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Suman Debnath for AWS

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# An Introduction to Decision Tree and Ensemble Methods – Part 1

In this day and age, there is a lot of buzz around Machine Learning(ML) and Artificial Intelligence(AI). And why not, after all, we all are consumers of ML directly or indirectly; irrespective of our professions. AI/ML is a fascinating field, generates a whole lot of excitement around it, and rightly so. In this tutorial series, we will try to explore and demystify the complicated world of {math, equations, and theory} that functions in tandem to bring out the "magic" which we experience on many application(s)/software(s). The idea is to discuss AI/ML algorithms in detail, implement it from scratch(wherever applicable), and enable the readers to answer "How?" rather than "What?". And while we discuss all of these, we shall demonstrate everything on AWS platform using different services as applicable. Having said that, I am a learner as most of you; trying to get a better understanding of this field with each passing day and I just wish to share my learning as I go along with a broader group . Your inputs/feedback are always welcome, anything that would help me improve this process.

But before we go ahead, I would also like to thank my teacher, Srikanth Varma Sir, for guiding me and 100s of thousands of students like me across the globe. Without him, I wouldn't have dreamt of getting into this wonderful world of Machine Learning. This write up is completely based on the class I have attended from his course at AppliedAI on Decision Tree.

# An Introduction to Decision Tree

In this tutorial, we will explore one of the most rampantly used and fundamental Machine Learning model, Decision Tree(DT). DT is a very powerful model which can help us to classify labelled data and make predictions. It also enlightens us with lots of information about the data and most importantly, it's effortlessly easy to interpret.

If you are a software engineer, you would probably know “if-else” conditions, and we all love it, because it’s very simple to understand, imagine and code. A decision tree can be thought of nothing but a “nested if-else classifier”.

Decision tree, is one of the classifiers we have in the world of machine learning, which closely resembles with human reasoning. It is also one of model we have, which comes under the category of supervised machine learning. In supervised machine learning, we are always given with the input data (also referred as features or independent features) and class labels(also referred as target feature or dependent feature).

Supervised learning is the machine learning task of learning a function that maps an input to an output based on example input-output pairs. It infers a function from labeled training data consisting of a set of training examples. In supervised learning, each example is a pair consisting of an input object (typically a vector) and a desired output value.

Let’s try to understand this with a simple example, suppose we have a data set of 50 fruits, out of which few are lemons and few are apples, and we are given fruit colour and fruit size as the input feature(so these are our 2 independent features).

The decision tree for this problem, might look like this:

But the question is, given a dataset, how can we build a tree like this ? To understand this, we need to look into the "math" behind this, which we will see in the next section. But before that, let's try to learn some key terminologies we must be aware of to work with Decision Tree:

• NODE: Each time we ask a question or make a decision stump, we represent the same as a NODE.
• ROOT: The topmost node of the tree which we start questioning with.
• INTERIOR: Any node, except the ROOT node, where we again ask a question.
• LEAF: When we reach a point where we don’t ask a question, but instead make a decision, we call it as LEAF node.

So here is the general DT structure example:

Decision trees are supervised learning algorithms, which means, we need to have labelled dataset and it can be used for both, classification and regression tasks, which means we can have it for categorical data or continuous data.

Training flow of a Decision Tree:

• Prepare the labelled data set, with independent feature{1, 2, 3, …, n} and dependent feature(target or class label).
• Try to pick the best feature as the root node and thereafter, use intelligent strategies to split the nodes into multiple branches.
• Grow the tree until we get a stopping criteria, i.e. the leaf node which would be the actual prediction when we make any query or ask for prediction.
• Pass through the prediction data query through the tree until we arrive at some leaf node
• Once we get the leaf node, we have the prediction!! :)

# Math behind Decision Tree

Now that we know how a Decision Tree looks like, next step to think about is(and it’s the most important task to accomplish), how can we go from training data to a decision tree ? And to understand this, we need to go over a bunch of very important concepts.

## Entropy

Entropy is a very interesting concept in the field of Information Theory. It is the notion of the impurity of the data, now what is this new term impurity of the data?

