{ "source_file": "0930", "source_platform": "Medium", "author": "Serafeim Loukas, PhD", "title_listed": "Is your model overfitting? Or maybe underfitting? An example using a neural network in python", "keywords": "", "domain": "机器学习", "content_type": "深度技术解析", "is_paid_flag": "否", "url": "https://towardsdatascience.com/is-your-model-overfitting-or-maybe-underfitting-an-example-using-a-neural-network-in-python-4faf155398d2/", "publish_date": "2020-06-24", "corpus_stage": "", "notes": "", "id": "c7c613f5b7a5", "collected_at": "2026-10-02T08:22:13", "title": "Is your model overfitting? Or maybe underfitting? An example using a neural network in python | Towards Data Science", "body_markdown": "![Revisit consent button](../images/body-df29beacd7496220cc94.svg)\nWe value your privacy\nWe use cookies to enhance your browsing experience, serve personalised ads or content, and analyse our traffic. 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Or maybe underfitting? An example using a neural network in python\nOverfitting, underfitting, generalization ability, cross-validation. Everything simply explained. I also provide a python example using a...\n[Serafeim Loukas, PhD](https://towardsdatascience.com/author/seralouk/)\nJune 24, 20207 min read\n# Is your model overfitting? Or maybe underfitting? An example using a neural network\n### Overfitting, underfitting, generalization ability, cross-validation. Everything simply explained. I also provide a python example using a neural network.\n![Figure created by the author.](../images/002.png)\nFigure created by the author.\nLearn this step by step with the interactive [AI and Data Scientist](https://roadmap.sh/ai-data-scientist) and [Machine Learning](https://roadmap.sh/machine-learning) roadmaps.\n## 1. Introduction\nMost of the times, the cause of **poor** **performance** for a machine learning (ML) model is either **overfitting** or **underfitting.** A good model should be able to **generalize** and overcome both the overfitting and underfitting problems. **But what is overfitting? But what is underfitting? When does it mean for a model to be able to generalize the learned function/rule ?**\nRead on and you will be able to answer all these questions.\n* * *\n * **NEW** : After a great deal of hard work and staying behind the scenes for quite a while, we're excited to now offer our expertise through a platform, the \"[**Data Science Hub**](https://www.patreon.com/TheDataScienceHub\\))\" on Patreon (). This hub is our way of providing you with **bespoke consulting services** and comprehensive **responses to all your inquiries** , ranging from Machine Learning to strategic data analytics planning.\n\n\n* * *\n## 2. What is generalization in ML\n**Generalization** of a ML model refers to how **well** the rules/patterns/functions **learned** by the ML model, apply to specific examples **not seen by the model when it was learning**. This is usually called the **unseen** **set or** the **test** **set**.\nThe goal of a good ML model is to generalize well from the training data to any data that is coming from the problem's domain. **This allows the prediction of some data that the model has NEVER seen before (i.e. making prediction in the future).**\n* * *\nAnother resource. Learn Data Science and ML with the help of an 🤖 AI-powered tutor. Start here h[ttps://aigents.co/learn ](https://aigents.co/learn)choose a topic and he will show up where you need him. No paywall, no signups, no ads.\n* * *\n## 3. What is Overfitting in Machine Learning\n> Overfitting means that our ML model is modeling (has learned) the training data too well.\nFormally, **overfitting** referes to the situation where a model learns the data but also the noise that is part of **training data** to the extent that it **negatively** **impacts** the **performance** of the model on **new unseen data**.\nIn other worlds, the noise (i.e. random fluctuations) in the training set is learned as rules/pattenrs by the model. However, these noisy learned representations do not apply to new unseen data and thus, the model's performance (i.e. accuracy, MSE, MAE) is negatively impacted.\n_A textbook case of overfitting is when the_ _**model's error**_ _on the_ _**training**_ _set (i.e. during training) is_ _**very**_ _**low**_ _but then, the model's_ _**error**_ _on the_ _**test**_ _**set**_ _(i.e. unseen samples) is_ _**large**_ _!