Changelog

Append-only log of wiki ingests.

2026-04-20

• Initialized vault structure. Created raw/ and wiki/ folders, index.md, and CHANGELOG.md.
• Ingested week 1. Created: weeks/week-01.md, concepts/supervised-learning.md, concepts/logistic-regression.md, concepts/sigmoid-function.md, concepts/generalization.md, concepts/decision-boundary.md, concepts/discriminative-vs-generative-models.md (stub). Updated index.md.

2026-04-26

• Ingested week 2. Created: weeks/week-02.md, concepts/maximum-likelihood-estimation.md, concepts/cross-entropy-loss.md, concepts/gradient-descent.md, concepts/convex-function.md, concepts/taylor-polynomial.md, concepts/hessian-matrix.md, concepts/newton-raphson-method.md, concepts/iteratively-reweighted-least-squares.md. Updated index.md.
• Enhanced taylor-polynomial.md. Added “Why polynomials?” motivation, “Coefficients as Independent Derivative Controls” with the $n!$ cascade explanation, and a “Convergence and Radius of Convergence” section with three new active-recall questions.
• Removed empty gradient-descent.md stub at vault root. It was shadowing the populated wiki/concepts/gradient-descent.md in Obsidian’s wikilink resolution.
• Ingested week 3. Created: weeks/week-03.md, concepts/non-linear-transformation.md, concepts/support-vector-machine.md, concepts/margin.md, concepts/quadratic-programming.md. Updated index.md.
• Cross-referenced Notion exports (raw/p1.zip, raw/p2.zip). Enhanced generalization.md with the “Closeness vs Attainability” two-pillars framing and marble-jar metaphor; added Strengths and Limitations section to logistic-regression.md; added “MLE is the source of standard loss functions” table (Bernoulli → cross-entropy, Gaussian → MSE, etc.) to maximum-likelihood-estimation.md; added the “linear in $\varphi$-space, non-linear in original” reframing to non-linear-transformation.md.
• Ingested week 4. Created: weeks/week-04.md, concepts/lagrangian.md, concepts/kkt-conditions.md, concepts/kernel-trick.md, concepts/mercers-condition.md, concepts/gaussian-kernel.md, concepts/polynomial-kernel.md. Updated index.md. Covers SVM dualisation, KKT and complementary-slackness as the structural source of support-vector sparsity, the kernel trick, Mercer’s condition and composition rules, and the polynomial / Gaussian kernels.

2026-04-28

• Ingested week 8. Created: weeks/week-08.md, concepts/bayesian-linear-regression.md, concepts/ridge-regression.md, concepts/hoeffding-inequality.md, concepts/generalization-bound.md. Updated index.md. Two-part week: (1) Bayesian regression — Gaussian prior + Gaussian likelihood → closed-form Gaussian posterior; MAP estimate is exactly ridge regression, so L2 regularisation is the negative log of a Gaussian prior (regularisation = prior). (2) Learning theory — Hoeffding’s inequality bounds $|E_{\text{in}}-E_{\text{out}}|$ with probability $\ge 1-2e^{-2{ϵ}^{2}N}$; union bound over $M$ hypotheses gives the generalization bound $E_{\text{out}}\le E_{\text{in}}+\sqrt{(1/2N)\log (2M/\delta )}$. The two opposing forces ($M$ small for tight bound vs $M$ large for good fit) formalise the bias-variance trade-off. Sets up VC dimension via the dichotomy/effective-$M$ idea.

2026-04-27

• Ingested week 7. Created: weeks/week-07.md, concepts/linear-regression.md, concepts/ordinary-least-squares.md, concepts/design-matrix.md, concepts/gaussian-distribution.md, concepts/bayes-law.md. Updated index.md. Covers the pivot from classification to regression, OLS via the normal equation $\mathbf{w}=({\mathbf{\Phi }}^{\top }\mathbf{\Phi }{)}^{-1}{\mathbf{\Phi }}^{\top }\mathbf{y}$, basis expansion (linear in parameters, non-linear in inputs), and the probabilistic interpretation that justifies squared error: under additive Gaussian noise, MLE for $\mathbf{w}$ is identical to OLS. Frames this as the regression analog of week 2’s logistic-regression-as-MLE result — the noise model determines the loss.
• Reorganised image assets. Created raw/images/ and renamed all 22 dated Screenshot 2026-04-26 at *.pm.png files to descriptive content-based names (e.g., svm-intro.png, kernel-trick-input-feature-space.png, soft-margin-c-effect.png). Updated all 22 references across the wiki. Obsidian’s ![[name]] syntax resolves by basename so paths didn’t need changing — just filenames.
• Added visuals to weekly synthesis pages. Embedded soft-margin motivation, slack-geometric, primal-comparison, and $C$-effect figures across week-05.md, slack-variables.md, and soft-margin-svm.md. Cross-referenced the SVM primal→dual chain, kernel-trick input→feature-space, and Gaussian bell-curve into week-04.md (same images already used in concept pages — Obsidian shares a single asset across all references).
• Added cross-week synthesis pages. Created topics/optimization-algorithms.md (compares GD, Newton-Raphson/IRLS, SMO — when each applies, cost, role of curvature/constraints) and topics/classification-approaches.md (compares LogReg, hard-margin SVM, soft-margin SVM — same hypothesis form, different fitting criteria, hinge vs cross-entropy as the structural source of SVM sparsity). Motivated by the week-6 revision lecture which presents these groupings as the module’s organising structure. Updated index.md.
• Ingested week 5. Created: weeks/week-05.md, concepts/soft-margin-svm.md, concepts/slack-variables.md, concepts/sequential-minimal-optimization.md. Updated index.md. Covers the soft-margin relaxation (slack variables, hyperparameter $C$, the box constraint $0\le a\le C$), the three-way support-vector partition from KKT (non-SV / margin-SV / bound-SV), and the SMO decomposition algorithm — including why two multipliers is the minimum updateable subset, the analytic update rule, clipping to feasibility, and pair-selection heuristics.
• Embedded slide screenshots. Added the SVM intro and non-linear-margin pictures to support-vector-machine.md; the distance-to-hyperplane and max-margin pictures to margin.md; the input/feature-space cartoon to kernel-trick.md; the bell-curve and decision-boundary plots to gaussian-kernel.md; the SVM primal→dual derivation chain to lagrangian.md; the differential-curvature ellipses, difficult-topology plot, and steepest-descent paraboloid to gradient-descent.md; the linear-classifier+sigmoid figure to logistic-regression.md; and the log-likelihood-to-cross-entropy derivation to cross-entropy-loss.md.