# Machine Learning: Regression Algorithms

Every industrial sector aims to harness machine learning as an essential tool to foster modern automation and innovation. From stock price prediction and fraud detection to financial systems, machine learning algorithms have a wide range of applications. All these utilize algorithms to learn relationships within the data and make predictions based on patterns extracted from the dataset. These algorithms can be classified into supervised or unsupervised algorithms. Typically supervised algorithms comprise data with labels while unsupervised algorithms have unlabelled data.

In this article, we will discuss regression algorithms that are a part of supervised learning techniques. We will compare them with classification techniques and explore how they learn relationships within datasets.

## Understanding classification and regression

The goal of machine learning techniques is to make accurate predictions. Prediction is the process of identifying missing pieces from numerical data for new observations. Classification and regression techniques rely on a set of input features to make predicts but differ in the type of the output variable being predicted.

In classification, we have a set of predefined categories or classes that we want to assign to an input instance based on its features and attributes. These categories are finite and discrete, meaning that each input instance can belong to only one of them, so, there is no in-between. The accuracy of a classification algorithm depends on finding class designations correctly by projecting a set of input parameters onto the data.

For example, when classifying an email as spam or not spam based on its features, we could use classification based on input features such as subject lines, attachments, or addresses. The output would be a class label of either `spam` or `not spam`. Any email instance would fall under this category, so there is no in-between like a little bit spammy` or such cases. The accuracy would be defined by how a predictor can correctly “guess” the values based on new data and attributes.

In regression algorithms, we train a model to make predictions based on input features where output is a continuous numerical value that represents the target variable. The algorithm learns the relationship between input features and the target variable to make accurate predictions for new instances. Using the same spam email problem, regression would use labeled data to predict the likelihood of an email being spam or not spam rather than assigning class labels by using continuous probability such as the spam score. This makes regression models more flexible when the target variable is continuous and a precise or fine-grained estimate is needed. It is a common approach in fields like finance, stocks, and investment portfolios.

## Differences between classification and regression algorithms

– In regression, the output variable is a continuous or numerical value, while in classification, the output is categorical or discrete. This means that regression models are well-suited for predicting values within a range, while classification models focus on making predictions based on a class or output label.

– Regression algorithms aim to make estimates by mapping a function based on existing input parameters to improve accuracy on new data points. On the other hand, classification algorithms map an input variable with discrete output variables. This means that regression models aim to find the relationship between input and output variables in a continuous domain, while classification models aim to find decision boundaries that can separate the different classes.

– Regression models usually involve fitting a linear or nonlinear function to the data, such as a straight line or a polynomial curve, to predict the output variable. On the other hand, classification models use algorithms such as logistic regression, decision trees, or support vector machines to find the boundary between different classes. Additionally, classification algorithms can either be binary classifiers, which predict two classes, or multiclass classifiers, which predict more than two classes.

## Examples of machine learning regression algorithms

### Linear regression

Linear regression is a modeling approach that uses a straight line(the line of regression) to represent the relationship between a dependent variable and one or more independent variables. The line of regression is fitted among the data to predict new data points to find the optimal values for the feature weights that minimize prediction error. Simple linear regression involves two variables: an independent variable (X) that affects the dependent variable (Y) that is being predicted. The goal is to find the equation of a straight line that predicts the value of the independent variable with maximum accuracy or minimum error. This approach answers the question, “For a given value of X, what will be the predicted value of Y?”. It is widely used in fields such as economics, finance, marketing, and engineering.

#### Pros

• Linear regression is one of the simplest machine-learning algorithms to implement, even for beginners. With just a few lines of code, you can train a model for predicting a continuous output variable based on one or more input variables. This simplicity makes it a popular choice for small datasets and prototyping.
• Linear regression assumes a linear relationship between the input variables and the output variable thus simplifying results interpretation. This assumption simplifies the interpretation of results and how a change in certain input variables affects the output variable.
• Linear regression is a valuable tool for addressing overfitting by using regularization, cross-validation, and reduction techniques. This is particularly useful when working with noisy data or when the number of input variables is high. By improving the model’s ability to generalize, these techniques enhance its predictive power on unseen data. It’s straightforward and practical, making it a popular choice for many applications where interpretability and computational efficiency are essential, such as in financial modeling and risk analysis.

#### Cons

• Linear regression can be sensitive to outliers in the input variables, which can affect its performance. If not handled correctly, outliers can distort the line of best fit and lead to incorrect estimates, particularly when the data already has a high level of variability, such as in financial modeling.
• Most real-world problems are more complex than a simple linear relationship between input and output variables. Linear regression’s reliance on a linear approach can make it inefficient in cases where sophisticated or nonlinear relationships exist, limiting its practical use.

### Decision tree regression

Trees have wide applications in the computer science domain, including machine learning. The tree data structure consists of two primary components: nodes and branches. A decision tree is a hierarchical representation of a dataset and its attributes that guide decisions from the root to the leaf nodes. Decision trees are non-parametric, which means they predict the value of the target variable by learning the rules inferred from the data features, without making any assumptions about the underlying data distribution. Each node in a decision tree represents an attribute, and each branch represents a decision based on the attribute’s value. Decision trees are widely used in a variety of real-world applications that involve discretes sets of categorical values such as medical diagnosis, energy consumption prediction, and many more.

#### Pros

– Missing outliers and values have less impact on a decision tree data which simplifies the cleaning and preparation of data. The model further simplies this by generating insights with probabilities and alternative strategies for decision making.

– Decision trees can be used for both regression and classification tasks, and can model nonlinear relationships in complex data, making them a versatile tool for predictive modeling.