_\n* * *\n## 4. What is Underfitting in Machine Learning\n> Underfitting means that our ML model can neither model the training data nor generalize to new unseen data.\nA model that underfits the data will have poor performance on the training data. For example, in a scenario where someone would use a linear model to capture non-linear trends in the data, the model would underfit the data.\n_A textbook case of underfitting is when the model's error on_ _**both**_ _the_ _**training**_ _and_ _**test**_ _sets (i.e. during training and testing) is very high._\n## 5. The sweet spot and good models\nIt is obvious that there is a trade-off between overfitting and underfitting.\n> Ideally, a good model is a model that finds the sweet spot between underfitting and overfitting.\nWhich is the sweet spot?\n> The sweet spot is defined as the point where the model's error on the training set and the test (unseen) test set remain both low.\n> In other words, the sweet spot is the spot where the error on the test set starts to increase and, at the same time, the model's error on the training set is acceptable (low).\n## 6. How to (potentially) limit Overfitting\nThe most common problem in the ML learning filed is **overfitting**.\n**Action that could (potentially) limit overfitting:**\n 1. We can use a **Cross-validation** (CV) scheme.\n 2. **Reduce** the **complexity** of the model (make the model less complex).\n\n\n_When it comes to solution 1 i.e.__**the use of cross-validation**_ , the most famous CV scheme is the **KFolds** cross-validation. Using a KFolds scheme, we train and test your model k-times on different subsets of the training data and estimate a performance metric using the test (unseen) data. Other options include the Leave-_one_ -out cross-validation (**LOOCV**), the Leave-P-out cross-validation (**LpOCV**) and others.\n![KFold visually represented. Figure created by the author.](../images/001.png)\nKFold visually represented. Figure created by the author.\n_When it comes to solution 2 i.e.__**reducing the complexity of the model**_ can help reduce the overfitting. For example, if someone is using an SVM model with RBF kernel then reducing the complexity would mean to use a linear kernel. In another case, if someone is fitting a polynomial to some data, then reducing the complexity would mean to fit a linear model instead (linear regression).\n## 7. How to (potentially) limit Underfitting\nIn that case, there are 2 gold standard approaches:\n 1. Try another model\n 2. Increase the complexity of the current model\n\n\nSolution 1 is trivial. Concerning solution 2, an example an be the following: if someone is fitting a linear regression to some data, then **increasing** the **complexity** would mean to fit a polynomial model.\n## 8. Conclusions\n**Overfitting** **or underfitting** are the most common causes of **poor** **performance** for most machine learning (ML) models. Additionally, overfitting is more common than underfitting.\n * **Overfitting** is when the model's error on the training set (i.e. during training) is very low but then, the model's error on the test set (i.e. unseen samples) is large!\n * **Underfitting** is when the model's error on **both** the **training** and **test** sets (i.e. during training and testing) is very high.\n\n\nTo overcome these problems, **cross-validation** is usually used in order to estimate the model's performance on **unseen** data.\n## BONUS: Working example in Python\n### The dataset\nWe will use the Iris Dataset as we have done in all my previous posts. The dataset contains **four** **features** (length and width of sepals and petals) of **50** samples of **three** **species** of Iris (Iris **setosa** , Iris **virginica** and Iris **versicolor**).\n### The model\nWe will use **a multilayer perceptron** (MLP) [**regressor**](https://scikit-learn.org/stable/modules/generated/sklearn.neural_network.MLPRegressor.html). A MLP is a class of [feedforward](https://en.wikipedia.org/wiki/Feedforward_neural_network) [artificial neural network](https://en.wikipedia.org/wiki/Artificial_neural_network) (ANN). The term MLP is used ambiguously, sometimes loosely to _any_ feedforward ANN, sometimes strictly to refer to networks composed of multiple layers of [perceptrons](https://en.wikipedia.org/wiki/Perceptron).