Learn AI in Minutes

Foundational concepts in data, statistics, machine learning, and generative AI. Every note is a standalone interactive Marimo notebook with concept intuition, mathematical formulations, code examples, and practical takeaways.

Linear Algebra & Matrix Foundations

1. Note 00: Systems of Linear Equations

   Linear combinations, row vs column perspectives, and invertibility

2. Note 01: Inner Products and Angles

   Dot products, projection, geometric angles, and Hilbert spaces

3. Note 02: Vector Norms and Metrics

   L1, L2, Lp norms, distances, and unit ball geometries

4. Note 03: Hyperplanes and Halfspaces

   Decision boundaries, affine sets, and separating hyperplanes

5. Note 04: Rank-One Matrices

   Outer products, low-rank factorization, and matrix approximations

6. Note 05: Orthogonality

   Orthogonal vectors, bases, projections, and Gram-Schmidt process

7. Note 06: Moore-Penrose Pseudoinverse

   Pseudoinverse and least-squares solutions for overdetermined systems

8. Note 07: Spectral Decomposition

   Eigendecomposition, symmetric matrices, and singular value decomposition

9. Note 08: Matrix Calculus

   Derivatives of vector and matrix expressions for optimization

10. Note 09: Condition Number

    Numerical stability, matrix sensitivity, and multicollinearity diagnostics

Probability & Statistical Foundations

1. Note 10: Chebyshev Inequality

   Distribution-free probability bounds and concentration

2. Note 11: Empirical CDF

   Empirical distribution functions and non-parametric inference

3. Note 12: Multivariate Normal Distribution

   Multivariate Gaussian geometry, covariance matrices, and density contours

4. Note 13: Unbiased vs Consistent Estimators

   Core properties of statistical estimators and sample size behavior

5. Note 14: Distribution of Minimum

   Order statistics and extreme value distributions

6. Note 15: Mutual Information

   Information theory, entropy, and non-linear feature dependence

7. Note 16: Point-Biserial Correlation

   Measuring association between continuous and binary variables

8. Note 17: Jensen's Inequality

   Convexity, expectation inequalities, and bounds in learning algorithms

Applied Statistics & Correlation

1. Note 18: Cramer's V

   Strength of association between categorical variables

2. Note 19: Kendall's Tau-b

   Non-parametric rank correlation robust to ties

3. Note 20: Spurious Correlation

   Confounders, lurking variables, and Simpson's paradox

4. Note 21: Kruskal-Wallis Test

   Non-parametric ANOVA for comparing multiple groups

5. Note 22: ACF and PACF

   Autocorrelation and partial autocorrelation for time series modeling

6. Note 23: Exponential Moving Averages

   EMA smoothing, momentum, and initial bias correction

7. Note 24: Adjusted R-Squared

   Penalizing model complexity in linear regression

8. Note 25: Predictive R-Squared

   Leave-one-out cross-validation and generalization performance

9. Note 26: Hotelling's T-Squared

   Multivariate hypothesis testing and group mean comparisons

Multivariate Methods & Dimensionality

1. Note 27: Principal Component Analysis

   Dimensionality reduction via covariance eigendecomposition

2. Note 28: Factor Analysis

   Latent variable modeling and unobserved factor estimation

3. Note 29: Canonical Correlation Analysis

   Maximizing correlation between two multidimensional variable sets

4. Note 30: Correspondence Analysis

   Geometric visualization of contingency tables and categorical associations

5. Note 31: Gaussian Mixture Models

   Soft clustering, Expectation-Maximization, and density estimation

Machine Learning Models & Diagnostics

1. Note 32: Elastic Net Regression

   Balancing L1 and L2 penalties for correlated feature selection

2. Note 33: Huber Loss

   Robust regression combining squared and absolute error penalties

3. Note 34: Mahalanobis Distance

   Covariance-scaled distance metrics for outlier detection

