# Ensemble learning algorithm examples

Ensemble methods are techniques that create multiple models and then combine them to produce improved results. Ensemble methods usually produces more accurate solutions than a single model would. This has been the case in a number of machine learning competitions, where the winning solutions used ensemble methods. In the popular Netflix Competition, the winner used an ensemble method to implement a powerful collaborative filtering algorithm.

Another example is KDD where the winner also used ensemble methods. You can also find winners who used these methods in Kaggle competitions, for example here is the interview with the winner of CrowdFlower competition. It is important that we understand a few terminologies before we continue with this article. This model is then used for making predictions.

This algorithm can be any machine learning algorithm such as logistic regression, decision tree, etc. In this blog post I will cover ensemble methods for classification and describe some widely known methods of ensemble: voting, stacking, bagging and boosting.

Voting and averaging are two of the easiest ensemble methods. They are both easy to understand and implement. Voting is used for classification and averaging is used for regression.

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Each base model can be created using different splits of the same training dataset and same algorithm, or using the same dataset with different algorithms, or any other method. The following Python-esque pseudocode shows the use of same training dataset with different algorithms. According to the above pseudocode, we created predictions for each model and saved them in a matrix called predictions where each column contains predictions from one model.

Every model makes a prediction votes for each test instance and the final output prediction is the one that receives more than half of the votes. If none of the predictions get more than half of the votes, we may say that the ensemble method could not make a stable prediction for this instance.

Although this is a widely used technique, you may try the most voted prediction even if that is less than half of the votes as the final prediction. Unlike majority voting, where each model has the same rights, we can increase the importance of one or more models.

In weighted voting you count the prediction of the better models multiple times. Finding a reasonable set of weights is up to you.

In simple averaging method, for every instance of test dataset, the average predictions are calculated. This method often reduces overfit and creates a smoother regression model. The following pseudocode code shows this simple averaging method:. Weighted averaging is a slightly modified version of simple averaging, where the prediction of each model is multiplied by the weight and then their average is calculated. The following pseudocode code shows the weighted averaging:.

Stacking, also known as stacked generalization, is an ensemble method where the models are combined using another machine learning algorithm. The basic idea is to train machine learning algorithms with training dataset and then generate a new dataset with these models. Then this new dataset is used as input for the combiner machine learning algorithm.

As you can see in the above pseudocode, the training dataset for combiner algorithm is generated using the outputs of the base algorithms. In the pseudocode, the base algorithm is generated using training dataset and then the same dataset is used again to make predictions.

But as we know, in the real world we do not use the same training dataset for prediction, so to overcome this problem you may see some implementations of stacking where training dataset is splitted.

Below you can see a pseudocode where the training dataset is split before training the base algorithms:. In the bagging algorithm, the first step involves creating multiple models. These models are generated using the same algorithm with random sub-samples of the dataset which are drawn from the original dataset randomly with bootstrap sampling method. In bootstrap sampling, some original examples appear more than once and some original examples are not present in the sample. If you want to create a sub-dataset with m elements, you should select a random element from the original dataset m times.

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And if the goal is generating n dataset, you follow this step n times.For the same set of data, different algorithms behave differently. For example, if we want to predict the price of houses given for some dataset, some of the algorithms that can be used are Linear Regression and Decision Tree Regressor.

Both of these algorithms will interpret the dataset in different ways and thus make different predictions. One of the key distinctions is how much bias and variance they produce. There are 3 types of prediction error: bias, variance, and irreducible error. The other two types of errors, however, can be reduced because they stem from your algorithm choice.

High bias can cause an algorithm to miss the relevant relations between features and target outputs underfitting. Bias is an assumption made by a model to make the target function easier to learn. Models with high bias are less flexible and are not fully able to learn from the training data.

In the given figure, we use a linear model, such as linear regression, to learn from the model. As we can see, the regression line fails to fit the majority of the data points and thus, this model has high bias and low learning power. Generally, models with low bias are preferred. High variance can cause an algorithm to model the random noise in the training data, rather than the intended outputs overfitting. Variance defines the deviation in prediction when switching from one dataset to another.

