Overfitting and Underfitting With Machine Learning Algorithms

The cause of poor performance in machine learning is either overfitting or underfitting the data.

In this post, you will discover the concept of generalization in machine learning and the problems of overfitting and underfitting that go along with it.

Let’s get started.

Overfitting and Underfitting With Machine Learning Algorithms

Overfitting and Underfitting With Machine Learning Algorithms
Photo by Ian Carroll, some rights reserved.

Approximate a Target Function in Machine Learning

Supervised machine learning is best understood as approximating a target function (f) that maps input variables (X) to an output variable (Y).

Y = f(X)

This characterization describes the range of classification and prediction problems and the machine algorithms that can be used to address them.

An important consideration in learning the target function from the training data is how well the model generalizes to new data. Generalization is important because the data we collect is only a sample, it is incomplete and noisy.

Get your FREE Algorithms Mind Map

Machine Learning Algorithms Mind Map

Sample of the handy machine learning algorithms mind map.

I've created a handy mind map of 60+ algorithms organized by type.

Download it, print it and use it. 

Download For Free


Also get exclusive access to the machine learning algorithms email mini-course.

 

 

Generalization in Machine Learning

In machine learning we describe the learning of the target function from training data as inductive learning.

Induction refers to learning general concepts from specific examples which is exactly the problem that supervised machine learning problems aim to solve. This is different from deduction that is the other way around and seeks to learn specific concepts from general rules.

Generalization refers to how well the concepts learned by a machine learning model apply to specific examples not seen by the model when it was learning.

The goal of a good machine learning model is to generalize well from the training data to any data from the problem domain. This allows us to make predictions in the future on data the model has never seen.

There is a terminology used in machine learning when we talk about how well a machine learning model learns and generalizes to new data, namely overfitting and underfitting.

Overfitting and underfitting are the two biggest causes for poor performance of machine learning algorithms.

Statistical Fit

In statistics, a fit refers to how well you approximate a target function.

This is good terminology to use in machine learning, because supervised machine learning algorithms seek to approximate the unknown underlying mapping function for the output variables given the input variables.

Statistics often describe the goodness of fit which refers to measures used to estimate how well the approximation of the function matches the target function.

Some of these methods are useful in machine learning (e.g. calculating the residual errors), but some of these techniques assume we know the form of the target function we are approximating, which is not the case in machine learning.

If we knew the form of the target function, we would use it directly to make predictions, rather than trying to learn an approximation from samples of noisy training data.

Overfitting in Machine Learning

Overfitting refers to a model that models the training data too well.

Overfitting happens when a model learns the detail and noise in the training data to the extent that it negatively impacts the performance of the model on new data. This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize.

Overfitting is more likely with nonparametric and nonlinear models that have more flexibility when learning a target function. As such, many nonparametric machine learning algorithms also include parameters or techniques to limit and constrain how much detail the model learns.

For example, decision trees are a nonparametric machine learning algorithm that is very flexible and is subject to overfitting training data. This problem can be addressed by pruning a tree after it has learned in order to remove some of the detail it has picked up.

Underfitting in Machine Learning

Underfitting refers to a model that can neither model the training data nor generalize to new data.

An underfit machine learning model is not a suitable model and will be obvious as it will have poor performance on the training data.

Underfitting is often not discussed as it is easy to detect given a good performance metric. The remedy is to move on and try alternate machine learning algorithms. Nevertheless, it does provide a good contrast to the problem of overfitting.

A Good Fit in Machine Learning

Ideally, you want to select a model at the sweet spot between underfitting and overfitting.

This is the goal, but is very difficult to do in practice.

To understand this goal, we can look at the performance of a machine learning algorithm over time as it is learning a training data. We can plot both the skill on the training data and the skill on a test dataset we have held back from the training process.

Over time, as the algorithm learns, the error for the model on the training data goes down and so does the error on the test dataset. If we train for too long, the performance on the training dataset may continue to decrease because the model is overfitting and learning the irrelevant detail and noise in the training dataset. At the same time the error for the test set starts to rise again as the model’s ability to generalize decreases.

The sweet spot is the point just before the error on the test dataset starts to increase where the model has good skill on both the training dataset and the unseen test dataset.

You can perform this experiment with your favorite machine learning algorithms. This is often not useful technique in practice, because by choosing the stopping point for training using the skill on the test dataset it means that the testset is no longer “unseen” or a standalone objective measure. Some knowledge (a lot of useful knowledge) about that data has leaked into the training procedure.

There are two additional techniques you can use to help find the sweet spot in practice: resampling methods and a validation dataset.

How To Limit Overfitting

Both overfitting and underfitting can lead to poor model performance. But by far the most common problem in applied machine learning is overfitting.

