Mastering Machine Learning Algorithms

Learn simple linear regression with one independent variable, estimate beta0 and beta1, fit the regression line, make predictions, and minimize mean squared error; extend to multilinear regression.

Explore logistic regression as a classification method using the log of y by 1 minus y. Fit coefficients like beta naught and b1 to predict probabilities for a binary outcome.

Derive the logistic regression probability p(x) from the log-odds; transform to the sigmoid form and prepare to fit the model to data.

Explore impurity in decision trees and learn how entropy, Gini index, and classification error quantify node homogeneity, guiding pure splits and homogeneous leaves.

Explore how decision trees build from impurities to purity using entropy and information gain, compare id3, c4.5, c5.0, cart, and ensemble methods while detailing splitting, pruning, and stopping criteria.

Explore how the KNN algorithm classifies a new data point by computing distances to all stored instances in 2D, selecting k nearest neighbors, and assigning the majority class.

Learn how to pick the best k in kNN by evaluating error rates across k values with a confusion matrix and classification report, favoring odd k like 3 or 5.

The lecture explains Bayes theorem and its use in classification, including calculating conditional probabilities and total probability, introduces Naive Bayes for binary targets, and walks through a skull fracture example.

Explore how to apply distance measures such as Euclidean distance, Hamming distance, and cosine similarity to real-world problems, from finding the nearest warehouse to detecting text similarity and recommending products.

Explore how distance measures like Euclidean, Manhattan, Minkowski, Hamming, and cosine similarity drive clustering, classification, and anomaly detection across k-means, hierarchical, dbscan, KNN, and outlier techniques.

Explore the k-means cost function, which minimizes the within-cluster sum of squared distances to centroids using Euclidean distance, for clusters of sizes n_i, and stopping when centroids stop changing.

Segment retail customers using k-means clustering on annual income and spending score, normalize with z-score standardization, and explore fraud detection via cosine similarity with a 0.7 threshold.

Discover how the elbow method helps choose the optimal number of clusters in k-means by analyzing the within-cluster sum of squares (inertia) and plotting the elbow curve.

Segment retail customers with k-means clustering and evaluate using the silhouette score, identify the optimal number of clusters, normalize data, plot results, and cross-check with elbo.

Initialize random points in a low-dimensional space, compute pairwise similarities with probability distributions in high- and low-dimensional spaces, and minimize a loss via gradient-based optimization until convergence.

Explore the bias-variance tradeoff, understand how model complexity affects underfitting and overfitting, and see how ensemble learning balances algorithms to improve prediction accuracy.

Explore three simple ensemble methods—maximum voting, averaging, and weighted averaging—implemented with sklearn to blend decision trees, k-NN, and logistic regression for classification and regression tasks.

Demonstrate the 63.21% rule in sampling with replacement and show that about 63% of data points are selected at least once in bootstrap samples for bagging.

Explore how random forest, a powerful ensemble learning algorithm extending bagging, handles high cardinality feature spaces with random feature selection and data subsampling to aggregate diverse trees for final predictions.

Tune random forest hyperparameters such as n estimators, max features, and class weight to balance unbalanced data, bootstrap options, max samples, and the out-of-the-bag score.

Master stacking ensemble learning by training diverse base models on a training set, using cross-validated predictions to train a meta model, typically logistic regression, for final test predictions.

Compare bagging and boosting by examining sampling methods and how weak learners are weighted. Bagging builds parallel subsamples with replacement; boosting updates sequentially and focuses on misclassified cases.

Gradient boosting trains weak learners sequentially to correct prior errors using residuals, while tuning the learning rate and estimator count to control learning and prevent overfitting.

Explore how a gradient boosting regressor predicts housing prices by iteratively fitting decision trees to residuals, updating with learning rate, and summing boosted predictions across estimators.

Leave-one-out cross validation is a special case of leave-p-out with p=1, testing one data point at a time, expensive for large datasets but usable for very small ones.

Explore how models learn parameters during training and how hyperparameters set before learning influence optimization methods like gradient descent, regularization, normalization, and solver choices across linear, logistic, and multilinear regression.