Let’s take an example, we have this node:

We can say that, this node is pure because there is only one class, no ambiguity in the class label(i.e. it’s all APPLE), Now, let’s say this node:

We can say, that it's little less pure w.r.t to the previous node, as there is some small amount of ambiguity that exists in the class label(as few LEMONs are present, along with APPLE). And finally, let’s see this node:

This is very much an impure node, as we have mixed classes(red APPLE, green APPLE, and yellow LEMON).

Now, let’s go back to the definition of Entropy, it’s the notion of impurity of a node, in other words, the more the impurity the more the entropy and vice versa.

Let’s say we have Random Variable, X, where x can be x1, x2, x3, x4…xn
Then, mathematically, Entropy can be defined as(also known as Shannon's entropy) this:

where,
k = ranges from 1 through n
H(x) = entropy of x
P(k) = Probability of random variable X when (X = k)

Now, let’s take an example to understand it little better,

In this dataset(D), Play Ball is the target class, and the random variable, X. And it can take only two values, “Yes” or “No”. So,

P(k=Yes) => 9/14 = 0.64
P(k=No) => 5/14 = 0.36

Therefore, the Entropy of “Play Ball” on the dataset(D), would be:

If we think intuitively, what this essentially means is:

• Higher the Entropy, more impure the dataset is.
• Lower the Entropy, more pure the dataset is.

## Information Gain(IG)

Now that we have an idea of what an Entropy is, the next important concept to look into is Information Gain(IG). Let’s continue with the same example as above, where we have the Entropy, H(“Play Ball”) or in other words, Entropy of the target label, “Play Ball” is 0.94. Now, let’s say we split the dataset with “Outlook” feature set, then our dataset would look like this:

Now, we get 3 small sub-datasets(D1, D2, and D3), based on the different values we have for the feature “Outlook”(i.e. Rainy, Overcast and Sunny). So, if now compute the Entropy of each of this small sub-dataset on the same target class “Play ball”, it would be:

Now, the Weighted Entropy after breaking the dataset to D1, D2 and D3 would be:

So, the Information Gain of the dataset D, when we break it based on feature, Outlook, would be:

Information Gain(Outlook)= Entropy(D) − Weighted Entropy after breaking the dataset

Similarly, we can find the IG based on other features as well(for Temperature, Humidity and Windy)

Now, if we have the information gain of all these 4 features, and it’s very clear that, the information gain of the feature “Outlook” is the largest, which indirectly says that this feature(“Outlook”) gives us the maximum amount of information about the target class(“Play ball”).

Hence, Decision Tree would use this feature as the ROOT node of the tree. And once the data is split, we need to further check each of the small sub tree and perform the same activity and decide the next feature which has the highest IG, so that we can split the dataset further to get to leaf node.

# How to build a Tree

With the understanding of what is Entropy and IG, we can build a tree, and here is the algorithmic steps:

1. First the entropy of the total dataset is calculated for the target label/class.
2. The dataset is then split on different features.
3. The entropy for each branch is calculated. Then it is added proportionally, to get total weighted entropy for the split.
4. The resulting entropy is subtracted from the entropy before the split.
5. The result is the Information Gain.
6. The feature that yields the largest IG is chosen for the decision node.
7. Repeat step #2 to #6, for each subset of the data(for each internal node) until:
• All the dependent features are exhausted.
• The stopping criteria are met.

Few of the stopping criteria used are:

• no. of levels of tree from the root node(or in other words, depth of the tree)
• Minimum no. of observations in the parent/child node(e.g. 10% of the training data)
• Minimum reduction of impurity index

# Algorithm behind decision tree

So far, we have discussed about Entropy as one of the ways to find the impurity of a node, but there are other techniques available to split the data, like Gini Impurity, Chi-Square, Variance, etc.. However, we have different algorithms to implement a Decision Tree model, and each uses different techniques to identify the impurity of a node, and hence the split. For example:

• ID3(Iterative Dichotomiser 3) algorithm - uses Entropy
• CART algorithm - uses Gini Impurity Index
• C4.5 - uses Gain Ratio

Thankfully, we do not have to do all this(like calculating Entropy, IG, implement ID3, etc.), we have lots of libraries/packages available in Python which we can use to solve a problem with decision tree.

