Machine Learning Mastery (Integrated Theory+Practical HW)

Explore correlation analysis to measure the strength and direction of relationships between two variables using scatter plots and the correlation coefficient, distinguishing positive, negative, and non-linear patterns.

Explore how correlation analysis measures linear relationships using the correlation coefficient from -1 to 1, identifying strong positive, strong negative, and near-zero (weak) relationships, and distinguishing linear from non-linear patterns.

Learn how linear regression models the positive relationship between square feet and price. Build a best-fit line to predict house prices from size using supervised learning.

Learn how linear regression uses the equation y = theta0 + theta1 x to fit the best line through data, predicting house prices from size by adjusting theta0 and theta1.

Evaluate a linear regression line using the sum of squared errors by comparing predicted values to actual data, guiding the fit of the slope and intercept from training points.

Minimize the sum of squared errors between y and the prediction t0 + t1 x to learn the best parameters that fit the data.

we plot a data set and fit a linear model y = theta0 + theta1 x, comparing parameter choices by squared errors and the cost function to find best fit.

Plot the squared difference as a convex parabola in theta, revealing a global minimum. Differentiate and set to zero, or derive the normal equation to find the best theta.

Visualize the cost function as a convex surface with a global minimum. Set the derivative to zero to derive the normal equation (X^T X)^{-1} X^T y, compared with gradient descent.

Learn the intuition behind gradient descent: optimize a convex cost function toward a global minimum, update theta iteratively from random starts, and balance step size to avoid overshooting.

Learn gradient descent to minimize the sum of squared errors by iteratively updating parameters from a random start using a step size, converging to the global minimum for best fit.

See how gradient descent uses the learning rate, alpha, as the step size to minimize cost and reach the global minimum, avoiding overshoot or slow convergence.

Plot the cost versus iterations to verify gradient descent and that the squared errors decrease toward the optimum, adjusting the learning rate if necessary.

Learn how learning rate shapes gradient descent convergence using learning curves. Adjust alpha to reach the global minimum fast; too high or too small rates hinder convergence.

This lecture covers linear regression with a hypothesis line, the sum of squared errors cost function, and the derivative for gradient descent to fit from training data.

Derive the cost function and its gradient for linear regression, then use gradient descent to reach the global minimum. Expand the cost and differentiate with respect to the variables.

Read housing data in Python, perform exploratory analysis and statistics, then apply linear regression with gradient descent to predict price from square feet and living area, evaluating on unseen data.

Learn to load housing data in Python, explore feature correlations with a correlation matrix and seaborn visuals, and build a simple linear regression model to predict price from square feet.

Split the data into training and test sets to train a linear regression model mapping square feet and living area to price, then evaluate predictions on unseen data.

Defines a linear regression hypothesis for one or more features, like square feet and bedrooms, to predict price. Illustrates vectorized prediction with X and theta and notes gradient descent optimization.

Define the linear regression cost function in Python by computing squared errors between predictions and actual labels, summing them, and dividing by 2m to get cost, then outline gradient descent.

Master gradient descent for linear regression in Python with vectorized code. Derive the cost function, apply derivatives and step sizes, and update parameters using X, y, and hypothesis.

Learn to implement linear regression in Python by defining hypothesis, cost, and gradient descent, then fit a line to data and compare costs to reach a global minimum.

Apply gradient descent to fit a linear regression line on training data, then evaluate the hypothesis-based predictions on unseen data using test and validation sets.

Master linear regression in Python by using a built-in library as a black box, apply stochastic gradient descent, and evaluate mean squared error on unseen data with 80/20 train-test split.

Learn the end-to-end machine learning pipeline from raw data to predictions, including feature extraction, data processing, selecting features, training a linear regression model, and evaluating on unseen data.

Build on single-variable regression by introducing multiple features to fit our linear regression model, using different features rather than just square feet.

Explore how multivariate linear regression uses multiple features, such as square feet living and bedrooms, to predict housing prices and fit a regression surface.

Demonstrate how the multivariate regression hypothesis uses multiple features and coefficients, and how vectorized form with x0, x1, x2, x3 and the X matrix yields predictions via dot products.

Explore the vectorized derivative of the squared error cost function for multi-feature linear regression, and apply gradient descent to minimize prediction error on a housing dataset.

Scale features to the same range using normalization so gradient descent can learn mappings reliably and reach the global minimum in housing price prediction.