\ntext\n\n```\nfrom sklearn.neural_network import MLPRegressor \nfrom sklearn.metrics import mean_absolute_error\nimport numpy as np\nfrom sklearn.model_selection import validation_curve\nfrom sklearn.datasets import load_iris\nimport matplotlib.pyplot as plt\nfrom sklearn.model_selection import KFold\nnp.random.seed(0)\nplt.style.use('ggplot')\n```\n\nLet's load the **iris** **data** :\ntext\n\n```\niris = load_iris()\nX, y = iris.data, iris.target\n```\n\nWe will use **KFolds** **cross** -**validation** with 20 folds (**K=20)** to evaluate the **generalization** **ability** of our model. **Within each fold we will estimate the training and test error using the training and test sets, respectively.**\ntext\n\n```\nkf = KFold(n_splits=20)\nlist_training_error = []\nlist_testing_error = []\n```\n\ntext\n\n```\nfor train_index, test_index in kf.split(X):\n X_train, X_test = X[train_index], X[test_index]\n y_train, y_test = y[train_index], y[test_index]\n model = MLPRegressor()\n model.fit(X_train, y_train)\n y_train_data_pred = model.predict(X_train)\n y_test_data_pred = model.predict(X_test)\n```\n\ntext\n\n```\n fold_training_error = mean_absolute_error(y_train, y_train_data_pred) \n fold_testing_error = mean_absolute_error(y_test, y_test_data_pred)\n list_training_error.append(fold_training_error)\n list_testing_error.append(fold_testing_error)\n```\n\nPlot the MAE of the training phase and the MAE of the testing phase:\ntext\n\n```\nplt.subplot(1,2,1)\nplt.plot(range(1, kf.get_n_splits() + 1), np.array(list_training_error).ravel(), 'o-')\nplt.xlabel('number of fold')\nplt.ylabel('training error')\nplt.title('Training error across folds')\nplt.tight_layout()\n```\n\ntext\n\n```\nplt.subplot(1,2,2)\nplt.plot(range(1, kf.get_n_splits() + 1), np.array(list_testing_error).ravel(), 'o-')\nplt.xlabel('number of fold')\nplt.ylabel('testing error')\nplt.title('Testing error across folds')\nplt.tight_layout()\n```\n\ntext\n\n```\nplt.show()\n```\n\n![](../images/002.png)\nLet's now interpret the results and try to spot overfitting and underfitting points.\n**Reminder** :\n * Overfitting is when the model's error on the training set (i.e. during training) is very low but then, the model's error on the test set (i.e. unseen samples) is large!\n * Underfitting is when the model's error on both the training and test sets (i.e. during training and testing) is very high.\n\n\nAn **underfitting** point can be identified at fold number 10. During the 10th fold, the error on the training set and test set is at the same time high! So the model underfits the portion of the training data that are passed in for training in fold 10.\nAn **overfitting** point (not really extreme) can be seen at fold 20. The training MAE is around 0.16 and for the same fold the MAE on the test set is above 0.20.\n**Disclaimer** : These are not extreme cases of overfitting/underfitting but I just wanted to make my point and connect it with the theory I discussed in this article.\n* * *\nThat's all folks ! Hope you liked this article!\n* * *\n## Stay tuned & support this effort\nIf you liked and found this article useful, **follow** me to be able to see all my new posts.\nHere is my profile. Click on **Follow !**\n> [**Serafeim Loukas - Towards Data Science**](https://towardsdatascience.com/@seralouk)\nQuestions? Post them as a comment and I will reply as soon as possible.\n* * *\n## Latest posts\n> [**Time-Series Forecasting: Predicting Stock Prices Using Facebook's Prophet Model**](https://towardsdatascience.com/time-series-forecasting-predicting-stock-prices-using-facebooks-prophet-model-9ee1657132b5)\n> [**ROC Curve Explained using a COVID-19 hypothetical example: Binary & Multi-Class Classification...**](https://towardsdatascience.com/roc-curve-explained-using-a-covid-19-hypothetical-example-binary-multi-class-classification-bab188ea869c)\n> [**Support Vector Machines (SVM) clearly explained: A python tutorial for classification problems...**](https://towardsdatascience.com/support-vector-machines-svm-clearly-explained-a-python-tutorial-for-classification-problems-29c539f3ad8)\n> [**PCA clearly explained - How, when, why to use it and feature importance: A guide in Python**](https://towardsdatascience.com/pca-clearly-explained-how-when-why-to-use-it-and-feature-importance-a-guide-in-python-7c274582c37e)\n> [**Everything you need to know about Min-Max normalization in Python**](https://towardsdatascience.com/everything-you-need-to-know-about-min-max-normalization-in-python-b79592732b79)\n> [**How Scikit-Learn's StandardScaler works**](https://towardsdatascience.com/how-and-why-to-standardize-your-data-996926c2c832)\n* * *\n## Get in touch with me\n * **LinkedIn** : \n * **ResearchGate** : \n * **EPFL** **profile** : \n * **Stack** **Overflow** : \n\n\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. 