Decision trees can suffer from high variance which makes their results fragile to the specific training data used.
Building multiple models from samples of your training data, called bagging, can reduce this variance, but the trees are highly correlated.
Random Forest is an extension of bagging that in addition to building trees based on multiple samples of your training data, it also constrains the features that can be used to build the trees, forcing trees to be different. This, in turn, can give a lift in performance.
In this tutorial, you will discover how to implement the Random Forest algorithm from scratch in Python.
After completing this tutorial, you will know:
The difference between bagged decision trees and the random forest algorithm.
How to construct bagged decision trees with more variance.
How to apply the random forest algorithm to a predictive modeling problem.
Kick-start your project with my new bookMachine Learning Algorithms From Scratch, includingstep-by-step tutorials and thePython source code files for all examples.
Let’s get started.
Update Jan/2017: Changed the calculation of fold_size in cross_validation_split() to always be an integer. Fixes issues with Python 3.
Update Feb/2017: Fixed a bug in build_tree.
Update Aug/2017: Fixed a bug in Gini calculation, added the missing weighting of group Gini scores by group size (thanks Michael!).
Update Aug/2018: Tested and updated to work with Python 3.6.
How to Implement Random Forest From Scratch in Python Photo byInspireFate Photography, some rights reserved.
Description
This section provides a brief introduction to the Random Forest algorithm and the Sonar dataset used in this tutorial.
Random Forest Algorithm
Decision trees involve the greedy selection of the best split point from the dataset at each step.
This algorithm makes decision trees susceptible to high variance if they are not pruned. This high variance can be harnessed and reduced by creating multiple trees with different samples of the training dataset (different views of the problem) and combining their predictions. This approach is called bootstrap aggregation or bagging for short.
A limitation of bagging is that the same greedy algorithm is used to create each tree, meaning that it is likely that the same or very similar split points will be chosen in each tree making the different trees very similar (trees will be correlated). This, in turn, makes their predictions similar, mitigating the variance originally sought.
We can force the decision trees to be different by limiting the features (rows) that the greedy algorithm can evaluate at each split point when creating the tree. This is called the Random Forest algorithm.
Like bagging, multiple samples of the training dataset are taken and a different tree trained on each. The difference is that at each point a split is made in the data and added to the tree, only a fixed subset of attributes can be considered.
For classification problems, the type of problems we will look at in this tutorial, the number of attributes to be considered for the split is limited to the square root of the number of input features.
The result of this one small change are trees that are more different from each other (uncorrelated) resulting predictions that are more diverse and a combined prediction that often has better performance that single tree or bagging alone.
Sonar Dataset
The dataset we will use in this tutorial is the Sonar dataset.
This is a dataset that describes sonar chirp returns bouncing off different surfaces. The 60 input variables are the strength of the returns at different angles. It is a binary classification problem that requires a model to differentiate rocks from metal cylinders. There are 208 observations.
It is a well-understood dataset. All of the variables are continuous and generally in the range of 0 to 1. The output variable is a string “M” for mine and “R” for rock, which will need to be converted to integers 1 and 0.
By predicting the class with the most observations in the dataset (M or mines) the Zero Rule Algorithm can achieve an accuracy of 53%.
Download the dataset for free and place it in your working directory with the filenamesonar.all-data.csv.
Tutorial
This tutorial is broken down into 2 steps.
Calculating Splits.
Sonar Dataset Case Study.
These steps provide the foundation that you need to implement and apply the Random Forest algorithm to your own predictive modeling problems.
1. Calculating Splits
In a decision tree, split points are chosen by finding the attribute and the value of that attribute that results in the lowest cost.
For classification problems, this cost function is often the Gini index, that calculates the purity of the groups of data created by the split point. A Gini index of 0 is perfect purity where class values are perfectly separated into two groups, in the case of a two-class classification problem.
Finding the best split point in a decision tree involves evaluating the cost of each value in the training dataset for each input variable.
For bagging and random forest, this procedure is executed upon a sample of the training dataset, made with replacement. Sampling with replacement means that the same row may be chosen and added to the sample more than once.
