Regression in ML (Gemini)
Machine Learning regression is a supervised learning technique used to predict a continuous numerical output (also known as the "dependent variable," "target," or "label") based on one or more "input features" (also called "independent variables" or "predictors").
Goal: The primary goal of a regression algorithm is to find a "best-fit line" or "curve" that accurately represents the relationship between the input features and the continuous output. This line/curve then allows the model to make predictions on new, unseen data.
Relationship between variables: Regression helps to understand how changes in the input features affect the continuous output.
Labeled Data: The bedrock of the entire process, providing the correct answers for the algorithm to learn from.
Input Features (X) and Output Labels (y): The defined variables the model works with.
A Regression Algorithm: The specific mathematical model and learning process chosen (e.g., linear regression, decision tree).
A Loss Function: A mathematical measure of how well the model is performing, which the algorithm tries to minimize.
An Optimization Algorithm: The method used to adjust the model's parameters to minimize the loss function (e.g., gradient descent).
Training and Testing: A systematic approach to learning from data and evaluating generalization performance.
Iterating through these steps a regression model learns to identify complex patterns and relationships within the data, enabling it to make accurate continuous predictions on new, real-world scenarios.
Common regression algorithms:
Linear Regression
Purpose: To model the linear relationship between a dependent continuous variable and one or more independent variables. It predicts a continuous numerical output.
Assumptions: Assumes a linear relationship, normally distributed errors, no multicollinearity, and homoscedasticity (constant variance of errors).
Example: Predicting house prices based on size, number of bedrooms, and location.
Polynomial Regression
Purpose: To model non-linear relationships between the independent variable(s) and the dependent continuous variable by fitting a polynomial equation.
Mechanism: It uses a linear model framework but incorporates polynomial features..
Example Use: Modeling the growth rate of a population over time, which might follow a curved path.
Logistic Regression
Purpose: Primarily a classification algorithm, despite "regression" in its name. It models the probability of a binary outcome (e.g., 0 or 1, Yes or No, True or False) using a logistic (sigmoid) function.
Mechanism: It takes a linear combination of inputs, similar to linear regression, but then squashes the result into a probability between 0 and 1 using the sigmoid function.
Example Use: Predicting whether an email is spam or not spam, classifying a tumor as malignant or benign, or predicting customer churn (leaving a service).
Ridge Regression
Purpose: A type of regularized linear regression that helps prevent overfitting, especially when dealing with multicollinearity (highly correlated independent variables) or a large number of features.
Lasso Regression (Least Absolute Shrinkage and Selection Operator)
Purpose: Another type of regularized linear regression that not only prevents overfitting but also performs feature selection.
Example Use: Identifying the most important features in a dataset for predicting a continuous outcome, or simplifying a model by reducing the number of predictors.
Elastic Net Regression
Purpose: Combines the penalties of both Ridge and Lasso regression. It's useful when there are multiple correlated features.
Example Use: When you suspect multicollinearity and also want to perform feature selection, often performing better than Lasso when there are groups of correlated variables.
Decision Tree Regression
Purpose: To model non-linear relationships and interactions by recursively splitting the data into subsets based on feature values, creating a tree-like structure. The prediction at each leaf node is typically the average of the target values in that node.
Mechanism: Works by partitioning the feature space into a set of rectangles, and then fitting a simple model (like a constant value) in each rectangle.
Example Use: Predicting patient recovery time based on various medical attributes, or estimating property value based on diverse features.
Random Forest Regression
Purpose: An ensemble learning method that improves upon single decision trees by building multiple decision trees during training and outputting the average of their individual predictions. This helps reduce overfitting and improve robustness.
Mechanism: Each tree in the forest is trained on a random subset of the data and a random subset of features.
Example Use: Highly effective for a wide range of regression problems, often providing high accuracy and good generalization.
Support Vector Regression (SVR)
Purpose: An extension of Support Vector Machines (SVMs) to handle regression problems. It aims to find a function that deviates from the true target value by a certain margin (epsilon) while also trying to keep the function as flat as possible.
Mechanism: Instead of minimizing the error, SVR minimizes the "epsilon-insensitive loss function," meaning errors within a certain margin are ignored.
Example Use: Time series forecasting, financial modeling, or any regression task where finding a robust fit is crucial.
This list covers some of the most common and important regression techniques, emphasizing Logistic Regression's role in classification despite its name.
Core Idea: Fitting a "Best-Fit" Line
The central concept of (linear) regression is to find the "best-fit" straight line (or a hyperplane in higher dimensions) that best represents the relationship between the input features and the output.
This line is essentially a mathematical equation that can then be used to predict new output values for given input values.
Feature Engineering: Creating new features from existing ones that might better capture the underlying relationships (e.g., combining "number of bathrooms" and "number of half-baths" into a single "total bathrooms" feature).