In other words, it defines how much the predictions of a model will change from one dataset to another. It can also be defined as the amount that the estimate of the target function will change if different training data is used.

In the given figure, we can see a non-linear model such as SVR Support Vector Regressor tries to generate a polynomial function that passes through all the data points. This may seem like the perfect model, but such models are not able to generalize the data well and perform poorly on data that has not been seen before. Ideally, we want a model with low variance. But there seem to be tradeoffs between the bias and variance.

This is known as a bias-variance tradeoff. Hence when we decrease one, the other increases, and vice versa. The general principle of an ensemble method in Machine Learning to combine the predictions of several models.

These are built with a given learning algorithm in order to improve robustness over a single model. Ensemble methods can be divided into two groups:. Most ensemble methods use a single base learning algorithm to produce homogeneous base learners, i.

For example, Random forests Parallel ensemble method and Adaboost Sequential ensemble methods. Some methods use heterogeneous learners, i. This leads to heterogeneous ensembles. For ensemble methods to be more accurate than any of its members, the base learners have to be as accurate and as diverse as possible. In Scikit-learnthere is a model known as a voting classifier.

This is an example of heterogeneous learners.Selecting a machine learning algorithm for a predictive modeling problem involves evaluating many different models and model configurations using k-fold cross-validation.

The super learner is an ensemble machine learning algorithm that combines all of the models and model configurations that you might investigate for a predictive modeling problem and uses them to make a prediction as-good-as or better than any single model that you may have investigated. The super learner algorithm is an application of stacked generalizationcalled stacking or blending, to k-fold cross-validation where all models use the same k-fold splits of the data and a meta-model is fit on the out-of-fold predictions from each model.

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There are many hundreds of models to choose from for a predictive modeling problem; which one is best? These are open questions in applied machine learning.

The best answer we have at the moment is to use empirical experimentation to test and discover what works best for your dataset. In practice, it is generally impossible to know a priori which learner will perform best for a given prediction problem and data set.

This involves selecting many different algorithms that may be appropriate for your regression or classification problem and evaluating their performance on your dataset using a resampling technique, such as k-fold cross-validation. The algorithm that performs the best on your dataset according to k-fold cross-validation is then selected, fit on all available data, and you can then start using it to make predictions.

Consider that you have already fit many different algorithms on your dataset, and some algorithms have been evaluated many times with different configurations. You may have many tens or hundreds of different models of your problem. Why not use all those models instead of the best model from the group?

The super learner algorithm involves first pre-defining the k-fold split of your data, then evaluating all different algorithms and algorithm configurations on the same split of the data. All out-of-fold predictions are then kept and used to train a that learns how to best combine the predictions. The algorithms may differ in the subset of the covariates used, the basis functions, the loss functions, the searching algorithm, and the range of tuning parameters, among others.

The results of this model should be no worse than the best performing model evaluated during k-fold cross-validation and has the likelihood of performing better than any single model. The super learner is related to the stacking algorithm introduced in neural networks context …. The meta-model takes in predictions from base-models as input and predicts the target for the training dataset as output:.

For example, if we had 50 base-models, then one input sample would be a vector with 50 values, each value in the vector representing a prediction from one of the base-models for one sample of the training dataset.

If we had 1, examples rows in the training dataset and 50 models, then the input data for the meta-model would be 1, rows and 50 columns. The input to the meta-model is the out-of-fold out-of-sample predictions. By training a meta-model on out-of-sample predictions of other models, the meta-model learns how to both correct the out-of-sample predictions for each model and to best combine the out-of-sample predictions from multiple models; actually, it does both tasks at the same time.

Importantly, to get an idea of the true capability of the meta-model, it must be evaluated on new out-of-sample data. That is, data not used to train the base models. It can work just as well for classification predicting a class labelalthough it is probably best to predict probabilities to give the meta-model more granularity when combining predictions. Each base-model is fit on the entire training dataset so that the model can be used later to make predictions on new examples not seen during training.This comprehensive article serves as an important prequel to this post if you are a newbie or would just like to brush up the concepts of bias and variance before diving in with full force in the sea of Ensemble modelling.