#### Cons

– Determining the appropriate depth of a decision tree can be challenging because it is difficult to determine the optimal level of granularity for each feature, and because deeper trees can easily overfit the data.

– Overfitting or over-complex trees that do not generalize data efficiently can be reduced in decision trees through techniques like tree-stopping and pruning, but these methods may not be effective in addressing complex and unseen scenarios making the resulting model unstable.

– Adding more training data to an existing decision tree can alter the entropy values, which are used to determine the optimal splits in the tree, and can therefore change the structure of the entire tree and affect its stability and accuracy. For instance, it might create a biased algorithm towards the dominant nodes, having larger values and features.

### Random forest regression

Random forest is a powerful meta-estimator that utilizes ensemble and bootstrapping techniques to make accurate predictions. In ensemble learning, multiple models are trained on the same data and their results are averaged to improve accuracy.

Random forest achieves this by fitting a number of decision trees on each subset of the data. The errors in each decision tree are independent of the others, which results in a more accurate prediction. Random forest models can extract relationships in both linear and non-linear features by randomly sampling subsets of the dataset over a given number of iterations, or by creating multiple random decision trees. When the results of the decision trees are aggregated, the prediction is much stronger and more accurate.

#### Pros

– Random forest is a versatile algorithm that can be used for both classification and regression problems. Because it is based on decision trees, it can handle input features with high dimensionality and noisy data.

– The ensemble technique used in random forest improves estimates by aggregating results from multiple decision trees. By doing so, it overcomes the limitations and errors of any individual tree. This aggregation is crucial to minimizing overfitting and bias in the model.

– Random forest considers every possible decision tree based on a dataset, allowing it to easily fill in missing pieces and maintain high accuracy.

#### Cons

– Random forest algorithms lack interpretability, making it difficult to understand how the model made its predictions. This is because it creates multiple decision trees with random subsets of the data, and the final prediction is an average of all the trees making it hard to identify which features were most important in making the final prediction.

– When a model becomes too complex, it can memorize the training data instead of generalizing to new data, leading to overfitting. Random Forest is prone to overfitting if it creates too many trees, which can cause its performance to degrade on new data. To address this, it is important to tune the hyperparameters such as the number of trees and maximum depth.

### Polynomial regression

In some cases, the relationship between variables may not be linear and can only be described by a nonlinear function. This is where polynomial regression comes in handy. By fitting a polynomial function to the data to capture the nonlinearity, polynomial regression is key in making an approximation of the relationship between variables.

#### Pros

– Polynomial regression can be used on datasets of any size, making it a flexible modeling technique for a wide range of applications.

– Polynomial regression can model non-linear relationships between variables, which is crucial in complex datasets. The polynomial function approximates the shape of the relationship between the variables more accurately while reducing the computational complexity.

#### Cons

– Polynomial regression models can be overly sensitive to outliers, which can significantly affect the accuracy of the analysis. Additionally, detecting outliers in nonlinear regression is challenging, and there are fewer model validation methods available which affect the degree of variance and bias.

### Lasso regression

Regression models with many predictors can suffer from overfitting, where the model becomes too complex and fits the noise in the data instead of the underlying relationships. Lasso regression, which denotes( Least Absolute shrinkage and selection operator) is a regularization technique used to prevent overfitting and improve feature selection and accuracy of predictions in high-dimensional regression problems.

In lasso regression, a penalty term that is proportional to absolute values and model’s coefficients is added to the cost function that the model is trying to minimize. By doing this, the algorithm shrinks the coefficients towards zero, effectively reducing the contribution of less important features in the model. This process results in feature selection and leads to a simpler and more interpretable model.

Lasso regression uses L1 regularization, which adds a penalty equal to the absolute value of the magnitude of the coefficients. This leads to sparse solutions where many of the coefficients are set to zero. The degree of regularization is controlled by a hyperparameter that can be tuned to achieve the desired balance between model complexity and accuracy.

#### Pros

– Lasso models uses the L1 penalty mechanism to prevent overfitting, which makes them more intuitive and less complex than other methods like Ridge regression.

– One of the main advantages of LASSO models is their ability to perform feature selection. During training, the Lasso algorithm shrinks the coefficients of the “less important” or “less interesting” features to zero, effectively removing them from the model. This reduces the number of features and hence improves model efficiency and selection of important parameters.

#### Cons

– The coefficients generated by Lasso models are biased because the L1 penalty shrinks the coefficients towards zero, which means that the true magnitude of the relationship between the features and the expected outcome may not be accurately represented.

– Lasso regression models may struggle with datasets that have many correlated features. The algorithm assumes that one feature set gets selected arbitrarily and others are dropped from the model. This introduces bias and estimation errors and makes the model unstable.

– Lasso regression relies on hyperparameter tuning to regulate the size of the L1 penalty, which adds complexity to the model. Choosing the right value for the L1 penalty can be a difficult task and requires expertise.

## Conclusion

Data fuels the field of machine learning while algorithms play critical role in mapping features and relationships. Modern development of machine learning workloads is however a complex one. With vast datasets, a need for model versioning and standards across large teams demands that businesses have to adopt a unified approach that helps them ship with speed and confidence. A common approach is implementing a feature store to provide a complete lifecycle when building data pipelines, training models, and scaling deployments in a centralized and automated workflow. Combining the power of algorithms such as regression and industry standards approach that guarantee accuracy and efficiency is a crucial step in driving positive business outcomes with cost efficiency, model performance and reusability feature engineering across multiple projects.