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Or maybe underfitting? An example using a neural network in python\nOverfitting, underfitting, generalization ability, cross-validation. Everything simply explained. I also provide a python example using a...\n[Serafeim Loukas, PhD](https://towardsdatascience.com/author/seralouk/)\nJune 24, 20207 min read\n# Is your model overfitting? Or maybe underfitting? An example using a neural network\n### Overfitting, underfitting, generalization ability, cross-validation. Everything simply explained. I also provide a python example using a neural network.\n![Figure created by the author.](https://assets.insightmediagroup.io/media/wp-content/uploads/2020/06/1rNuI7uiadp5g_p6WRDZehQ.png)\nFigure created by the author.\nLearn this step by step with the interactive [AI and Data Scientist](https://roadmap.sh/ai-data-scientist) and [Machine Learning](https://roadmap.sh/machine-learning) roadmaps.\n## 1. Introduction\nMost of the times, the cause of **poor** **performance** for a machine learning (ML) model is either **overfitting** or **underfitting.** A good model should be able to **generalize** and overcome both the overfitting and underfitting problems. **But what is overfitting? But what is underfitting? When does it mean for a model to be able to generalize the learned function/rule ?**\nRead on and you will be able to answer all these questions.\n* * *\n * **NEW** : After a great deal of hard work and staying behind the scenes for quite a while, we're excited to now offer our expertise through a platform, the \"[**Data Science Hub**](https://www.patreon.com/TheDataScienceHub\\))\" on Patreon (). This hub is our way of providing you with **bespoke consulting services** and comprehensive **responses to all your inquiries** , ranging from Machine Learning to strategic data analytics planning.\n\n\n* * *\n## 2. What is generalization in ML\n**Generalization** of a ML model refers to how **well** the rules/patterns/functions **learned** by the ML model, apply to specific examples **not seen by the model when it was learning**. This is usually called the **unseen** **set or** the **test** **set**.\nThe goal of a good ML model is to generalize well from the training data to any data that is coming from the problem's domain. **This allows the prediction of some data that the model has NEVER seen before (i.e. making prediction in the future).**\n* * *\nAnother resource. Learn Data Science and ML with the help of an 🤖 AI-powered tutor. Start here h[ttps://aigents.co/learn ](https://aigents.co/learn)choose a topic and he will show up where you need him. No paywall, no signups, no ads.\n* * *\n## 3. What is Overfitting in Machine Learning\n> Overfitting means that our ML model is modeling (has learned) the training data too well.\nFormally, **overfitting** referes to the situation where a model learns the data but also the noise that is part of **training data** to the extent that it **negatively** **impacts** the **performance** of the model on **new unseen data**.\nIn other worlds, the noise (i.e. random fluctuations) in the training set is learned as rules/pattenrs by the model. However, these noisy learned representations do not apply to new unseen data and thus, the model's performance (i.e. accuracy, MSE, MAE) is negatively impacted.\n_A textbook case of overfitting is when the_ _**model's error**_ _on the_ _**training**_ _set (i.e. during training) is_ _**very**_ _**low**_ _but then, the model's_ _**error**_ _on the_ _**test**_ _**set**_ _(i.e. unseen samples) is_ _**large**_ _!_\n* * *\n## 4. What is Underfitting in Machine Learning\n> Underfitting means that our ML model can neither model the training data nor generalize to new unseen data.\nA model that underfits the data will have poor performance on the training data. For example, in a scenario where someone would use a linear model to capture non-linear trends in the data, the model would underfit the data.