Overfitting is such a problem because the evaluation of machine learning algorithms on training data is different from the evaluation we actually care the most about, namely how well the algorithm performs on unseen data.

There are two important techniques that you can use when evaluating machine learning algorithms to limit overfitting:

  1. Use a resampling technique to estimate model accuracy.
  2. Hold back a validation dataset.

The most popular resampling technique is k-fold cross validation. It allows you to train and test your model k-times on different subsets of training data and build up an estimate of the performance of a machine learning model on unseen data.

A validation dataset is simply a subset of your training data that you hold back from your machine learning algorithms until the very end of your project. After you have selected and tuned your machine learning algorithms on your training dataset you can evaluate the learned models on the validation dataset to get a final objective idea of how the models might perform on unseen data.

Using cross validation is a gold standard in applied machine learning for estimating model accuracy on unseen data. If you have the data, using a validation dataset is also an excellent practice.

Further Reading

This section lists some recommended resources if you are looking to learn more about generalization, overfitting and underfitting in machine learning.

Summary

In this post, you discovered that machine learning is solving problems by the method of induction.

You learned that generalization is a description of how well the concepts learned by a model apply to new data. Finally, you learned about the terminology of generalization in machine learning of overfitting and underfitting:

  • Overfitting: Good performance on the training data, poor generliazation to other data.
  • Underfitting: Poor performance on the training data and poor generalization to other data

Do you have any questions about overfitting, underfitting or this post? Leave a comment and ask your question and I will do my best to answer it.


Frustrated With Machine Learning Math?

Mater Machine Learning Algorithms

See How Algorithms Work in Minutes

…with just arithmetic and simple examples

Discover how in my new Ebook: Master Machine Learning Algorithms

It covers explanations and examples of 10 top algorithms, like:
Linear Regression, k-Nearest Neighbors, Support Vector Machines and much more…

Finally, Pull Back the Curtain on
Machine Learning Algorithms

Skip the Academics. Just Results.

Click to learn more.


52 Responses to Overfitting and Underfitting With Machine Learning Algorithms

  1. Kieron March 21, 2016 at 5:08 am #

    Loving the website Jason! We are currently looking at building a platform to connect data scientists and the like to companies http://www.kortx.co.uk

  2. Gary August 25, 2016 at 8:03 pm #

    Hi Jason,
    Are resampling and hold-out (the two options for limiting overfitting) mutually exclusive, or do they often get used together? Would using both render one of the techniques redundant?
    Thanks

    • Jason Brownlee August 26, 2016 at 10:32 am #

      Hi Gary,

      Typically you want to pick one method to estimate the performance of your algorithm. Generally, k-fold cross validation is the recommended method. Using two such approaches in conjunction does not really make sense, at least to me off the cuff.

  3. Bruno August 29, 2016 at 6:27 pm #

    Thank you Jason for these article,

    I applied you recipe quite successfully! Nevertheless, I remarked that cross validation does not prevent from overfitting.
    Depending on data and algorithm, it can be very easy to get low error rate using cross validation but overfitting.
    Did use saw that already ?

    This is the reason why I’m using two steps :
    1. compare means of train set score with test set score to check I do not overfit to much, and adjust algorithm parameters
    2. compute cross validation to get the general performance using previous parameters.

    Am I wrong while doing this procedure ?
    Many Thanks!

    • Jason Brownlee August 30, 2016 at 8:27 am #

      I agree Bruno, CV is a technique to reduce overfitting, but must be employed carefully (e.g. no of folds).

      The human is biased, so you also limit the number of human-in-the-loop iterations, because we will encourage the method to overfit, even with CV. Therefore it is also a good idea to hold back a validation dataset that is only evaluated once for final model selection.

      You procedure looks fine, consider adding a validation dataset for use after CV.

  4. Bruno September 5, 2016 at 6:43 pm #

    Jason, I can’t figure out how to use the validation set
    Do you use it to check for performance agreement/no overfiting with CV score ?

    Which score (and error) do you use as model performance : the one computed from the validation set or the one from the CV ?

    Thank a lot

    • Jason Brownlee September 6, 2016 at 9:46 am #

      Hi Bruno,

      I would suggest using the CV to estimate the skill of a model.

      I would further suggest that the validation dataset can be used as a smoke test. For example, the error should be within 2-3 standard deviations of the mean error estimate of the CV, e.g. “reasonable”.

      Finally, once you pick a model, you can go ahead and train it on all your training data and start using it to make predictions.

      I hope that helps.

  5. Bruno September 7, 2016 at 5:39 pm #

    Hi Jason,
    ‘got it!
    Many thanks for your clear answers and your time.

