Regression in machine learning (ML) is a fundamental concept used to predict continuous values based on input features. Whether estimating housing prices or forecasting sales, regression models establish relationships between variables. In this article, we’ll break down the different types of regression models, the algorithms behind them, and when each method is best applied. You’ll also discover how regression works, its practical use cases, and the advantages and challenges associated with using regression in machine learning.
Table of contents
- What is regression?
- Types of regression models
- Algorithms used for regression
- Examples of regression
- Benefits of regression
- Challenges of regression
What is regression in machine learning?
Regression is a type of supervised learning used to predict continuous values based on input data. It estimates the relationships between variables to predict and explain various things, such as house prices, stock market trends, or weather conditions. Regression models map input features to a continuous target variable, enabling precise numerical predictions.
For example, using weather data from the past week, a regression model can forecast tomorrow’s rainfall. The values it predicts are continuous, meaning they can fall anywhere on a numerical scale—such as temperature measured to decimal points or sales revenue projected for upcoming months.
Regression vs. classification: What’s the difference?
While regression predicts continuous outcomes, classification focuses on predicting discrete categories or classes. For example, a regression model might predict the exact amount of rainfall tomorrow, whereas a classification model might predict whether it will rain at all (yes or no). The key difference is that regression deals with numerical values, while classification assigns data to predefined categories.
In some cases, it’s possible to adapt the output of a regression model to a classification task and vice versa, but the two approaches are generally suited for different types of problems.
Regression: algorithm, model, or analysis?
Regression is sometimes referred to as regression analysis, a broad statistical term used to describe the search for continuous relationships between observations and outcomes. A regression algorithm is a specific mathematical tool designed to identify these relationships. When an algorithm is used to train a machine learning model, the result is called a regression model.
These three terms—regression analysis, regression algorithm, and regression model—are often used interchangeably, but they each represent a different aspect of the regression process.
Types of regression in machine learning
Regression models come in many forms, each designed to handle different relationships between input data and predicted outcomes. While linear regression is the most frequently used and relatively easy to understand, other models, like polynomial, logistic, and Bayesian regression, are better suited for more complex or specialized tasks. Below are some of the main types of regression models and when they’re typically used.
Simple and multiple (linear) regression
Linear regression, a popular regression technique, is known for its ease of interpretation, quick training, and reliable performance across various applications. It estimates the relationship between explanatory and target variables using straight lines. Simple linear regression involves one explanatory variable, whereas multiple linear regression involves two or more. Generally, when someone is discussing regression analysis, they mean linear regression.
Polynomial regression
If straight lines fail to explain the relationship between observed variables and expected results satisfactorily, a polynomial regression model might be a better option. This model seeks continuous, complex relationships and can identify patterns best described using curves or a combination of curves and straight lines.
Logistic regression
When the relationship between observations and the predicted values is not continuous (or discrete), logistic regression is the most common tool for the job. Discrete in this context means situations where fractions or real numbers aren’t as relevant (say, if predicting how many customers will walk into a coffee shop, logistic regression will answer 4 or 5 instead of something harder to interpret, like 4.35).
The most well-known form of logistic regression is binary regression, which predicts the answers to binary (i.e., yes/no) questions; typically, logistic regression is binary. More complex variations, such as multinomial regression, predict answers for questions that offer more than two choices. Logistic models, at their core, rely on selecting one of several functions to convert continuous inputs into discrete ones.
Bayesian regression
Linear and other regression techniques require substantial training data to make accurate predictions. In contrast, Bayesian regression is an advanced statistical algorithm that can make reliable predictions with less data, provided some of the data’s statistical properties are known or can be estimated. For example, predicting new product sales during the holiday season might be challenging for linear regression due to a lack of sales data for the new product. A Bayesian regression can predict sales data with higher accuracy by assuming the new product’s sales follow the same statistical distribution as the sales of other similar products. Typically, Bayesian regressions assume data follows a Gaussian statistical distribution, leading to the interchangeable use of the terms Bayesian and Gaussian regression.
