Machine Learning
“Master closed-form regression math, Ridge/Lasso shrinkage, SVM maximum margin geometry, decision tree impurity, neural backpropagation, and unsupervised manifolds for GATE DA.”
A rigorous, first-principles academic study notebook covering supervised regression and classification models, kernel methods, ensemble architectures, multilayer perceptrons, clustering, dimensionality reduction, and model validation metrics. Designed specifically to match the highest-yield requirements of the official GATE Data Science & Artificial Intelligence (DA) curriculum.
Structured Notes & Exam Lens
A · B.Tech Structured Study Sequence
6 Sections · Full CurriculumLinear Regression & Regularization (OLS, Ridge, Lasso)
Ordinary Least Squares (OLS) normal equations, geometric column-space projection, multicollinearity, Ridge (L2) shrinkage, and Lasso (L1) sparsity.
Minimizing Residual Sum of Squares (RSS), matrix calculus derivations, and projection onto the column space.
Shrinkage mechanics, solving ill-conditioned matrices, L1 subgradients, and feature selection.
Logistic Regression, k-NN, Naive Bayes & LDA
Sigmoid activation, log-odds, binary cross-entropy MLE, k-Nearest Neighbors distance metrics, Naive Bayes with Laplace smoothing, and Fisher's Linear Discriminant Analysis (LDA).
Sigmoid mapping, maximum likelihood estimation, odds ratios, and linear decision boundaries.
Voronoi decision cells, non-parametric boundary complexity, conditional independence, and add-1 smoothing.
Maximizing between-class separation while minimizing within-class variance, Fisher's ratio, and Bayes optimal boundaries.
Decision Trees (ID3, CART) & Ensemble Methods
Shannon Entropy, Information Gain, Gini Impurity, CART pruning, Bootstrap Aggregation (Bagging), Random Forests, and AdaBoost.
Impurity splitting metrics, ID3 vs CART, continuous feature thresholds, and cost-complexity pruning.
Bootstrap aggregation, decorrelating trees, out-of-bag validation, and adaptive sample reweighting.
Support Vector Machines (SVM) & Kernel Methods
Maximum margin hyperplane geometry, hard/soft margin primal-dual formulations, support vectors, and non-linear Mercer kernels.
Geometric margin 2/||w||, Lagrangian multipliers, KKT complementary slackness, and slack variables.
Inner products in Hilbert spaces, Polynomial kernels, Gaussian RBF, and Mercer positive semi-definiteness.
Multilayer Perceptrons & Backpropagation Math
Perceptrons, activation functions (Sigmoid, Tanh, ReLU), Universal Approximation, multivariable chain rule, and Backpropagation updates.
Overcoming linear separability, Universal Approximation Theorem, and ReLU non-saturating gradients.
Backward error propagation, intermediate sensitivity deltas, computational graphs, and SGD updates.
Clustering, PCA & Model Evaluation Metrics
K-Means, K-Medoids, Hierarchical clustering linkages, Principal Component Analysis, ROC-AUC, and the Bias-Variance tradeoff.
Lloyd's WCSS convergence, K-means++ initialization, PAM medoids, and single/complete linkage dendrograms.
Covariance matrix diagonalization, maximizing projection variance, eigenvalues, and t-SNE manifolds.
Precision, Recall, Specificity, F1 harmonic mean, ROC curves, and the mathematical bias-variance decomposition.
B · GATE 2027 Syllabus Scope
Official syllabus scope and related lesson coverage; topics outside the syllabus are marked as enrichment.
- •Supervised Learning: Linear regression, simple and multiple, ridge and lasso, logistic regression, k-NN, naive Bayes, linear discriminant analysis (LDA)
- •Decision Trees & Ensembles: ID3, CART, entropy, Gini impurity, random forests, bagging, boosting (AdaBoost)
- •Support Vector Machines: Linear and non-linear SVM, maximum margin, slack variables, dual formulation, kernel trick
- •Neural Networks: Multi-layer perceptrons, activation functions, loss functions, backpropagation algorithm
- •Unsupervised Learning: K-means, k-medoids, hierarchical clustering, dimensionality reduction (PCA, t-SNE)
- •Model Evaluation: Confusion matrix, precision, recall, F1-score, ROC-AUC, bias-variance tradeoff, cross-validation
Interactive Labs & Verified PYQs
Revision & Rapid Review Sheets
Authoritative Textbooks & Video Lectures
All notes in this notebook cross-reference standard academic literature. We do not pretend student notes substitute for classical texts — they guide you through them.
Curated lectures from verified educators (Gate Smashers, Neso Academy, Knowledge Gate, and MIT OCW) selected specifically for difficult concept visualizations.
These notes are open and maintained together.
Found a factual mistake? Have a clearer explanation or mental model? Created a useful diagram or worked out a tricky GATE question? Help make this notebook better for every student who opens it next.