We can update this procedure for Random Forest. Instead of enumerating all values for input attributes in search if the split with the lowest cost, we can create a sample of the input attributes to consider.
This sample of input attributes can be chosen randomly and without replacement, meaning that each input attribute needs only be considered once when looking for the split point with the lowest cost.
Below is a function nameget_split() that implements this procedure. It takes a dataset and a fixed number of input features from to evaluate as input arguments, where the dataset may be a sample of the actual training dataset.
The helper functiontest_split() is used to split the dataset by a candidate split point andgini_index() is used to evaluate the cost of a given split by the groups of rows created.
We can see that a list of features is created by randomly selecting feature indices and adding them to a list (calledfeatures), this list of features is then enumerated and specific values in the training dataset evaluated as split points.
Now that we know how a decision tree algorithm can be modified for use with the Random Forest algorithm, we can piece this together with an implementation of bagging and apply it to a real-world dataset.
2. Sonar Dataset Case Study
In this section, we will apply the Random Forest algorithm to the Sonar dataset.
The example assumes that a CSV copy of the dataset is in the current working directory with the file namesonar.all-data.csv.
The dataset is first loaded, the string values converted to numeric and the output column is converted from strings to the integer values of 0 and 1. This is achieved with helper functionsload_csv(),str_column_to_float() andstr_column_to_int() to load and prepare the dataset.
We will use k-fold cross validation to estimate the performance of the learned model on unseen data. This means that we will construct and evaluate k models and estimate the performance as the mean model error. Classification accuracy will be used to evaluate each model. These behaviors are provided in thecross_validation_split(),accuracy_metric() andevaluate_algorithm() helper functions.
We will also use an implementation of the Classification and Regression Trees (CART) algorithm adapted for bagging including the helper functionstest_split() to split a dataset into groups,gini_index() to evaluate a split point, our modifiedget_split() function discussed in the previous step,to_terminal(),split() andbuild_tree() used to create a single decision tree,predict() to make a prediction with a decision tree,subsample() to make a subsample of the training dataset andbagging_predict() to make a prediction with a list of decision trees.
A new function namerandom_forest() is developed that first creates a list of decision trees from subsamples of the training dataset and then uses them to make predictions.
As we stated above, the key difference between Random Forest and bagged decision trees is the one small change to the way that trees are created, here in theget_split() function.
The complete example is listed below.
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# Random Forest Algorithm on Sonar Dataset
fromrandomimportseed
fromrandomimportrandrange
fromcsvimportreader
frommathimportsqrt
# Load a CSV file
defload_csv(filename):
dataset=list()
withopen(filename,'r')asfile:
csv_reader=reader(file)
forrowincsv_reader:
ifnotrow:
continue
dataset.append(row)
returndataset
# Convert string column to float
defstr_column_to_float(dataset,column):
forrowindataset:
row[column]=float(row[column].strip())
# Convert string column to integer
defstr_column_to_int(dataset,column):
class_values=[row[column]forrowindataset]
unique=set(class_values)
lookup=dict()
fori,valueinenumerate(unique):
lookup[value]=i
forrowindataset:
row[column]=lookup[row[column]]
returnlookup
# Split a dataset into k folds
defcross_validation_split(dataset,n_folds):
dataset_split=list()
dataset_copy=list(dataset)
fold_size=int(len(dataset)/n_folds)
foriinrange(n_folds):
fold=list()
whilelen(fold)<fold_size:
index=randrange(len(dataset_copy))
fold.append(dataset_copy.pop(index))
dataset_split.append(fold)
returndataset_split
# Calculate accuracy percentage
defaccuracy_metric(actual,predicted):
correct=0
foriinrange(len(actual)):
ifactual[i]==predicted[i]:
correct+=1
returncorrect/float(len(actual))*100.0
# Evaluate an algorithm using a cross validation split
A k value of 5 was used for cross-validation, giving each fold 208/5 = 41.6 or just over 40 records to be evaluated upon each iteration.