# Problem

Here is the dataset. The data set contains wifi signal strength observed from 7 wifi devices on a smartphone collected in indoor space(4 different rooms)? The task is to predict the location(which room) from wifi signal strength. Form more details check here

## Amazon SageMaker Notebook

Before we get into code, we would spin an Amazon SageMaker Notebook, it’s a fully managed ML compute instance running the Jupyter Notebook App. It manages creating the instance and related resources for us, we are going to use Amazon SageMaker Notebook, rather than using local Jupyter-Notebook on our laptop(and we will later see why?)

We will use Jupyter notebooks within our notebook instance to prepare and process data, write code to train models, deploy models to Amazon SageMaker hosting, and test or validate your models. For this tutorial, since we are going to have a small dataset, we will not be deploying the model, but going forward for the upcoming tutorials we are going to solve various complex problem wherein we would deploy the model as well.

2. Search of SageMaker under Find Services search bar

3. Click on the side menu, Notebook -> Notebook Instances and then click on Create notebook Instance

4. Specify the instance type, and click Create notebook instance.

5. Wait for the instance till the Status changes from Pending to InService

6. Once its InService, click on Open Jupyter

So, now our Jupyter Notebook is up and running. One of the best part of SageMaker Notebook is it being completely managed and all the different framework comes out of the box, for example, if we click on New and try to create a new notebook, we will see list of different kernels available, we don’t have to worry about installing, maintaining the updates, etc.

OK, we are all set now, lets go back the problem statement we have in hand and start coding.

Lets load the modules we will need to work with this problem, we will be using scikit-learn machine learning library

### Decision Tree Classifier

Let's create a small function which will return a decision tree classifier

Here, the function takes 2 arguments,

• X_train: Input or Independent Features and
• y_train: Class or Target Label

Then we use DecisionTreeClassifier classifier from scikit-learn library, this function takes many arguments(which are also commonly know as hyperparameters), and here we are using one of them, criterion: The function to measure the quality of a split. Supported criteria are “gini” for the gini impurity and “entropy” for the information gain.

And this function returns clf_tree: the decision tree classifier which we will be using for inference(prediction) later.

Here, after loading the data in a df: Pandas DataFrame, we insert the column names and separates the Input Features(X DataFrame) and Target Label(Y DataFrame)

### Splitting the dataset

Now, we will split the whole dataset into training and testing(we will use 20% of the total data points for testing),

Now we can see the first 5 data points:

### Decision Tree Classifier

We can see that this classifier can be tuned with many parameters(often times, its called hyper-parameters. For more details on what each hyper parameters mean, we can refer to the documentation

We have used one of the hyper-parameter here criterion, as "entropy", which mean that the classifier will use entropy to calculate the IG, which would be ultimately used to split the data in the background.

### Predicting the result on the test data

Finally, we can use our Decision Tree Classifier object clf_tree to make some prediction on my testing data(X_test)

### Evaluating the Performance

Now, that we got the prediction(y_pred), we can validate it with the actual labels (y_test) of this test data.

We did a lot in these last few lines of code, and we saw some new terms, accuracy, precision, recall, f1-score and confusion matrix

These all were Model Performance Metrics, we will have one tutorial dedicated to different Model Performance Metrics as we have many and not only these which are mentioned here, but for now, we can think of these as:

• accuracy : It simply measures, how accurately the model predicted, e.g. if we have 10 test data points, and out of 10, only 8 data points are predicted correctly by the classifier, then the accuracy would be 80%, which also means accuracy can lie between 0 to 1
• precision: The precision is the ratio tp / (tp + fp) where tp is the number of true positives and fp the number of false positives. The precision is intuitively the ability of the classifier not to label as positive a sample that is negative.
• recall: The recall is the ratio tp / (tp + fn) where tp is the number of true positives and fn the number of false negatives. The recall is intuitively the ability of the classifier to find all the positive samples.
• f1-score: The F1 score can be interpreted as a weighted average of the precision and recall, where an F1 score reaches its best value at 1 and worst score at 0. The relative contribution of precision and recall to the F1 score are equal. Mathematically it is defined by: 2 * (precision * recall) / (precision + recall)

### Visualize A Decision Tree

Finally, we will try to visualize how our Decision Tree looks like, and we can do so, using a library graphviz

This is finally how the tree from the above classifier would look like. You can also download it from here

Next, we will explore some other algorithm and solve some problem. You may like to get the code/jupyter-notebook from git repo

## Reference

You may like to visit the below mentioned course, books and source links which were referred to for the tutorial: