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1890 learning items

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Quiz

MML-07-04: Backpropagation Mechanics in Multi-Layer Perceptrons

Master the core mathematical principles of MML-07-04: Backpropagation Mechanics in Multi-Layer Perceptrons. This comprehensive assessment progresses from accessible conceptual foundations through step-by-step analytical derivations, diagnostic counterexamples, and real-world machine learning implementations. Topics covered include Trace forward propagation and layerwise affine and activation transformations., Derive error vectors \boldsymbol{\delta}^{[l]} and recursive backpropagation equations., Compute weight and bias parameter gradients from propagated error vectors., as well as advanced diagnostics and synthesis. Prerequisites: QS 7.3.. Designed for machine learning researchers, data scientists, and engineers.

mathematics

Oct 31, 2026

45 questions

Quiz

MML-11-06: Forward vs. Reverse KL: Mean-Seeking vs. Mode-Seeking Dynamics

Master the core mathematical principles of MML-11-06: Forward vs. Reverse KL: Mean-Seeking vs. Mode-Seeking Dynamics. This comprehensive assessment progresses from analytical comparisons through optimization dynamics and generative model architectures. Topics covered include Forward KL ($$\min_Q D_{KL}(P \parallel Q)$$, zero-avoiding, mean-seeking, moment matching), Reverse KL ($$\min_Q D_{KL}(Q \parallel P)$$, zero-forcing, mode-seeking), variational inference ELBO identity, alpha-divergence interpolation, Expectation Propagation, and mode collapse dynamics. Designed for machine learning researchers, data scientists, and engineers.

mathematics

Oct 31, 2026

35 questions

Quiz

MML-11-05: Kullback-Leibler (KL) Divergence: Properties, Asymmetry & Information Projection

Master the core mathematical principles of MML-11-05: Kullback-Leibler (KL) Divergence: Properties, Asymmetry & Information Projection. This comprehensive assessment progresses from fundamental definitions through information geometry and machine learning applications. Topics covered include definition of KL divergence $$D_{KL}(P \parallel Q)$$, Gibbs' inequality ($$D_{KL} \ge 0$$), asymmetry ($$D_{KL}(P \parallel Q) \ne D_{KL}(Q \parallel P)$$), Pinsker's inequality and Total Variation bound, relation to cross-entropy ($$H(P, Q) = H(P) + D_{KL}(P \parallel Q)$$), closed-form multivariate Gaussian KL, and I-projections. Designed for machine learning researchers, data scientists, and engineers.

mathematics

Oct 31, 2026

40 questions

Quiz

MML-11-04: Differential Entropy of Continuous Distributions & The Maximum Entropy Principle

Master the core mathematical principles of MML-11-04: Differential Entropy of Continuous Distributions & The Maximum Entropy Principle. This comprehensive assessment progresses from continuous density derivations through coordinate transformation sensitivity and calculus of variations. Topics covered include differential entropy $$h(X) = -\int p(x) \log p(x) \, dx$$, negative entropy values, scale transformation effects ($$h(AX) = h(X) + \log |\det(A)|$$), maximum entropy principle under moment constraints (uniform on bounded interval, exponential on non-negative half-line, Gaussian on fixed variance), and Boltzmann entropy. Designed for machine learning researchers, data scientists, and engineers.

mathematics

Oct 31, 2026

30 questions

Quiz

MML-11-03: Mutual Information & Information Theoretic Independence

Master the core mathematical principles of MML-11-03: Mutual Information & Information Theoretic Independence. This comprehensive assessment progresses from accessible conceptual foundations through non-linear dependence metrics and representation learning. Topics covered include definition of mutual information $$I(X; Y)$$, non-negativity and symmetry, relation to joint and conditional entropy, information theoretic independence criterion ($$I(X; Y) = 0 \iff X \perp Y$$), data processing inequality, and InfoMax principle. Designed for machine learning researchers, data scientists, and engineers.

mathematics

Oct 31, 2026

30 questions

Quiz

MML-11-02: Joint Entropy, Conditional Entropy & Information Chain Rule

Master the core mathematical principles of MML-11-02: Joint Entropy, Conditional Entropy & Information Chain Rule. This comprehensive assessment progresses from accessible conceptual foundations through multidimensional derivations and chain rules. Topics covered include joint entropy $$H(X, Y)$$, conditional entropy $$H(Y \mid X)$$, the chain rule of entropy ($$H(X, Y) = H(X) + H(Y \mid X)$$), conditioning reduces entropy theorem ($$H(X \mid Y) \le H(X)$$), Markov chain information monotonicity, and entropy Venn diagrams. Designed for machine learning researchers, data scientists, and engineers.