Deep trees were constructed with a max depth of 10 and a minimum number of training rows at each node of 1. Samples of the training dataset were created with the same size as the original dataset, which is a default expectation for the Random Forest algorithm.
The number of features considered at each split point was set to sqrt(num_features) or sqrt(60)=7.74 rounded to 7 features.
A suite of 3 different numbers of trees were evaluated for comparison, showing the increasing skill as more trees are added.
Running the example prints the scores for each fold and mean score for each configuration.
This section lists extensions to this tutorial that you may be interested in exploring.
Algorithm Tuning. The configuration used in the tutorial was found with a little trial and error but was not optimized. Experiment with larger numbers of trees, different numbers of features and even different tree configurations to improve performance.
More Problems. Apply the technique to other classification problems and even adapt it for regression with a new cost function and a new method for combining the predictions from trees.
Did you try any of these extensions? Share your experiences in the comments below.
Review
In this tutorial, you discovered how to implement the Random Forest algorithm from scratch.
Specifically, you learned:
The difference between Random Forest and Bagged Decision Trees.
How to update the creation of decision trees to accommodate the Random Forest procedure.
How to apply the Random Forest algorithm to a real world predictive modeling problem.
Do you have any questions? Ask your questions in the comments below and I will do my best to answer.
Discover How to Code Algorithms From Scratch!
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It covers18 tutorials with all the code for12 top algorithms, like: Linear Regression, k-Nearest Neighbors, Stochastic Gradient Descent and much more...
Finally, Pull Back the Curtain on Machine Learning Algorithms
Hi Jason, Firstly, thanks for your work on this site – I’m finding it to be a great resource to start my exploration in python machine learning!
Now, I’m working through your python machine learning mini course and I’m up to Lesson 09: spot checking algorithms. You suggest testing the random forest which has lead me to this blog post where I’m tyring to run the recipe but get thrown the following:
Traceback (most recent call last): File “test.py”, line 203, in scores = evaluate_algorithm(dataset, random_forest, n_folds, max_depth, min_size, sample_size, n_trees, n_features) File “test.py”, line 57, in evaluate_algorithm folds = cross_validation_split(dataset, n_folds) File “test.py”, line 42, in cross_validation_split index = randrange(len(dataset_copy)) File “//anaconda/lib/python3.5/random.py”, line 186, in randrange raise ValueError(“empty range for randrange()”) ValueError: empty range for randrange()
I’ve spent the better part of the last hour trying to work out what I may be doing wrong.. unfortunately I’m really new to coding so I’m finding it very difficult. I think i’ve narrowed to the following possibilities: 1. possibly a problem with the evaluate_algorithm function that has been defined..? 2. possibly an issue using randrange in python 3.5.2? 3. possibly a problem with the definition of “dataset”?
I think it’s either #1 because I can run the code without issue up until line 202 or #3 because dataset is the common thread in each of the returned lines from the error..?
Hi Jason, I was able to get the code to run and got the results as posted on this page. My question what next? How do you use these results to make classification on new data?
Traceback (most recent call last): File “rf2.py”, line 203, in scores = evaluate_algorithm(dataset, random_forest, n_folds, max_depth, min_size, sample_size, n_trees, n_features) File “rf2.py”, line 68, in evaluate_algorithm predicted = algorithm(train_set, test_set, *args) File “rf2.py”, line 181, in random_forest tree = build_tree(sample, max_depth, min_size, n_features) File “rf2.py”, line 146, in build_tree split(root, max_depth, min_size, n_features, 1) File “rf2.py”, line 120, in split left, right = node[‘groups’] TypeError: ‘NoneType’ object is not iterable
Works in python 3.x also. The division in line 45 : fold_size = len(dataset) / n_folds renders a float which remains valid when length of dataset_copy goes to zero. randrange(0) gives this error.
Replacing this line with fold_size = len(dataset) // n_folds gives an integer and the loop executes properly
This was a fantastic tutorial thanks you for taking the time to do this! I was wondering if you had any suggestions for serialization or the tree for use against other similar data sets, would pickling working for this structure? Thanks for you help!