\n_A textbook case of underfitting is when the model's error on_ _**both**_ _the_ _**training**_ _and_ _**test**_ _sets (i.e. during training and testing) is very high._\n## 5. The sweet spot and good models\nIt is obvious that there is a trade-off between overfitting and underfitting.\n> Ideally, a good model is a model that finds the sweet spot between underfitting and overfitting.\nWhich is the sweet spot?\n> The sweet spot is defined as the point where the model's error on the training set and the test (unseen) test set remain both low.\n> In other words, the sweet spot is the spot where the error on the test set starts to increase and, at the same time, the model's error on the training set is acceptable (low).\n## 6. How to (potentially) limit Overfitting\nThe most common problem in the ML learning filed is **overfitting**.\n**Action that could (potentially) limit overfitting:**\n 1. We can use a **Cross-validation** (CV) scheme.\n 2. **Reduce** the **complexity** of the model (make the model less complex).\n\n\n_When it comes to solution 1 i.e.__**the use of cross-validation**_ , the most famous CV scheme is the **KFolds** cross-validation. Using a KFolds scheme, we train and test your model k-times on different subsets of the training data and estimate a performance metric using the test (unseen) data. Other options include the Leave-_one_ -out cross-validation (**LOOCV**), the Leave-P-out cross-validation (**LpOCV**) and others.\n![KFold visually represented. Figure created by the author.](https://assets.insightmediagroup.io/media/wp-content/uploads/2020/06/1Rpz58-KQdziQ-YXtpL1Kvg.png)\nKFold visually represented. Figure created by the author.\n_When it comes to solution 2 i.e.__**reducing the complexity of the model**_ can help reduce the overfitting. For example, if someone is using an SVM model with RBF kernel then reducing the complexity would mean to use a linear kernel. In another case, if someone is fitting a polynomial to some data, then reducing the complexity would mean to fit a linear model instead (linear regression).\n## 7. How to (potentially) limit Underfitting\nIn that case, there are 2 gold standard approaches:\n 1. Try another model\n 2. Increase the complexity of the current model\n\n\nSolution 1 is trivial. Concerning solution 2, an example an be the following: if someone is fitting a linear regression to some data, then **increasing** the **complexity** would mean to fit a polynomial model.\n## 8. Conclusions\n**Overfitting** **or underfitting** are the most common causes of **poor** **performance** for most machine learning (ML) models. Additionally, overfitting is more common than underfitting.\n * **Overfitting** is when the model's error on the training set (i.e. during training) is very low but then, the model's error on the test set (i.e. unseen samples) is large!\n * **Underfitting** is when the model's error on **both** the **training** and **test** sets (i.e. during training and testing) is very high.\n\n\nTo overcome these problems, **cross-validation** is usually used in order to estimate the model's performance on **unseen** data.\n## BONUS: Working example in Python\n### The dataset\nWe will use the Iris Dataset as we have done in all my previous posts. The dataset contains **four** **features** (length and width of sepals and petals) of **50** samples of **three** **species** of Iris (Iris **setosa** , Iris **virginica** and Iris **versicolor**).\n### The model\nWe will use **a multilayer perceptron** (MLP) [**regressor**](https://scikit-learn.org/stable/modules/generated/sklearn.neural_network.MLPRegressor.html). A MLP is a class of [feedforward](https://en.wikipedia.org/wiki/Feedforward_neural_network) [artificial neural network](https://en.wikipedia.org/wiki/Artificial_neural_network) (ANN). The term MLP is used ambiguously, sometimes loosely to _any_ feedforward ANN, sometimes strictly to refer to networks composed of multiple layers of [perceptrons](https://en.wikipedia.org/wiki/Perceptron).\ntext\n\n```\nfrom sklearn.neural_network import MLPRegressor \nfrom sklearn.metrics import mean_absolute_error\nimport numpy as np\nfrom sklearn.model_selection import validation_curve\nfrom sklearn.datasets import load_iris\nimport matplotlib.pyplot as plt\nfrom sklearn.model_selection import KFold\nnp.random.seed(0)\nplt.style.use('ggplot')\n```\n\nLet's load the **iris** **data** :\ntext\n\n```\niris = load_iris()\nX, y = iris.data, iris.target\n```\n\nWe will use **KFolds** **cross** -**validation** with 20 folds (**K=20)** to evaluate the **generalization** **ability** of our model. **Within each fold we will estimate the training and test error using the training and test sets, respectively.