mathematics

Oct 31, 2026

30 questions

Quiz

MML-11-01: Information Content, Surprise & Shannon Entropy of Discrete Distributions

Master the core mathematical principles of MML-11-01: Information Content, Surprise & Shannon Entropy of Discrete Distributions. This comprehensive assessment progresses from accessible conceptual foundations through analytical derivations and coding theorems. Topics covered include Hartley and Shannon self-information ($$I(x) = -\log_2 P(x)$$), axiomatic characterization of Shannon entropy, concavity and non-negativity, uniform distribution maximum entropy bounds, binary entropy function, and Shannon noiseless source coding. Designed for machine learning researchers, data scientists, and engineers.

mathematics

Oct 31, 2026

30 questions

Quiz

MML-10-09: ANOVA (F-Tests), Chi-Square Contingency and Non-Parametric Rank Tests

Master the core mathematical principles of MML-10-09: ANOVA ($$F$$-tests), Chi-Square Contingency & Non-Parametric Rank Tests. This comprehensive assessment progresses from accessible conceptual foundations through step-by-step variance partitioning, contingency matrix calculations, and robust rank-based inference. Topics covered include one-way and two-way ANOVA, sum-of-squares partitioning, post-hoc corrections (Bonferroni, Tukey HSD), Chi-square goodness-of-fit and independence tests, Mann-Whitney U, and Wilcoxon signed-rank tests. Designed for machine learning researchers, data scientists, and engineers.

mathematics

Oct 31, 2026

30 questions

Quiz

MML-10-08: Parametric Tests: Z-tests, Student's t-tests, Welch's t-test & Paired tests

Master the core mathematical principles of MML-10-08: Parametric Tests: Z-tests, Student's t-tests, Welch's t-test & Paired tests. This comprehensive assessment progresses from accessible conceptual foundations through step-by-step analytical derivations, diagnostic checks, and machine learning model validation. Topics covered include one-sample and two-sample Z-tests, Student's t-tests, Welch's t-test with Satterthwaite degrees of freedom, paired sample t-tests, normality diagnostics, and power analysis. Designed for machine learning researchers, data scientists, and engineers.

mathematics

Oct 31, 2026

35 questions

Quiz

MML-09-06: The Exponential Family: Natural Parameters, Sufficient Statistics & Log-Partition

Identify natural parameters, sufficient statistics, base measures, and log-partition functions across common distribution families. Derive moment identities and convexity, then diagnose redundant statistics, moving support, and unstable canonical-parameter calculations. Normal-law notation uses variance as its second parameter; Gamma rates are stated explicitly. 40 questions combining single-select and multiselect formats, with worked explanations and feedback for every choice. Prerequisites: QS 9.5. Cognitive range: Tier 2–4. The local authored sequence progresses from accessible checks to computations, modeling diagnostics, and derivation recognition within that range. Reference: [Mathematics for Machine Learning, Chapter 6](https://mml-book.github.io/book/mml-book.pdf).

mathematics

Oct 31, 2026

40 questions

Quiz

MML-09-05: Beta, Gamma & Dirichlet Distributions

Study Gamma integrals and distributions, Beta probability densities, and Dirichlet probability vectors on a simplex. Compute moments, modes, concentration effects, component marginals, and normalized-Gamma sampling constructions. Every Gamma calculation states whether its parameter is rate or scale; posterior updating belongs to the next questionset. 35 questions combining single-select and multiselect formats, with worked explanations and feedback for every choice. Prerequisites: QS 9.4. Cognitive range: Tier 2–3. The local authored sequence progresses from accessible checks to computations, modeling diagnostics, and derivation recognition within that range. Reference: [Mathematics for Machine Learning, Chapter 6](https://mml-book.github.io/book/mml-book.pdf).

mathematics

Oct 31, 2026

35 questions

Quiz

MML-09-04: Linear Transformations, Affine Mappings & Sums of Gaussians

Propagate Gaussian laws through linear and affine maps, combine Gaussian signals and noise, and construct samples from covariance factors. Analyze whitening, support rank, dependence assumptions, and nonlinear-layer failures. Normal-law notation uses variance or covariance as its second parameter. 35 questions combining single-select and multiselect formats, with worked explanations and feedback for every choice. Prerequisites: QS 9.3. Cognitive range: Tier 2–3. The local authored sequence progresses from accessible checks to computations, modeling diagnostics, and derivation recognition within that range. Reference: [Mathematics for Machine Learning, Chapter 6](https://mml-book.github.io/book/mml-book.pdf).

mathematics

Oct 31, 2026

35 questions