Supervised Learning - Regression & Regularization

This section covers the fundamentals of supervised learning through regression techniques, focusing on linear regression, gradient descent, evaluation metrics, and polynomial regression.

Linear & Polynomial Regression

This section introduces linear and polynomial regression, key supervised learning techniques used for predicting continuous values.

Linear Regression

This section provides an overview of linear regression, a fundamental supervised learning technique for modeling relationships between continuous variables.

Simple And Multiple Linear Regression

This section covers the principles of simple and multiple linear regression, focusing on the modeling of relationships between target and predictor variables.

Simple Linear Regression

Simple linear regression models the relationship between a single independent variable and a dependent variable to make predictions.

Mathematical Foundation (The Equation Of A Line)

This section covers the fundamental equation of simple linear regression, which models the relationship between a dependent and an independent variable.

Multiple Linear Regression

Multiple Linear Regression extends simple linear regression by using multiple independent variables to predict a dependent variable.

Mathematical Foundation (Generalizing The Line)

This section discusses the principles of multiple linear regression, expanding from simple linear regression to accommodate multiple independent variables.

Assumptions Of Linear Regression

The assumptions of linear regression ensure the validity and reliability of the model’s predictions and interpretations.

Gradient Descent

Gradient Descent is an iterative optimization algorithm used in machine learning to minimize the cost function by adjusting model parameters towards the minimum error.

Batch Gradient Descent

Batch Gradient Descent is an optimization algorithm that computes the gradient of the cost function using the entire training dataset to minimize error in predictions.

Stochastic Gradient Descent (Sgd)

Stochastic Gradient Descent (SGD) is an optimization algorithm used for minimizing the cost function in machine learning, particularly when dealing with large datasets.

Mini-Batch Gradient Descent

Mini-Batch Gradient Descent is an efficient optimization algorithm that combines the advantages of both Batch and Stochastic Gradient Descent, improving performance in training machine learning models.

Evaluation Metrics

Evaluation metrics are objective measures used to determine the performance of regression models by comparing predicted values against actual observed values.

Mean Squared Error (Mse)

Mean Squared Error (MSE) is an evaluation metric used to measure the performance of regression models by calculating the average of the squared differences between actual and predicted values.

Root Mean Squared Error (Rmse)

RMSE is a metric that measures the average magnitude of errors in predictions, offering a clearer interpretation by being in the same units as the original dependent variable.

Mean Absolute Error (Mae)

Mean Absolute Error (MAE) is a metric that evaluates the accuracy of a regression model by measuring the average magnitude of errors in a set of predictions, without considering their direction.

R-Squared (R²)

R-squared (R²) is a statistical measure that indicates the proportion of variance in the dependent variable explained by the independent variables in a regression model.

Polynomial Regression

Polynomial regression is an extension of linear regression that models non-linear relationships by introducing polynomial features.

Bias-Variance Trade-Off

The Bias-Variance Trade-off is a fundamental concept in machine learning that explains the relationship between model complexity and its ability to generalize to unseen data.

Bias

Bias refers to the systematic error introduced by a model's simplifying assumptions, making it less capable of accurately capturing the underlying data relationships.

Variance

Variance refers to the model's sensitivity to fluctuations in the training data, often leading to overfitting.

The Trade-Off

The Bias-Variance Trade-off balances model complexity against accuracy in predictive modeling, impacting generalization capabilities.

Lab: Implementing And Evaluating Various Regression Models, Including Polynomial Regression

This section explores practical implementations of linear and polynomial regression models, along with essential evaluation metrics and the Bias-Variance Trade-off.

Lab Objectives

This section outlines the objectives for a lab focused on regression analysis and model evaluation techniques.

Prepare Data For Regression

This section discusses the foundational steps required to prepare data for regression models in supervised learning.

Implement Simple Linear Regression

This section explains the fundamentals of simple linear regression, including its equation, components, application, and the process of optimizing the model.

Implement Multiple Linear Regression

Multiple Linear Regression extends simple linear regression by using multiple independent variables to predict a dependent variable.

Explore Gradient Descent

Gradient Descent is an essential optimization algorithm used to minimize the cost function in machine learning models, including linear regression.

Train And Predict

This section discusses the critical process of training machine learning regression models and making predictions, emphasizing the importance of evaluation metrics and the balance between bias and variance.

Master Evaluation Metrics

This section discusses the fundamental evaluation metrics used to assess the performance of regression models, including their mathematical formulation and interpretation.

Implement Polynomial Regression

Polynomial Regression extends linear regression by allowing for the modeling of non-linear relationships by incorporating polynomial features.

Analyze The Bias-Variance Trade-Off In Action

The Bias-Variance Trade-off explains the two key sources of error in machine learning models: bias and variance, highlighting the balance between the model's complexity and its ability to generalize to unseen data.

Model Visualization

Model visualization is key to understanding how predictions align with actual data, enabling clearer interpretations of regression models.