Hi Jason, great tutorial! Just a question about the function build_tree: when you evaluate the root of the tree, shouldn’t you use the train sample and not the whole dataset?
I mean:
root = get_split(train, n_features) rather than root = get_split(dataset, n_features)
Can I ask also what are the main differences of this algorithm if you want adapt it to a regression problem rather than classification?
Hello Jason great approach. I’m wondering if you have any tips about transforming the above code in order to support multi-label classification. Thank you very much !!!
Hello Jason, I like the approach that allows a person to ‘look under the hood’ of these machine learning methods. I look forward to learning more of the machine learning methods this way.
Random forest is completely new to me. I have a dataset that could use random forest regression. I would like to know what changes are needed to make random forest classification code (above) into random forest regression. This was asked earlier by Alessandro but I didn’t understand the reply. Random forest regression is not explained well as far as I can tell.
Thanks for the advice with random forest regression.
On the sonar dataset, I plotted a 60 x 60 correlation matrix from the data. Many of the successive rows, and even not so close rows, are highly correlated. For instance, row 17 and column 18 have the following correlation:
Number of Observations: 131 Number of Degrees of Freedom: 2
R-squared: 0.870 Rmse: 0.1046 F statistic 863.
and columns 14 and 15 have the correlation
Number of Observations: 131 Number of Degrees of Freedom: 2
R-squared: 0.8554 Rmse: 0.0708 F statistic 763.
What impact does this correlation have on the use of random forest? What can be done to remove or measure the effect of the correlation?
Also, for this dataset I was able to get the following results:
n_folds = 5 max_depth = 12 min_size = 1 sample_size = 0.75 for n_trees in [1, 5, 19]:
71.875%, 73.438%, 82.031%
Thanks for the great work. I am trying to absorb it all.
I don’t think RF is too affected by highly corrected features. Nevertheless, try removing some and see how it impacts model skill. I’d love to hear what you discover.
how did you find correlation and why would it create a problem.I am kinda new to this so I would like to know these things from experts like you.Thank you.
Hello Jason,thanks for awesome tutorial,can you please explain following things> 1.what is function of this line : row_copy[-1] = None : because it works perfectly without this line 2.When i tried n_trees=[3,5,10] it returned following result in which accuracy decreases with more trees> Trees: 3 Scores: [63.41463414634146, 51.21951219512195, 68.29268292682927, 68.29268292682927, 63.41463414634146] Mean Accuracy: 62.927% Trees: 5 Scores: [65.85365853658537, 60.97560975609756, 60.97560975609756, 60.97560975609756, 58.536585365853654] Mean Accuracy: 61.463% Trees: 10 Scores: [48.78048780487805, 60.97560975609756, 58.536585365853654, 70.73170731707317, 53.65853658536586] Mean Accuracy: 58.537%
test_split has return two values but here groups = test_split(index, row[index], dataset) just one variable, can anyone explain that, please, thanks a lot
Hi Jason, I am trying to learn RF through your sample example. But while running the code I am getting an error. I am using Ipython Notebook.
in split(node, max_depth, min_size, n_features, depth) 6 # Create child splits for a node or make terminal 7 def split(node, max_depth, min_size, n_features, depth): —-> 8 left, right = node[‘groups’] 9 del(node[‘groups’]) 10 # check for a no split
in split(node, max_depth, min_size, n_features, depth) 6 # Create child splits for a node or make terminal 7 def split(node, max_depth, min_size, n_features, depth): —-> 8 left, right = node[‘groups’] 9 del(node[‘groups’]) 10 # check for a no split
Hello, Jason Thank you very much for your lessons. You code worked perfectly. Now I am trying to use different dataset, which has also string values. And having difficulty with it. Is it even possible? I keep getting errors that cannot convert string to integer.
Hi Jason, your implementation helps me a lot! However, I have a question here: on each split, the algorithm randomly selects a subset of features from the total features and then pick the best feature with the best gini score. Then, is it possible for a tree that a single feature is used repeatedly during different splits? since in get_split(), the line index = randrange(len(dataset[0])-1) basically pick features from the whole pool. Could you explain this? Thanks!