  6. Lijo November 2, 2016 at 7:23 am #

    Hi Jason,
    I was wondering why cant we use a validation dataset and then find the sweet spot by comparing our model with the training set and validation dataset, what are the disadvantages of using this procedure?

    • Jason Brownlee November 2, 2016 at 9:13 am #

      Hi Lijo,

      It’s hard. Your approach may work fine, but on some problems it may lead to overfitting. Experiment and see.

      The knowledge of how well the model does on the held out (invisible) validation set is being fed back into model selection, influencing the training process.

  7. Wan. November 18, 2016 at 11:43 am #

    my constant value is around 111.832 , is that called overfitting? I’m doing a logistic regression to predict malware detection with data traffic 5000 records, i did feature selection technique in rapid miner extracting 7 features out of 56 and do the statistical logistic regression in SPSS . three, significant feature selected out of 7, At last, I need to draw threshold graph where cut off is 80% from the probability value. like I said, my constant is high and performance 97%. please advise.

    • Jason Brownlee November 19, 2016 at 8:40 am #

      Hi Wan,

      Overfitting refers to learning the training dataset set so well that it costs you performance on new unseen data. That the model cannot generalize as well to new examples.

      You can evaluate this my evaluating your model on new data, or using resampling techniques like k-fold cross validation to estimate the performance on new data.

      Does that help?

  8. John January 27, 2017 at 9:42 pm #

    Great explanation, as always. If you feel like correcting a small typo:
    “Underfitting refers to a model that can neither model the training data **not** generalize to new data.” (I’m not a native English speaker but think it should be “nor”).

    • Jason Brownlee January 28, 2017 at 7:39 am #

      Thanks John, I fixed a few typos including the one you pointed out.

  9. Saqib Qamar May 1, 2017 at 5:28 pm #

    Hi Jason,
    Great tutorial regarding overfitting…

    Thanks a lot

  10. hang May 11, 2017 at 5:35 am #

    Is the solution to a XOR problem a overfit?

    It cannot be solved with 2 units, and one output?

    • Jason Brownlee May 11, 2017 at 8:35 am #

      Perhaps underfit – as in under-provisioned to be able to solve it. Or even ill-suited.

  11. machine_learner May 25, 2017 at 8:01 pm #

    Hi Jason, great article!

    So just to confirm, cross-validation doesn’t actually prevent overfitting, it’s just used to give you an idea of how well your model would perform on unseen data, and then you can modify the parameters to improve its performance? I.E. It’s just an evaluation technique

    Hope you reply in time as I got an exam on this! Cheers

  12. Yolower July 9, 2017 at 10:21 am #

    How do you solve underfitting?

  13. geekWolf August 29, 2017 at 1:13 am #

    Hello,

    In both OF and UF has poor performance on generalization. So, what is the solution to have a rich generalization ?

    Thank you.

    • Jason Brownlee August 29, 2017 at 5:08 pm #

      Careful tuning of your model 🙂

      There’s no silver bullet.

  14. Aniket Saxena November 7, 2017 at 2:01 am #

    What if my k-nearest neighbor classifier cause overfitting while making predictive model? How can i reduce overfitting in this case or more specifically, in classification problems? As wecan use regularization(ridge, lasso, elastic net) in case of regression problems to reduce overfitting, so can i use regularization in classification problems as well. Please help…..

  15. Aniket Saxena November 8, 2017 at 12:14 am #

    Thanks. I will check how it works and then i will get back to you with my results.

  16. Himanshu Chawla November 17, 2017 at 1:06 am #

    Hi Jason, Thanks for the wonderful article I have a small doubt..

    Do We perform cross validation with in subsets of training data or we do between training and test data..

    • Jason Brownlee November 17, 2017 at 9:26 am #

      Cross validation creates train/test sets multiple times to allow us to build and evaluate multiple models when making predictions on unseen data.

      • Himanshu Chawla November 17, 2017 at 9:17 pm #

        But those train/test datasets will be from training only

  17. Aakash January 2, 2018 at 5:43 am #

    Hi Jason,

    Your explanation of this is amazing and it truly helped me a lot. But I just have one question regarding the two important techniques we can use to limit overfitting.

    My question is that as the popular resampling technique to use is k-fold validation, what is the difference between this and bootstrapping?

    Looking forward to your answer,

    Thank You

    • Jason Brownlee January 2, 2018 at 3:58 pm #

      Bootstrapping draws random samples with replacement from a dataset whereas k-fold cross-valiation splits a dataset into non-overlapping subsets.

  18. Mohammad Ehtasham Billah February 7, 2018 at 8:44 am #

    Hi jason,
    Thanks for another great article!!
    Is it a good idea if a split data into 3 parts (training set, test set & validation set)? I will use the validation set only at the end of the project and use the test set sometimes to check whether the cross-validation accuracy matches the accuracy for the test set.