All the others in the audience can readily move on to know more about Ensemble modelling from my pen. I will resort to quoting some real life examples to simplify the concepts of what,why and how of the ensemble models with focus on bagging and boosting techniques. Scenario 1: You require a new pair of headphones. You would browse a few web technology portals and check the user reviews and would then compare different models that interest you while checking for their features and prices.

You will also probably ask your friends and colleagues for their opinion. Now, can take a look at the technical definition of Ensemble learning methods. Ensemble models in machine learning combine the decisions from multiple models to improve the overall performance.

They operate on the similar idea as employed while buying headphones. The main causes of error in learning models are due to noise, bias and variance. Ensemble methods help to minimize these factors. These methods are designed to improve the stability and the accuracy of Machine Learning algorithms. Before making it public, you wish to receive critical feedback to close down the potential loopholes, if any.

You can resort to one of the following methods, read and decide which method is the best:. No brownie points for guessing the answer :D Yes, of course we will roll with the third option.

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Now, pause and think what you just did. You took multiple opinions from a large enough bunch of people and then made an informed decision based on them. This is what Ensemble methods also do. Each of them will have a different version as to how does an elephant looks like because each of them is exposed to a different part of the elephant. Now, if we give them a task of submitting a report on elephant description, their individual reports will be able to describe only one part accurately as per their experience but collectively they can combine their observations to give a very accurate report on the description of an elephant.

Similarly, ensemble learning methods employ a group of models where the combined result out of them is almost always better in terms of prediction accuracy as compared to using a single model. Ensembles are a divide and conquer approach used to improve performance.

MODE: The mode is a statistical term that refers to the most frequently occurring number found in a set of numbers. In this technique, multiple models are used to make predictions for each data point.

The predictions by each model are considered as a separate vote.

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The prediction which we get from the majority of the models is used as the final prediction. For instance: We can understand this by referring back to Scenario 2 above. I have inserted a chart below to demonstrate the ratings that the beta version of our health and fitness app got from the user community.

Consider each person as a different model. Taking the average of the results. In this technique, we take an average of predictions from all the models and use it to make the final prediction. Taking weighted average of the results. This is an extension of the averaging method. All models are assigned different weights defining the importance of each model for prediction. For instance, if about 25 of your responders are professional app developers, while others have no prior experience in this field, then the answers by these 25 people are given more importance as compared to the other people.

For example: For posterity, I am trimming down the scale of the example to 5 people. But, to use them you must select a base learner algorithm.In statistics and machine learningensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone.

Supervised learning algorithms perform the task of searching through a hypothesis space to find a suitable hypothesis that will make good predictions with a particular problem. Ensembles combine multiple hypotheses to form a hopefully better hypothesis.

The term ensemble is usually reserved for methods that generate multiple hypotheses using the same base learner. Evaluating the prediction of an ensemble typically requires more computation than evaluating the prediction of a single model. In one sense, ensemble learning may be thought of as a way to compensate for poor learning algorithms by performing a lot of extra computation. On the other hand, the alternative is to do a lot more learning on one non-ensemble system.

An ensemble system may be more efficient at improving overall accuracy for the same increase in compute, storage, or communication resources by using that increase on two or more methods, than would have been improved by increasing resource use for a single method.

Fast algorithms such as decision trees are commonly used in ensemble methods for example, random forestsalthough slower algorithms can benefit from ensemble techniques as well. By analogy, ensemble techniques have been used also in unsupervised learning scenarios, for example in consensus clustering or in anomaly detection.

An ensemble is itself a supervised learning algorithm, because it can be trained and then used to make predictions. The trained ensemble, therefore, represents a single hypothesis. This hypothesis, however, is not necessarily contained within the hypothesis space of the models from which it is built. Thus, ensembles can be shown to have more flexibility in the functions they can represent.

This flexibility can, in theory, enable them to over-fit the training data more than a single model would, but in practice, some ensemble techniques especially bagging tend to reduce problems related to over-fitting of the training data. Empirically, ensembles tend to yield better results when there is a significant diversity among the models. While the number of component classifiers of an ensemble has a great impact on the accuracy of prediction, there is a limited number of studies addressing this problem.

