nodes of a decision node, this process is called Pruning.

The opposite of pruning is Splitting. A node, which is divided into sub-nodes is called a parent node of the sub-nodes; whereas the sub-nodes are called the child of the parent node. Let's take a look at the image below, which helps visualize the nature of partitioning carried out by a Regression Tree.

This shows an unpruned tree and a regression tree fit to a random dataset. Both the visualizations show a series of splitting rules, starting at the top of the tree. Notice that every split of the domain is aligned with one of the feature axes. The concept of axis parallel splitting generalises straightforwardly to dimensions greater than two. In order to build a regression tree, you first use recursive binary splititng to grow a large tree on the training data, stopping only when each terminal node has fewer than some minimum number of observations.

Recursive Binary Splitting is a greedy and top-down algorithm used to minimize the Residual Sum of Squares RSSan error measure also used in linear regression settings. The RSS, in the case of a partitioned feature space with M partitions is given by:. Beginning at the top of the tree, you split it into 2 branches, creating a partition of 2 spaces. You then carry out this particular split at the top of the tree multiple times and choose the split of the features that minimizes the current RSS.In this tutorial, we will cover all the important aspects of the Decision Trees in R.

We will build these trees as well as comprehend their underlying concepts. We will also go through their applications, types as well as various advantages and disadvantages.

Keeping you updated with latest technology trends, Join DataFlair on Telegram. Decision Trees are a popular Data Mining technique that makes use of a tree-like structure to deliver consequences based on input decisions.

One important property of decision trees is that it is used for both regression and classification. This type of classification method is capable of handling heterogeneous as well as missing data. Decision Trees are further capable of producing understandable rules. Furthermore, classifications can be performed without many computations.

As mentioned above, both the classification and regression tasks can be performed with the help of Decision Trees. You can perform either classification or regression tasks here. Decision Trees can be visualised as follows:. The Decision Tree techniques can detect criteria for the division of individual items of a group into predetermined classes that are denoted by n.

In the first step, the variable of the root node is taken. This variable should be selected based on its ability to separate the classes efficiently. This operation starts with the division of variable into the given classes. This results in the creation of subpopulations. This operation repeats until no separation can be obtained.

A tree exhibiting not more than two child nodes is a binary tree. The origin node is referred to as a node and the terminal nodes are the trees. The choice depends on the type of Decision Tree. Same goes for the choice of the separation condition. In the case of a binary variable, there is only one separation whereas, for a continuous variable, there are n-1 possibilities.

After finding the best separation, the operation is repeated to increase discrimination among the nodes. After finding the best separation, classes are split into child nodes.

We derive a variable out of this step. We choose the best separation criteria as:. O ij provides us with the left-hand side of the equality symbol and T ij provides the term on the right, independence test of X and Y is X 2. All types of dependent variables use it and we calculate it as follows:.

With an increase in distribution, the Gini index will also increase. However, with the increase in the purity of the node, the Gini index decreases. Wait a minute! Have you checked â€” Logistic Regression in R.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Data Science Stack Exchange is a question and answer site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field.

It only takes a minute to sign up. The dependent variable of this decision tree is Credit Rating which has two classes, Bad or Good. The root of this tree contains all observations in this dataset. The most influential attribute to determine how to classify a good or bad credit rating is the Income Level attribute.

The majority of the people out of in our sample that had a less than low income also had a bad credit rating. If I was to launch a premium credit card without a limit I should ignore these people. If I were to use this decision tree for predictions to classify new observations, are the largest number of class in a leaf used as the prediction?

Observation x has medium income, 7 credit cards and 34 years old. If Good, Bad is what you mean by credit rating, then Yes. And you are right with the conclusion that all the observations are contained in the root of the tree. Debatable Depends on how you consider something to be influential.

Some might argue that the number of cards might be the most influential, and some might agree with your point. So, you are both right and wrong here. Yesbut it would also be better if you consider the probability of getting a bad credit from these people. But, even that would turn out to be NO for this class, which makes your observation correct again.

Depends on the probability. So, calculate the probability from the leaves and then make a decision depending on that. Or much simpler, use a library like the Sklearn's decision tree classifier to do that for you.

Yesthis is a correct way of interpreting decision trees. You might be tempted to sway when it comes to selection of influential variables, but that is dependant on a lot of factors, including the problem statement, construction of the tree, analyst's judgement, etc. Yes, your interpretation is correct. Each level in your tree is related to one of the variables this is not always the case for decision trees, you can imagine them being more general.

X has medium income, so you go to Node 2, and more than 7 cards, so you go to Node 5. Now, you've reached a leaf node. And you had people like X who had a Good rating. So, based on only this information, you can say X probably has a Good rating. So, the decision tree has given you a quick, though approximate answer. Regarding the comment about "most influential" attribute, this really depends on the way the tree is constructed, and what definition of "influential" you use.A decision tree is a supervised machine learning model used to predict a target by learning decision rules from features.

As the name suggests, we can think of this model as breaking down our data by making a decision based on asking a series of questions. Let's consider the following example in which we use a decision tree to decide upon an activity on a particular day:.

Based on the features in our training set, the decision tree model learns a series of questions to infer the class labels of the samples. As we can see, decision trees are attractive models if we care about interpretability.

Although the preceding figure illustrates the concept of a decision tree based on categorical targets classificationthe same concept applies if our targets are real numbers regression. We will cover:. It includes an in-browser sandboxed environment with all the necessary software and libraries pre-installed, and projects using public datasets.

You can get started here! A decision tree is constructed by recursive partitioning â€” starting from the root node known as the first parenteach node can be split into left and right child nodes.