    How can I find out that the model I get after cross-validation is not overfitting? By immediately applying the model to the test set( not the final validation set)? I don’t want to wait until the end of the project to find out that my model is overfitting 🙂

    thanks

    • Jason Brownlee February 7, 2018 at 9:32 am #

      We can estimate the skill of the model with cross-validation, and confirm it with a held back test dataset.

      These are only estimates, we cannot know for sure whether we have over/underfit, but we work had to best robust estimates of model skill.

  19. Mohammad Ehtasham Billah February 7, 2018 at 8:54 am #

    How can I determine the no of folds i.e. k in K-fold cross-validation to avoid overfitting in the cross-validated model? Is there any rule of thumbs e.g. the ratio between the number of observations and K?

    Thanks

    • Jason Brownlee February 7, 2018 at 9:33 am #

      The number of samples in a fold should be representative of the broader dataset, if possible.

  20. Nil March 27, 2018 at 8:26 pm #

    Hi DR Jason,

    This is very good post. I have a question, if I have the following scores: accuracy on training 98%, accuracy on test 95% that means that I have overfitting problem in my model? or there a range of difference I have to consider that the is overfitting? I used K Fold CV and I am getting difference in scores of training and test.

    Best regards.

    • Jason Brownlee March 28, 2018 at 6:25 am #

      That is a good skill. I would stop there and start using the model.

      No need to post 100 times, I deleted the duplicates. All comments are moderated and will appear after I moderate them.

      • Nil March 30, 2018 at 1:08 am #

        Thank you DR. Jason,

        I apologize for the duplicates. I detected typing errors after send the question that is why I sent duplicated I was trying to correct. Next time I will make sure the text is well written before send.

        Maybe I misunderstood about overfitting because I understood that both the training and test accuracy must be equal or the test accuracy must be greater than the training accuracy. Because if the training accuracy is greater than test accuracy then the model has overfitted the training data.

        That made me confuse because when I train my model some times I get training accuracy of 95% and and test accuracy of 85% and so on depending on the shuffle and that differences make uncomfortable and without confidence that my model has learned enough. And I try to modify my programming code thinking that my code is not well written I and I never stop doing that until I find equal scores.

        Just to make sure If I find 95% of accuracy on training and 85% of accuracy on test I can’t be worried too? and I can use my model too? I understood the above answer but I need to make sure because I have two weeks now thinking my model is overfitting and trying to correct my code. And trying to find if there is an acceptable range of difference between accuracies to decide if the model has overfitted or no.

        Best regards.

        • Jason Brownlee March 30, 2018 at 6:40 am #

          Skill will never be identical on training and test, it is an ideal.

          Analysis of the learning curves can help to understand what might be going on. Sometimes nothing is going on – your model was fit and is good.

          • Nil March 30, 2018 at 11:29 pm #

            Understood,

            Thank you.

            Best Regards

  21. Michael April 7, 2018 at 7:34 pm #

    Hi,

    Thanks for a great post. I was just wondering if you have a academic source for

    “Overfitting is more likely with nonparametric models….”? Writing my thesis so would have to refer to something published

    Would you also agree that parametric models have a higher chance of underfitting the data as they put constraints on the target function?

    Thanks,

    Michael

    • Jason Brownlee April 8, 2018 at 6:20 am #

      Not offhand, Perhaps try some searches on google scholar and google books.

      Any good intro text on ml will say something similar.

  22. Farman May 5, 2018 at 1:56 am #

    Hi

    I have Two datasets i.e. S1 and S2 in my project. When I used 10-fold on S1, I get accuracy 92.34%, but I have also show results on S2 as testing(Independent) dataset. When I train my model on S1 and test on S2, I get results 74%, while existing methods accuracy is 86.43% on 10-fold and 80.65% on Independent test. How can I resolve my problem

  23. Nil May 9, 2018 at 6:08 pm #

    Hi DR Jason,

    Is there any reason to be worried when the training accuracy is less than the test accuracy?
    I am working on a Naive Bayes from scratch and I am getting 91.7% of accuracy on training set and 98.5% of accuracy on test set, and my doubt is if this results a acceptable because a I see the difference of scores is very high.

    Best regards.

    • Jason Brownlee May 10, 2018 at 6:26 am #

      Perhaps the test set is too small or not representative of the dataset?

      • Nil May 11, 2018 at 10:54 pm #

        Perhaps but I have 70 observations in training set and 394 observation on test set. And on data preparation I made my data binary 0 and 1 using a threshold. I am not using Naive Bayes for Gaussian distributed data, I am using Naive Bayes for categorical data.

Leave a Reply