Learn min max scaling to normalize features to the 0 to 1 range using (x - min) / (max - min), illustrated with bedroom data, and compare to standardization.

Apply standardization by transforming each feature to zero mean and unit variance. Compute (x - mean) / std for features such as bedrooms and square feet to produce standardized data.

Learn how standardization centers data by subtracting the mean and dividing by the standard deviation, producing centered, normalized data for a single feature.

Explore feature scaling and normalization to give input features equal importance for learning algorithms, with examples in linear regression and k-nearest neighbor, and explain when scaling is required.

Learn to implement multivariate linear regression in Python by loading data, standardizing square feet, living area, and bedrooms, and using an 80/20 train-test split to predict price.

Build a multivariate linear regression model in Python using gradient descent and a built-in library, with two features, feature scaling, and evaluation on training and unseen data.

Discover how regression learns feature-target relations from training data to predict unseen outcomes, then enhance models with feature engineering, preprocessing, and polynomial features for non-linear patterns.

Explore polynomial regression by extending linear regression with x squared to fit a quadratic trend, turning a linear model into a better fit with polynomial features and a built-in library.

Explore how polynomial regression in Python captures non-linear trends by comparing degree 1, 2, 5, and 20 polynomials, highlighting overfitting and the need to generalize to unseen data.

Explore underfitting and overfitting through linear and high-order polynomial regression to understand generalization, training versus unseen data, bias-variance tradeoffs, and meaningful learning vs rote memorization.

Explore how to use built-in Python polynomial features with linear regression to visualize fitting, assess underfitting and overfitting, and evaluate generalization on unseen data.

Learn how to choose a polynomial that generalizes to unseen data by comparing training and test errors across degrees, and use a validation set to prevent unfair test peeking.

Split data into training, validation, and test sets; use the validation (development) dataset to choose the best polynomial degree based on validation error; evaluate performance on an unseen test set.

Learn how training, validation (development), and test sets drive cross validation and fine tuning to evaluate model performance on unseen data using accuracy or error.

Explore the bias-variance tradeoff by contrasting underfitting with high bias and overfitting with high variance, and learn how data, features, and regularization help balance generalization.

Explore bias and variance with a simple diagram, showing how increasing model complexity lowers training error but raises validation error, and how underfitting and overfitting relate to generalization.

Learn how k-fold cross validation evaluates model performance by splitting data into k folds, training on k-1 folds, validating on the remaining fold, and averaging scores.

Master five-fold cross validation in python using scikit-learn to evaluate polynomial regression across degrees, comparing training and validation scores with validation curves to select the best generalizing degree.

Explore how grid search in python automates identifying the best parameter combinations, using cross validation and polynomial features, to optimize degree, intercept, and normalization for unseen data.

Explore learning curves to diagnose bias and variance and judge model generalization. Compare training and validation performance as data increases to decide whether to add data or change the model.

Examine how high bias causes poorly fitting models and high training and validation errors, and learn to use more complex models or adjust regularization to improve generalization.

Explore the high-variance learning curve where training error is low but validation error is high, and apply remedies like more training data, stronger regularization, and feature selection to generalize.

Demonstrates learning curves in Python by using linear regression and polynomial degrees, and shows how training and validation errors reveal bias, variance, and generalization through cross-validated curves.

Learn how linear regression with a single variable models relationships, extend to multivariate regression, and apply polynomial features and gradient descent to capture non-linear patterns.

Demonstrate how the decision tree regressor builds simple rules, splits data by depth, and predicts outcomes, contrasting it with linear, polynomial, and random forest and boosting methods.

Explore how decision trees handle classification and regression by learning rules from supervised data, with applications in credit risk assessment, credit scoring, and predicting customer churn.

Explore how neural networks map input features to outputs through input, hidden, and output layers, using neurons and weights to learn complex relationships via gradient descent for regression and classification.

Explore housing data with Python by performing feature engineering and exploratory analysis for modeling. Build regression and classification models and validate them using available data sets.

Learn to build and evaluate a housing price predictor with linear regression, using 80/20 data splits, normalization, cross-validation, learning curves, and bias-variance analysis.

Explore building a decision tree regressor in Python, tune max depth with grid search cross-validation, compare training and validation errors, and select the best depth based on validation performance.

Analyze learning curves to balance bias and variance when using a decision tree regressor, tune depth, and validate with test data before predicting real estate prices.