**\ntext\n\n```\nkf = KFold(n_splits=20)\nlist_training_error = []\nlist_testing_error = []\n```\n\ntext\n\n```\nfor train_index, test_index in kf.split(X):\n X_train, X_test = X[train_index], X[test_index]\n y_train, y_test = y[train_index], y[test_index]\n model = MLPRegressor()\n model.fit(X_train, y_train)\n y_train_data_pred = model.predict(X_train)\n y_test_data_pred = model.predict(X_test)\n```\n\ntext\n\n```\n fold_training_error = mean_absolute_error(y_train, y_train_data_pred) \n fold_testing_error = mean_absolute_error(y_test, y_test_data_pred)\n list_training_error.append(fold_training_error)\n list_testing_error.append(fold_testing_error)\n```\n\nPlot the MAE of the training phase and the MAE of the testing phase:\ntext\n\n```\nplt.subplot(1,2,1)\nplt.plot(range(1, kf.get_n_splits() + 1), np.array(list_training_error).ravel(), 'o-')\nplt.xlabel('number of fold')\nplt.ylabel('training error')\nplt.title('Training error across folds')\nplt.tight_layout()\n```\n\ntext\n\n```\nplt.subplot(1,2,2)\nplt.plot(range(1, kf.get_n_splits() + 1), np.array(list_testing_error).ravel(), 'o-')\nplt.xlabel('number of fold')\nplt.ylabel('testing error')\nplt.title('Testing error across folds')\nplt.tight_layout()\n```\n\ntext\n\n```\nplt.show()\n```\n\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2020/06/1rNuI7uiadp5g_p6WRDZehQ.png)\nLet's now interpret the results and try to spot overfitting and underfitting points.\n**Reminder** :\n * Overfitting is when the model's error on the training set (i.e. during training) is very low but then, the model's error on the test set (i.e. unseen samples) is large!\n * Underfitting is when the model's error on both the training and test sets (i.e. during training and testing) is very high.\n\n\nAn **underfitting** point can be identified at fold number 10. During the 10th fold, the error on the training set and test set is at the same time high! So the model underfits the portion of the training data that are passed in for training in fold 10.\nAn **overfitting** point (not really extreme) can be seen at fold 20. The training MAE is around 0.16 and for the same fold the MAE on the test set is above 0.20.\n**Disclaimer** : These are not extreme cases of overfitting/underfitting but I just wanted to make my point and connect it with the theory I discussed in this article.\n* * *\nThat's all folks ! Hope you liked this article!\n* * *\n## Stay tuned & support this effort\nIf you liked and found this article useful, **follow** me to be able to see all my new posts.\nHere is my profile. Click on **Follow !**\n> [**Serafeim Loukas - Towards Data Science**](https://towardsdatascience.com/@seralouk)\nQuestions? Post them as a comment and I will reply as soon as possible.\n* * *\n## Latest posts\n> [**Time-Series Forecasting: Predicting Stock Prices Using Facebook's Prophet Model**](https://towardsdatascience.com/time-series-forecasting-predicting-stock-prices-using-facebooks-prophet-model-9ee1657132b5)\n> [**ROC Curve Explained using a COVID-19 hypothetical example: Binary & Multi-Class Classification...**](https://towardsdatascience.com/roc-curve-explained-using-a-covid-19-hypothetical-example-binary-multi-class-classification-bab188ea869c)\n> [**Support Vector Machines (SVM) clearly explained: A python tutorial for classification problems...**](https://towardsdatascience.com/support-vector-machines-svm-clearly-explained-a-python-tutorial-for-classification-problems-29c539f3ad8)\n> [**PCA clearly explained - How, when, why to use it and feature importance: A guide in Python**](https://towardsdatascience.com/pca-clearly-explained-how-when-why-to-use-it-and-feature-importance-a-guide-in-python-7c274582c37e)\n> [**Everything you need to know about Min-Max normalization in Python**](https://towardsdatascience.com/everything-you-need-to-know-about-min-max-normalization-in-python-b79592732b79)\n> [**How Scikit-Learn's StandardScaler works**](https://towardsdatascience.com/how-and-why-to-standardize-your-data-996926c2c832)\n* * *\n## Get in touch with me\n * **LinkedIn** : \n * **ResearchGate** : \n * **EPFL** **profile** : \n * **Stack** **Overflow** : \n\n\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. 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