Mixed effects regression
Regression assumes that there is a nonrandom relationship between the observed data and the predicted data. Sometimes, this relationship is difficult to define due to complex interdependencies in the observed data or occasional random behavior. Mixed-effects models are regression models that include mechanisms to handle random data and other behaviors that are challenging to model. These models are also referred to interchangeably as mixed, mixed-effects, or mixed-error models.
Other regression algorithms
Regression is very well studied. There are many other, more complex or specialized regression algorithms, including those that use binomial, multinomial, and advanced mixed-effects techniques, as well as those that combine multiple algorithms. Multiple algorithms combined may be organized in sequential order, such as in multiple sequential layers, or run in parallel and then aggregated in some way. A system that runs multiple models in parallel is often referred to as a forest.
Algorithms used for regression analysis
Many types of regression algorithms are used in machine learning to generate regression models. Some algorithms are designed to build specific types of models (in which case the algorithm and model often share the same name). Others focus on improving aspects of existing models, such as enhancing their accuracy or efficiency. We’ll cover some of the more commonly used algorithms below. Before we do that, though, it’s important to understand how they are evaluated: Generally, it’s based on two key properties, variance and bias.
- Variance measures how much a model’s predictions fluctuate when trained on different datasets. A model with high variance may fit the training data very closely but perform poorly on new, unseen data—a phenomenon known as overfitting. Ideally, regression algorithms should produce models with low variance, meaning they generalize well to new data and are not overly sensitive to changes in the training set.
- Bias refers to the error introduced by approximating a real-world problem, which may be too complex, with a simplified model. High bias can cause underfitting, where the model fails to capture important patterns in the data, leading to inaccurate predictions. Ideally, bias should be low, indicating that the model effectively captures the relationships in the data without oversimplifying. In some cases, bias can be mitigated by improving the training data or by adjusting the parameters of the regression algorithm.
Simple and multiple (linear) regression
Simple linear regression analyzes the relationship between a single explanatory variable and a predicted outcome, making it the simplest form of regression. Multiple linear regression is more complicated and finds relationships between two or more variables and one result. They both find relationships that have a linear structure, based on linear equations that generally fit this pattern:
y = β + β1x + ε
Here y is a result to predict, x is a variable to predict it from, ε is an error to attempt to minimize, and β and β1 are values the regression is calculating.
Linear regression uses a supervised learning process to build associations between explanatory variables and predicted results. The learning process examines the training data repeatedly, improving parameters for underlying linear equations with each iteration over the data. The most common methods for evaluating parameter performance involve calculating average error values for all available data used in testing or training. Examples of error calculation methods include mean squared error (the average of squared distances between predictions and actual results), mean absolute error, and more complex methods such as the residual sum of squares (the total errors rather than the average).
Polynomial regression
Polynomial regression handles more complex problems than linear regression and requires solving systems of linear equations, usually with advanced matrix operations. It can find relationships in the data that curve, not just ones that can be represented by straight lines. When applied correctly, it will reduce variance for problems in which linear regression fails. It is also more difficult to understand, implement, and optimize since it depends on advanced mathematical concepts and operations.
A polynomial regression will try to solve equations that relate y and multiple x’s with polynomial-shaped equations that follow this pattern:
y = β + β1x + β2x2 + … + ε
The polynomial regression algorithm will both be looking for the ideal β values to use and the shape of the polynomial (how many exponents of x might be needed to define the relationship between y and each x?).
Lasso regression
Lasso regression (which stands for least absolute shrinkage and selection operator), also known as lasso, L1, and L1 norm regression, is a technique used to reduce overfitting and improve model accuracy. It works by applying a penalty to the absolute values of the model coefficients, effectively shrinking, or reducing, some coefficients to zero. This leads to simpler models where irrelevant features are excluded. The lasso algorithm helps prevent overfitting by controlling model complexity, making the model more interpretable without sacrificing too much accuracy.
Lasso is especially useful when explanatory variables are correlated. For example, in weather prediction, temperature and humidity may be correlated, leading to overfitting. Lasso reduces the effect of such correlations, creating a more robust model.
