File Name: classification and regression by random forest .zip
Breiman a,b has recently developed an ensemble classification and regression approach that displayed outstanding performance with regard prediction error on a suite of benchmark datasets. That the exceptional performance is attained with seemingly only a single tuning parameter, to which sensitivity is minimal, makes the methodology all the more remarkable. The individual trees comprising the forest are all grown to maximal depth. While this helps with regard bias, there is the familiar tradeoff with variance.
Metrics details. The Random Forest RF algorithm for regression and classification has considerably gained popularity since its introduction in Meanwhile, it has grown to a standard classification approach competing with logistic regression in many innovation-friendly scientific fields.
In this context, we present a large scale benchmarking experiment based on real datasets comparing the prediction performance of the original version of RF with default parameters and LR as binary classification tools. Most importantly, the design of our benchmark experiment is inspired from clinical trial methodology, thus avoiding common pitfalls and major sources of biases.
The mean difference between RF and LR was 0. As a side-result of our benchmarking experiment, we observed that the results were noticeably dependent on the inclusion criteria used to select the example datasets, thus emphasizing the importance of clear statements regarding this dataset selection process. We also stress that neutral studies similar to ours, based on a high number of datasets and carefully designed, will be necessary in the future to evaluate further variants, implementations or parameters of random forests which may yield improved accuracy compared to the original version with default values.
In the context of low-dimensional data i. This is especially true in scientific fields such as medicine or psycho-social sciences where the focus is not only on prediction but also on explanation; see Shmueli [ 1 ] for a discussion of this distinction. Our experience as authors, reviewers and readers is that random forest can now be used routinely in many scientific fields without particular justification and without the audience strongly questioning this choice. While its use was in the early years limited to innovation-friendly scientists interested or experts in machine learning, random forests are now more and more well-known in various non-computational communities.
In this context, we believe that the performance of RF should be systematically investigated in a large-scale benchmarking experiment and compared to the current standard: logistic regression LR. We make the—admittedly somewhat controversial—choice to consider the standard version of RF only with default parameters — as implemented in the widely used R package randomForest [ 3 ] version 4.
Our experience from statistical consulting is that applied research practitioners tend to apply methods in their simplest form for different reasons including lack of time, lack of expertise and the critical requirement of many applied journals to keep data analysis as simple as possible. Currently, the simplest approach consists of running RF with default parameter values, since no unified and easy-to-use tuning approach has yet established itself.
We simply acknowledge that the standard variant with default values is widely used and conjecture that things will probably not dramatically change in the short term. That is why we made the choice to consider RF with default values as implemented in the very widely used package randomForest —while admitting that, if time and competence are available, more sophisticated strategies may often be preferable.
As an outlook, we also consider RF with parameters tuned using the recent package tuneRanger [ 4 ] in a small additional study. Comparison studies published in literature often include a large number of methods but a relatively small number of datasets [ 5 ], yielding an ill-posed problem as far as statistical interpretation of benchmarking results are concerned.
In the present paper we take an opposite approach: we focus on only two methods for the reasons outlined above but design our benchmarking experiments in such a way that it yields solid evidence. A particular strength of our study is that we as authors are equally familiar with both methods. Neutrality and equal expertise would be much more difficult if not impossible to ensure if several variants of RF including tuning strategies and logistic regression were included in the study.
Most importantly, the design of our benchmark experiment is inspired by the methodology of clinical trials that has been developed with huge efforts for several decades. We follow the line taken in our recent paper [ 11 ] and carefully define the design of our benchmark experiments including, beyond issues related to neutrality outlined above, considerations on sample size i.
As an important by-product of our study, we provide empirical insights into the importance of inclusion criteria for datasets in benchmarking experiments and general critical discussions on design issues and scientific practice in this context. The goal of our paper is thus two-fold. Firstly we aim to present solid evidence on the performance of standard logistic regression and random forests with default values.
Secondly, we demonstrate the design of a benchmark experiment inspired from clinical trial methodology. The rest of this paper is structured as follows. This section gives a short overview of the existing methods involved in our benchmarking experiments: logistic regression LR , random forest RF including variable importance measures, partial dependence plots, and performance evaluation by cross-validation using different performance measures.
Let Y denote the binary response variable of interest and X 1 ,…, X p the random variables considered as explaining variables, termed features in this paper. As for all model-based methods, the prediction performance of LR depends on whether the data follow the assumed model.
