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Reading list

Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

Mean Squared Error: Definition and Formula

Ayushi Trivedi
Ayushi Trivedi 04 Jul, 2024
4 min read

Introduction

A basic idea in statistics and machine learning, mean squared error (MSE) is frequently used to gauge a model’s accuracy. It measures the variation between the values that a model predicts and the actual values. Due to its ease of use and efficiency in assessing model performance, MSE is frequently employed. We will study about mean squared error using examples in this article.

Overview

  • Learn how to define and express mean squared error mathematically.
  • Learn how to compute MSE for a set of variables that are actual and anticipated.
  • Acknowledge the MSE’s sensitivity to outliers and the ramifications for evaluating models.
  • MSE should be compared to other error metrics like Root Mean Squared Error and Mean Absolute Error.
  • Use the idea of MSE in real-world contexts like as forecasting, hyperparameter tuning, and model evaluation.

Table of contents

What is Mean Squared Error?

The mean squared error is the average of the squared differences between the expected and actual values. The mathematical notation for it is as follows:

Mean Squared Error: Overview, Examples, Concepts, and More

The squaring of errors ensures that positive and negative differences do not cancel each other out. Additionally, squaring emphasizes larger errors, making MSE sensitive to outliers.

Important Key Concepts

Let us learn important key concepts that are required for MSE.

Error Calculation

The error for each forecast is the difference between the expected and actual figures. This indicates how correct or inaccurate the prediction was, and it can be either positive or negative.

Averaging the Squared Errors

The sum of squared errors is divided by the number of observations to obtain the mean. This averaging ensures that MSE provides a measure of the average prediction error, scaled appropriately for the number of data points.

Sensitivity to Outliers

Because errors are squared before averaging, MSE is particularly sensitive to large errors. This means that models with occasional large errors will have a high MSE, reflecting poor performance.

Comparison with Other Metrics

  • Mean Absolute Error (MAE): Unlike MSE, MAE averages the absolute differences without squaring. While MAE is less sensitive to outliers, it doesn’t penalize large errors as heavily as MSE.
  • Root Mean Squared Error (RMSE): RMSE is the square root of MSE. It provides an error metric on the same scale as the original data, making it more interpretable.

Examples

We will now look into the examples of calculating MSE:

Example 1: Simple Linear Regression

Consider a simple linear regression model predicting house prices based on their size. Suppose we have the following data:

Actual Price ($) Predicted Price ($)
200,000 195,000
250,000 260,000
300,000 310,000
350,000 345,000
400,000 390,000

To calculate the MSE we need to go through certain steps.

Calculate the errors:

Mean Squared Error: Overview, Examples, Concepts, and More

Square the errors:

MSE

Sum the squared errors:

Mean Squared Error: Overview, Examples, Concepts, and More

Divide by the number of observations:

MSE

The MSE for this model is 70,000,000.

Example 2: Evaluating Multiple Models

Assume that the same data is predicted by two distinct models. The MSEs of Model A and Model B are 10,000 and 5,000, respectively. Model B is recommended since it has a lower MSE, which indicates reduced average prediction errors, even if both models seem to perform well.

Practical Applications

Let us explore some practical applications of mean squared error.

Model Evaluation

You frequently use MSE to assess how well regression models function. By comparing the mean square error (MSE) of various models, you can choose the model with the best prediction accuracy.

Hyperparameter Tuning

During model training, you can use MSE as a loss function to guide the optimization process. By minimizing MSE, you adjust the model parameters to reduce the average error.

Forecasting

In time series analysis, people use MSE to assess the accuracy of forecasts. Lower MSE values indicate more precise forecasts, which are essential for planning and decision-making.

Limitations

While MSE is a valuable metric, it has limitations:

  • Sensitivity to Outliers: MSE can be disproportionately affected by large errors.
  • Interpretability: Since MSE squares the errors, the units of MSE are the square of the original units, which can be less interpretable.

Conclusion

One important metric for evaluating the precision of predictive models is Mean Squared Error. It is a well-liked option for model comparison and evaluation due to its efficiency and simplicity. For a thorough analysis, one must take into account supplementary metrics like MAE and RMSE and be aware of its sensitivity to outliers. Understanding MSE and its ramifications enables improved model development and more precise predictions.

Frequently Asked Questions

Q1. What is MSE?

A. Mean Squared Error (MSE) is a metric used to measure the average of the squared differences between predicted and actual values in a dataset. It is commonly used to evaluate the accuracy of a model’s predictions.

Q2. Why is MSE sensitive to outliers?

A. MSE is sensitive to outliers because it squares the differences between predicted and actual values, which means larger errors have a disproportionately higher impact on the MSE value.

Q3. When should I use MSE over other error metrics?

A. People frequently use MSE in conjunction with other metrics like MAE and RMSE for a thorough assessment of model performance. It is a helpful tool for punishing greater errors, particularly in applications where large errors are undesirable.

beginnerserrorerrorsModelsoutliersPrediction
Ayushi Trivedi
Ayushi Trivedi 04 Jul, 2024

My name is Ayushi Trivedi. I am a B. Tech graduate. I have 3 years of experience working as an educator and content editor. I have worked with various python libraries, like numpy, pandas, seaborn, matplotlib, scikit, imblearn, linear regression and many more. I am also an author. My first book named #turning25 has been published and is available on amazon and flipkart. Here, I am technical content editor at Analytics Vidhya. I feel proud and happy to be AVian. I have a great team to work with. I love building the bridge between the technology and the learner.

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