A priori determining of ensemble size and the volume and velocity of big data streams make this even more crucial for online ensemble classifiers. Mostly statistical tests were used for determining the proper number of components. More recently, a theoretical framework suggested that there is an ideal number of component classifiers for an ensemble such that having more or less than this number of classifiers would deteriorate the accuracy.

It is called "the law of diminishing returns in ensemble construction. The Bayes optimal classifier is a classification technique. It is an ensemble of all the hypotheses in the hypothesis space. On average, no other ensemble can outperform it. Each hypothesis is given a vote proportional to the likelihood that the training dataset would be sampled from a system if that hypothesis were true.

To facilitate training data of finite size, the vote of each hypothesis is also multiplied by the prior probability of that hypothesis. The Bayes optimal classifier can be expressed with the following equation:.This post was co-written with Baptiste Rocca.

The purpose of this post is to intr o duce various notions of ensemble learning.

## Ensemble methods: bagging, boosting and stacking

We will give the reader some necessary keys to well understand and use related methods and be able to design adapted solutions when needed. We will discuss some well known notions such as boostrapping, bagging, random forest, boosting, stacking and many others that are the basis of ensemble learning.

In order to make the link between all these methods as clear as possible, we will try to present them in a much broader and logical framework that, we hope, will be easier to understand and remember.

In the first section of this post we will present the notions of weak and strong learners and we will introduce three main ensemble learning methods: bagging, boosting and stacking. Then, in the second section we will be focused on bagging and we will discuss notions such that bootstrapping, bagging and random forests.

In the third section, we will present boosting and, in particular, its two most popular variants: adaptative boosting adaboost and gradient boosting. Finally in the fourth section we will give an overview of stacking. In machine learning, no matter if we are facing a classification or a regression problem, the choice of the model is extremely important to have any chance to obtain good results.

This choice can depend on many variables of the problem: quantity of data, dimensionality of the space, distribution hypothesis…. A low bias and a low variance, although they most often vary in opposite directions, are the two most fundamental features expected for a model.

### Ensemble learning

This is the well known bias-variance tradeoff. In ensemble learning theory, we call weak learners or base models models that can be used as building blocks for designing more complex models by combining several of them. Most of the time, these basics models perform not so well by themselves either because they have a high bias low degree of freedom models, for example or because they have too much variance to be robust high degree of freedom models, for example.

In order to set up an ensemble learning method, we first need to select our base models to be aggregated. Most of the time including in the well known bagging and boosting methods a single base learning algorithm is used so that we have homogeneous weak learners that are trained in different ways. One important point is that our choice of weak learners should be coherent with the way we aggregate these models.

If we choose base models with low bias but high variance, it should be with an aggregating method that tends to reduce variance whereas if we choose base models with low variance but high bias, it should be with an aggregating method that tends to reduce bias. This brings us to the question of how to combine these models. We can mention three major kinds of meta-algorithms that aims at combining weak learners:. Very roughly, we can say that bagging will mainly focus at getting an ensemble model with less variance than its components whereas boosting and stacking will mainly try to produce strong models less biased than their components even if variance can also be reduced.

In the following sections, we will present in details bagging and boosting that are a bit more widely used than stacking and will allow us to discuss some key notions of ensemble learning before giving a brief overview of stacking.

In parallel methods we fit the different considered learners independently from each others and, so, it is possible to train them concurrently. This statistical technique consists in generating samples of size B called bootstrap samples from an initial dataset of size N by randomly drawing with replacement B observations.

Under some assumptions, these samples have pretty good statistical properties : in first approximation, they can be seen as being drawn both directly from the true underlying and often unknown data distribution and independently from each others. So, they can be considered as representative and independent samples of the true data distribution almost i.

The hypothesis that have to be verified to make this approximation valid are twofold. First, the size N of the initial dataset should be large enough to capture most of the complexity of the underlying distribution so that sampling from the dataset is a good approximation of sampling from the real distribution representativity. Second, the size N of the dataset should be large enough compared to the size B of the bootstrap samples so that samples are not too much correlated independence.

Notice that in the following, we will sometimes make reference to these properties representativity and independence of bootstrap samples: the reader should always keep in mind that this is only an approximation.If a driver is replaced during the race then bets will stand on his replacement.

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