In contrast, the RF method presented in the next section does not rely on any model. When building each tree, at each split, only a given number mtry of randomly selected features are considered as candidates for splitting.
RF is usually considered a black-box algorithm, as gaining insight on a RF prediction rule is hard due to the large number of trees. In this study we use the package randomForest [ 3 ] version 4. This section presents the most important parameters for RF and their common default values as implemented in the R package randomForest [ 3 ] and considered in our study. Note, however, that alternative choices may yield better performance [ 16 , 17 ] and that parameter tuning for RF has to be further addressed in future research.
The parameter ntree denotes the number of trees in the forest. Strictly speaking, ntree is not a tuning parameter see [ 18 ] for more insight into this issue and should be in principle as large as possible so that each candidate feature has enough opportunities to be selected. In practice, however, performance reaches a plateau with a few hundreds of trees for most datasets [ 18 ]. The parameter mtry denotes the number of features randomly selected as candidate features at each split.
A low value increases the chance of selection of features with small effects, which may contribute to improved prediction performance in cases where they would otherwise be masked by features with large effects. A high value of mtry reduces the risk of having only non-informative candidate features. The parameter nodesize represents the minimum size of terminal nodes. Setting this number larger yields smaller trees. The default value is 1 for classification. The parameter replace refers to the resampling scheme used to randomly draw from the original dataset different samples on which the trees are grown.
The performance of RF is known to be relatively robust against parameter specifications: performance generally depends less on parameter values than for other machine learning algorithms [ 19 ]. However, noticeable improvements may be achieved in some cases [ 20 ]. As a byproduct of random forests, the built-in variable importance measures VIM rank the variables i. The so-called Gini VIM has shown to be strongly biased [ 14 ]. The second common VIM, called permutation-based VIM, is directly based on the accuracy of RF: it is computed as the mean difference over the ntree trees between the OOB errors before and after randomly permuting the values of the considered variable.
The underlying idea is that the permutation of an important feature is expected to decrease accuracy more strongly than the permutation of an unimportant variable. VIMs are not sufficient in capturing the patterns of dependency between features and response. They only reflect—in the form of a single number—the strength of this dependency.
Partial dependence plots can be used to address this shortcoming. They can essentially be applied to any prediction method but are particularly useful for black-box methods which in contrast to, say, generalized linear models yield less interpretable results. Partial dependence plots PDPs offer insight of any black box machine learning model, visualizing how each feature influences the prediction while averaging with respect to all the other features.
The PDP method was first developed for gradient boosting [ 12 ]. The partial dependence of F on feature X j is the expectation. As an illustration, we display in Fig. The data points are represented in the left column, while the PDPs are displayed in the right column for RF, logistic regression as well as the true logistic regression model i. We see that RF captures the dependence and non-linearity structures in cases 2 and 3, while logistic regression, as expected, is not able to.
Example of partial dependence plots. Plot of the PDP for the three simulated datasets. Each line is related to a dataset. On the left, visualization of the dataset. On the right, the partial dependence for the variable X 1. In a k -fold cross-validation CV , the original dataset is randomly partitioned into k subsets of approximately equal sizes.
The considered performance measure is computed based on the test set. After the k iterations, the performances are finally averaged over the iterations. In our study, we perform 10 repetitions of stratified 5-fold CV, as commonly recommended [ 21 ]. In the stratified version of the CV, the folds are chosen such that the class frequencies are approximately the same in all folds. The stratified version is chosen mainly to avoid problems with strongly imbalanced datasets occurring when all observations of a rare class are included in the same fold.
In our study, this procedure is applied to different performance measures outlined in the next subsection, for LR and RF successively and for M real datasets successively. The Brier score is a commonly and increasingly used performance measure [ 22 , 23 ]. It measures the deviation between true class and predicted probability and is estimated as.
So far we have stated that the benchmarking experiment uses a collection of M real datasets without further specifications.
In practice, one often uses already formatted datasets from public databases. Some of these databases offer a user-friendly interface and good documentation which facilitate to some extent the preliminary steps of the benchmarking experiment search for datasets, data download, preprocessing. One of the most well-known database is the UCI repository [ 24 ]. Specific scientific areas may have their own databases, such as ArrayExpress for molecular data from high-throughput experiments [ 25 ].