RandomForestClassifier(bootstrap=True, class_weight=None, criterion=’gini’, max_depth=None, max_features=’auto’, max_leaf_nodes=None, min_impurity_split=1e-07, min_samples_leaf=1, min_samples_split=2, min_weight_fraction_leaf=0.0, n_estimators=10, n_jobs=1, oob_score=False, random_state=None, verbose=0, warm_start=False) I tried using number of trees =1,5,10 as per your example but not working could you pls say me where shld i need to make changes and moreover when i set randomstate = none each time i execute my accuracy keeps on changing but when i set a value for the random state giving me same accuracy.
Hi, I would like to change the code so it will work for 90% of data for train and 10% for test, with no folds. If I use n_folds = 1, I get an error. How can I change the code so it will work?
Thanks a lot. I would like to use your code since I made another internal change of the algorithm that can’t be done using scikit-learn. I think the major (may be the only) change is in the evaluate_algorithm function.
Can we implement random forest using fitctree in matlab?
There is a function call TreeBagger that can implement random forest. However, if we use this function, we have no control on each individual tree. Can we use the MATLAB function fitctree, which build a decision tree, to implement random forest? Thanks a lot.
I am trying to solve classification problem using RF, and each time I run RandomForestClassifier on my training data, feature importance shows different features everytime I run it. How can I make sure it gives me same top 5 features everytime I run the model ? Please let me know.
I would like to know the difference between sklearn randomforest and random forest algorithm implemented by oneself. Is there any weakness or something in sklearn randomforest?
Thanks for sharing! I wonder how fast is your implementation. (I guess I should try it out myself. 🙂
I was a master student in biostatistics and doing a thesis project which applied a modified random forest (no existing implementation) to solve a problem. I was and still I am only comfortable with R. I implemented the modified random forest from scratch in R. Although I tried hard to improve my code and implement some parts in C++ (via Rcpp package), it was still so slow… I noticed random forests packages in R or Python were all calling codes writing in C at its core.
So, would you mind estimate how fast is your implementation comparing to mainstream implementation (e.g. 10 times slower than Scikit-learn) ? I am new to Python. I should really try it myself but just can’t help ask for a quick answer for this to inspire me to learn Python! 🙂
I am new to python and doing a mini project for self learning. It will be helpful if you guide that how can I use this algorithm to predict the class of some test data.
Hi Jason, I might send another message but I am not sure if it had sent or not. I just wanted to say thank you for your informative website. this post was also and very comprehensive with full of integrated ideas and topics. If the python project is available I would appreciate if you send it.
Kudos for the good work sir, I have a quick question sir. How long did it take you to write such a wonderful piece of code up and what are the resources you used to help you sir? Thank you sir and kind regards.
hi, very nice explanation! but I am thinking what if I create a random forest from a dataset and then pass a single document to test it. what will be the method to pass a single document in the clf of random forest?
HI Jason, This is a great tutorial. I’ve been working on a random forest project in R and have been reading alot about using this method. I’m confused because some articles note that RF will NOT overfit, yet there seems to be a constant discussion about overfitting with RF in stackoverflow. Do RF models overfit? My second question pertains to the Gini decrease scores–are these impacted by correlated variables ? (I know RF handles correlated predictor variables fairly well). Final question– if using CV in caret, is train/test sample necessary? I have a very unbalanced outcome classifier and not a ton of data, so I didn’t want to split it further, unless absolutely necessary. Thank you!
i have ten variables one dependent and nine independent first i will take sample of independent then random sample of observation and after that of preductive model
I am running your code with python 3.7 in Spyder but I have this error : “left, right = node[‘groups’] TypeError: cannot unpack non-iterable NoneType object”.