These nodes can then be further split and they themselves become parent nodes of their resulting children nodes. For example, looking at the image above, the root node is Work to do? The Outlook node further splits into three child nodes. So, how do we know what the optimal splitting point is at each node? Starting from the root, the data is split on the feature that results in the largest Information Gain IG explained in more detail below. In an iterative process, we then repeat this splitting procedure at each child node until the leaves are pure â€” i.

In practice, this can result in a very deep tree with many nodes, which can easily lead to overfitting. Thus, we typically want to prune the tree by setting a limit for the maximal depth of the tree.

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In order to split the nodes at the most informative features, we need to define an objective function that we want to optimize via the tree learning algorithm. Here, our objective function is to maximize the information gain at each split, which we define as follows:.

Here, f is the feature to perform the split, DpDleftand Dright are the datasets of the parent and child nodes, I is the impurity measureNp is the total number of samples at the parent node, and Nleft and Nright are the number of samples in the child nodes.

We will discuss impurity measures for classification and regression decision trees in more detail in our examples below. But for now, just understand that information gain is simply the difference between the impurity of the parent node and the sum of the child node impurities â€” the lower the impurity of the child nodes, the larger the information gain.

Note that the above equation is for binary decision trees â€” each parent node is split into two child nodes only. If you have a decision tree with multiple nodes, you would simply sum the impurity of all nodes. We will start by talking about classification decision trees also known as classification trees. For this example, we will be using the Iris dataset, a classic in the field of machine learning. It contains the measurements of Iris flowers from three different species â€” SetosaVersicolorand Virginica.

These will be our targets. Our goal is to predict which category an Iris flower belongs to. The petal length and width in centimeters are stored as columns, which we also call the features of the dataset.

Using scikit-learnwe will now train a decision tree with a maximum depth of 4. The code is as follows:.The person will then file an insurance claim for personal injury and damage to his vehicle, alleging that the other driver was at fault. In order to grow our decision tree, we have to first load the rpart package. Then we can use the rpart function, specifying the model formula, data, and method parameters.

In this case, we want to classify the feature Fraud using the predictor RearEndso our call to rpart should look like. Notice the output shows only a root node. This is because rpart has some default parameters that prevented our tree from growing. Namely minsplit and minbucket. See what happens when we override these parameters. Now our tree has a root node, one split and two leaves terminal nodes. We can plot mytree by loading the rattle package and some helper packages and using the fancyRpartPlot function.

The decision tree correctly identified that if a claim involved a rear-end collision, the claim was most likely fraudulent. By default, rpart uses gini impurity to select splits when performing classification.

You can use information gain instead by specifying it in the parms parameter. Internally, rpart keeps track of something called the complexity of a tree. The complexity measure is a combination of the size of a tree and the ability of the tree to separate the classes of the target variable. This amount is specified by the complexity parameter, cpin the call to rpart.

Setting cp to a negative amount ensures that the tree will be fully grown. This is not always a good idea since it will typically produce over-fitted trees, but trees can be pruned back as discussed later in this article. One of the best ways to identify a fraudulent claim is to hire a private investigator to monitor the activities of a claimant. To do this, they can use a decision tree model based off some initial features of the claim.

If the insurance company wants to aggressively investigate claims i. To alter the default, equal penalization of mislabeled target classes set the loss component of the parms parameter to a matrix where the i,j element is the penalty for misclassifying an i as a j. The loss matrix must have 0s in the diagonal.

For example, consider the following training data.

BUT there was one fraudulent claim in the training dataset that was not a rear-end collision. If the insurance company wants to identify a high percentage of fraudulent claims without worrying too much about investigating non-fraudulent claims they can set the loss matrix to penalize claims incorrectly labeled as fraudulent three times less than claims incorrectly labeled as non-fraudulent.

Now our model suggests that Whiplash is the best variable to identify fraudulent claims.A decision tree is a machine learning algorithm that partitions the data into subsets. The partitioning process starts with a binary split and continues until no further splits can be made.

**StatQuest: Random Forests Part 1 - Building, Using and Evaluating**

Various branches of variable length are formed. The goal of a decision tree is to encapsulate the training data in the smallest possible tree. The rationale for minimizing the tree size is the logical rule that the simplest possible explanation for a set of phenomena is preferred over other explanations. Also, small trees produce decisions faster than large trees, and they are much easier to look at and understand.

There are various methods and techniques to control the depth, or prune, of the tree. Decision trees can be used either for classification, for example, to determine the category for an observation, or for prediction, for example, to estimate the numeric value. Using a decision tree for classification is an alternative methodology to logistic regression.

### Explanation of the Decision Tree Model

Using a decision tree for prediction is an alternative method to linear regression. See those methods for additional industry examples. The following example uses the credit scoring data set that was explained and used for the scoring application example in Creating a Scoring Application. Note: This list has been truncated for display purposes. Note: Do not change any of the default parameters. For more information on the default values, see Other User-Controlled Parameters.

The Summary of the Tree model for Classification appears, as shown in the following image. The default priors are proportional to the data counts. The input box is empty by default.

Consideration: As a rule, many programs and data miners will not attempt, or advise you, to split a node with less than 10 cases in it. The model output is described line by line. For illustration purposes, we have pruned the tree by lowering the Max Depth from the default to 3. Node Numbering. Nodes are labeled with unique numbers. The root node is 1. The following tree diagram generated by clicking the Draw button shows in color the node numbers for the tree described previously.

Only the terminal node numbers are displayed. For example, node 2 and 3 labels are not shown. Primary Split.