More recently, the OpenML database [ 26 ] has been initiated as an exchange platform allowing machine learning scientists to share their data and results. This database included as many as datasets in October when we selected datasets to initiate our study, a non-negligible proportion of which are relevant as example datasets for benchmarking classification methods.
When using a huge database of datasets, it becomes obvious that one has to define criteria for inclusion in the benchmarking experiment. Inclusion criteria in this context do not have any long tradition in computational science. The criteria used by researchers—including ourselves before the present study—to select datasets are most often completely non-transparent. It is often the fact that they select a number of datasets which were found to somehow fit the scope of the investigated methods, but without clear definition of this scope.
While the vast majority of researchers certainly do not cheat consciously, such practices may substantially introduce bias to the conclusion of a benchmarking experiment; see previous literature [ 27 ] for theoretical and empirical investigation of this problem. Independent of the problem of fishing for significance, it is important that the criteria for inclusion in the benchmarking experiment are clearly stated as recently discussed [ 11 ].
Such a modelling approach can be seen as a simple form of meta-learning —a well-known task in machine learning [ 29 ].
A similar approach using linear mixed models has been recently applied to the selection of an appropriate classification method in the context of high-dimensional gene expression data analysis [ 30 ]. Considering the potentially complex dependency patterns between response and features, we use RF as a prediction tool for this purpose. We refer to the previously published statistical framework [ 31 ] for a precise mathematical definition of the tested null-hypothesis in the case of the t-test for paired samples.
In this framework, the datasets play the role of the i. For large numbers and a two-sided test, the required number of datasets can be approximated as. Several R packages are used to implement the benchmarking study: mlr version 2.
Image classification. Machine learning. Error analysis. Ocean optics. Associative arrays.
Random forest is a type of supervised machine learning algorithm based on ensemble learning. Ensemble learning is a type of learning where you join different types of algorithms or same algorithm multiple times to form a more powerful prediction model. The random forest algorithm combines multiple algorithm of the same type i. The random forest algorithm can be used for both regression and classification tasks. As with any algorithm, there are advantages and disadvantages to using it. In the next two sections we'll take a look at the pros and cons of using random forest for classification and regression. Throughout the rest of this article we will see how Python's Scikit-Learn library can be used to implement the random forest algorithm to solve regression, as well as classification, problems.
Package 'randomForest'. March 25, Title Breiman and Cutler's Random Forests for Classification and. Regression. Version Date
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Random forest is an ensemble learning method used for classification, regression and other tasks. Random Forest builds a set of decision trees. Each tree is developed from a bootstrap sample from the training data. The final model is based on the majority vote from individually developed trees in the forest. For classification tasks, we use iris dataset. Connect it to Predictions. Finally, observe the predictions for the two models.
Metrics details. The Random Forest RF algorithm for regression and classification has considerably gained popularity since its introduction in Meanwhile, it has grown to a standard classification approach competing with logistic regression in many innovation-friendly scientific fields. In this context, we present a large scale benchmarking experiment based on real datasets comparing the prediction performance of the original version of RF with default parameters and LR as binary classification tools. Most importantly, the design of our benchmark experiment is inspired from clinical trial methodology, thus avoiding common pitfalls and major sources of biases. The mean difference between RF and LR was 0. As a side-result of our benchmarking experiment, we observed that the results were noticeably dependent on the inclusion criteria used to select the example datasets, thus emphasizing the importance of clear statements regarding this dataset selection process.
- Berkeley (statistics). “Classification & Regression Trees”. (with Friedman, Olshen, Stone). “Bagging”. “Random Forests”.
A random forest is an ensemble of a certain number of random trees, specified by the number of trees parameter. Each node of a tree represents a splitting rule for one specific Attribute. Only a sub-set of Attributes, specified with the subset ratio criterion, is considered for the splitting rule selection. This rule separates values in an optimal way for the selected parameter criterion. For classification the rule is separating values belonging to different classes, while for regression it separates them in order to reduce the error made by the estimation.
Multiple linear regression and random forest to predict and map soil properties using data from portable X-ray fluorescence spectrometer pXRF. The portable X-ray fluorescence spectrometer pXRF has been recently adopted to determine total chemical element contents in soils, allowing soil property inferences. However, these studies are still scarce in Brazil and other countries. The objectives of this work were to predict soil properties using pXRF data, comparing stepwise multiple linear regression SMLR and random forest RF methods, as well as mapping and validating soil properties.
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