Hello Dr. Jason, Thanks so much for this wonderful website and the amazing work you do over here. I went through your tutorial and had the same accuracy as found in it the tutorial. I realized that the attributes are selected with replacement so I made the modification and applied cross entropy loss for n_trees = [1, 5, 10, 15, 20]. I had the following accuracy metrics:
it looks like I wrote a comment to not proper article before 🙂
I am inspired and wrote the python random forest classifier from this site. I go one more step further and decided to implement Adaptive Random Forest algorithm. But I faced with many issues. I implemented the window, where I store examples. But unfortunately, I am unable to perform the classification. I cannot translate the learning step to be a little adaptive. I’m stuck.
Could you give me some advices, examples, how to overcome this issues ?
Could you explain me how is it possible, that every time I am running your script I always receive the same scores ? This means that in fact we do not implement random mechanism.
I need to print the predicted data set. But while printing, it is returning only the class value. I want to print the data with predicted class values “M” for mine and “R” for rock. I need the result as :
As I know, the tree should continue to make splits until either the max_depth is reached or the left observations are completely pure. But this code makes split even if the node is already pure (gini = 0), meaning that it makes leaves from the same node which both have class value zero, which is not feasible.
To make more clear: if you give to get_split() some number of rows with the same class values, it still makes a split, although it is already pure.
Should we add this condition to the get_split() function or did I understand something wrong?
How would the Random Forest Classifier from SKlearn perform in the same situation?
Given the 208 rows of the sonar dataset applied to the cross_validation_split function we only consider the first 205 rows of the given dataset, so the last 3 rows are simply ignored. Is this on purpose?
I understand your reasoning but that has the price of loosing the information given by those extra three rows. Isn‘t that bad?
What is the benefit of having all folds of the same size? I changed the code of that function accordingly and obviously got different accuracies than the ones you have got.
To my understanding to calculate the gini index for a given feature, first we need to iterate over ALL the rows and considering the value of that feature by the given row and add entries to the groups and KEEP them until we have processed all the rows of the dataset. Only now we can go ahead and calculate the gini index for that given feature.
However looking at the get_split function that doesn’t seem to be the case as we calculate the gini index on a single row basis at each step.
Sir, I tried this code for my dataset, it gives accuracy of 86.6%. How to predict for unlabeled data? yhat = model.predict(X). For this statement which will be ‘model’. Fit and predict methods are showing error. Can you please give some suggestions, since I am beginner to object-oriented concepts.
I’m wondering if you had any posts related to non-stationary inputs in a random forest.
I’m working on a project with non-stationary data and have found out that my random forest model from Scikit-learn is more accurate in the predictions when I use the non-stationary data directly as an input than when I difference it to achieve stationarity, so I would like to see how random forest deals with non-stationarity.
Hello Thanks for the awesome post I am running into an error, when running with my new data, but works well for your data. the error is ————————————————————————— IndexError Traceback (most recent call last) in 1 for n_trees in [1,5,10]: —-> 2 scores = evaluate_algorithm(data, random_forest, n_folds, max_depth, min_size, sample_size,n_trees,n_features) 3 print(‘Trees: %d’ % n_trees) 4 print(‘Scores: %s’ % scores) 5 print(‘Mean accuracy: %.3f%%’ % (sum(scores)/float(len(scores))))
in evaluate_algorithm(dataset, algorithm, n_folds, *args) 60 test_set.append(row_copy) 61 row_copy[-1] = None —> 62 predicted = algorithm(train_set, test_set, *args) 63 actual = [row[-1] for row in fold] 64 accuracy = accuracy_metric(actual, predicted)
in random_forest(train, test, max_depth, min_size, sample_size, n_trees, n_features) 181 for i in range(n_trees): 182 sample = subsample(train, sample_size) –> 183 tree = build_tree(sample, max_depth, min_size, n_features) 184 trees.append(tree) 185 predictions = [bagging_predict(trees, row) for row in test]
in get_split(dataset, n_features) 102 features = list() 103 while len(features) 104 index = randrange(len(dataset[0])-1) 105 if index not in features: 106 features.append(index)
IndexError: list index out of range
Any help would be very very helpful, thanks in advance