Ridge regression
Ridge regression (also known as L2, L2 norm, or Tikhonov regularization) is another technique to prevent overfitting, especially when multicollinearity (correlation among explanatory variables) is present. Unlike lasso, which can shrink coefficients to zero, Ridge regression adds a penalty proportional to the square of the model coefficients. The goal is to make small adjustments to coefficients without completely removing variables.
Examples of regression use cases
Regression models are widely used across various industries to make predictions based on historical data. By identifying patterns and relationships between variables, these models can provide valuable insights for decision-making. Below are three well-known examples of areas where regression is applied.
Weather analysis and prediction
Regression analysis can predict weather patterns, such as the expected temperature and rainfall for each day next week. Often, several different regression algorithms are trained on historical weather data, including humidity, wind speed, atmospheric pressure, and cloud cover. Hourly or daily measurements of these variables serve as features for the model to learn from, and the algorithm is tasked with predicting temperature changes over time. When multiple regression algorithms (an ensemble) are used in parallel to predict weather patterns, their predictions are typically combined through a form of averaging, such as weighted averaging.
Forecasting sales and revenue
In a business context, regression models are frequently used to forecast revenue and other key performance metrics. A multiple regression model might take in variables that influence sales volume, such as metrics from marketing campaigns, customer feedback, and macroeconomic trends. The model is then tasked with predicting sales and revenue for a specified future period. As new data becomes available, the model may be retrained or updated to refine its predictions based on the latest observations.
Predicting healthcare outcomes
Regression models have numerous applications in predicting health outcomes. For instance, Bayesian models might be used to estimate incidence rate ratios by learning from historical patient data. These models help answer questions like “What is likely to happen if we adjust the dosage of a drug?” Linear regression can be employed to identify risk factors, such as predicting changes in a patient’s health based on lifestyle adjustments. Logistic regression, commonly used for diagnosis, calculates the odds ratio for the presence of a disease based on the patient’s medical history and other relevant variables.
Benefits of regression
Regression algorithms and models, particularly linear regression, are foundational components of many machine learning systems. They are widely used because of the following benefits:
- They can be fast. Regression techniques can quickly establish relationships between multiple variables (features) and a target value, making them useful for exploratory data analysis and speeding up the training of machine learning models.
- They are versatile. Many regression models, such as linear, polynomial, and logistic regression, are well studied and can be adapted to solve a wide range of real-world problems, from prediction to classification tasks.
- They can be easy to implement. Linear regression models, for example, can be implemented without requiring complex mathematical or engineering techniques, making them accessible to data scientists and engineers at various skill levels.
- They are easy to understand. Regression models, particularly linear regression, offer interpretable outputs where the relationships between variables and their impact on the predicted outcome are often clear. This makes them useful for identifying trends and patterns in data that can inform further, deeper analysis. In some cases, regression models can trade off interpretability for higher accuracy, depending on the use case.
Challenges in regression
While regression models offer many benefits, they also come with their own set of challenges. Often, these challenges will be reflected in reduced performance or generalizability, particularly when working with complex problems or limited data. Below are some of the most common issues faced in regression analysis.
- Overfitting: Models often struggle to balance bias and variance. If a model is too complex, it can fit the historical data very well (reducing variance) but become biased when exposed to new data. This is often because the model memorizes the training data instead of learning a generalized abstraction.
- Underfitting: A model that is too simple for the problem at hand can suffer from high bias. It will show high error rates on both the training data and unseen data, indicating that it has not learned the underlying patterns. Excessive adjustments to correct high bias can lead to underfitting, where the model fails to capture the complexities of the data.
- Complex training data: Regression models typically assume that the observations used for training are independent. If the data contains complex relationships or inherent randomness, the model may struggle to build accurate and reliable predictions.
- Incomplete or missing data: Supervised regression algorithms require large amounts of data to learn patterns and account for corner cases. When dealing with missing or incomplete data, the model may not perform well, particularly when learning complex relationships that require extensive data coverage.
- Predictor variable selection: Regression models rely on humans to select the right predictor variables (features). If too many irrelevant variables are included, model performance can degrade. Conversely, if too few or the wrong variables are chosen, the model may fail to accurately solve the problem or make reliable predictions.