4. Note 35: Gini Impurity vs Entropy

   Split evaluation criteria for decision trees

5. Note 36: Agglomerative Clustering

   Hierarchical clustering, distance metrics, and dendrograms

6. Note 37: Natural Breaks (Jenks)

   1D clustering optimization for histogram and choropleth binning

7. Note 38: Oversampling and SMOTE

   Synthesizing minority class samples for imbalanced classification

8. Note 39: Permutation Feature Importance

   Model-agnostic feature importance via shuffling evaluation

9. Note 40: PCA vs Feature Agglomeration

   Linear dimensionality reduction versus hierarchical feature clustering

10. Note 41: Pseudo R-Squared

    Goodness-of-fit metrics for logistic regression and GLMs

11. Note 42: Multiclass Classification

    Softmax functions, cross-entropy loss, and decision regions

12. Note 43: Energy-Based Models

    Energy landscapes, Boltzmann distributions, and score matching

Interpretable AI

1. Note 44: Logistic Regression Interpretability

   Log-odds, odds ratios, and marginal feature effects

2. Note 45: Shapley Values and SHAP

   Game-theoretic feature attributions and local model explanations

3. Note 46: Model Counterfactuals

   Actionable recourse and minimal changes to alter model predictions

Deep Learning & Generative AI

1. Note 47: GELU Activation

   Gaussian Error Linear Units in modern Transformer models

2. Note 48: Temperature-Scaled Softmax

   Calibrating confidence and diversity in probability distributions

3. Note 49: Focal Loss

   Down-weighting easy examples for dense object detection and hard mining

4. Note 50: Attention Mechanism

   Scaled dot-product attention as value weighting by query-key similarity

5. Note 51: Causal Attention

   Autoregressive masking in decoder-only generative models

6. Note 52: Multi-Head Attention

   Parallel representation subspaces in Transformer blocks

7. Note 53: LayerNorm and RMSNorm

   Internal activation scaling and modern variance normalization

8. Note 54: Decoding Strategies

   Greedy search, beam search, top-k, and nucleus (top-p) sampling

9. Note 55: Perplexity

   Information-theoretic evaluation metric for autoregressive language models

10. Note 56: Reparameterization Trick

    Differentiable sampling through stochastic nodes via auxiliary noise

11. Note 57: Autoencoder Latent Space

    Deterministic bottleneck compression and feature representation

12. Note 58: PCA for Anomaly Detection

    Reconstruction error in reduced eigenspaces as anomaly scoring

13. Note 59: VAE on MNIST

    Variational Autoencoders with evidence lower bound (ELBO) optimization

14. Note 60: VAE Anomaly Detection

    Probabilistic reconstruction likelihood for out-of-distribution detection

Graphs & Applied Pipelines

1. Note 61: User-Item Interaction Matrix

   Bipartite graph representations for recommendation systems

Random Notes & Programming Patterns

1. Note 62: Grammar of Graphics

   Layered visualization specifications with plotnine

2. Note 63: Einstein Summation (einsum)

   Succinct multidimensional array contractions in NumPy and PyTorch

3. Note 64: Data Pivoting

   Reshaping and aggregating tabular datasets in Pandas

4. Note 65: GPU Acceleration (cuDF)

   Accelerating dataframe pipelines with GPU memory and parallelism

5. Algorithm: Kadanes Algorithm

   Algorithmic problem-solving and programming techniques.

6. Algorithm: Prefix Sum

   Algorithmic problem-solving and programming techniques.

7. Algorithm: Two Pointer

   Algorithmic problem-solving and programming techniques.

Subject Notes (Deep Dives)

1. Multivariate Analysis

   Advanced multivariate statistical techniques and geometric formulations (in progress).

2. Functional Data Analysis

   Infinite-dimensional representations, smoothing, and functional principal components (in progress).

Research Paper Notes

1. TabICLv2

   Tabular foundation model for in-context learning, classification, and regression (research notes).

2. LeJEPA

   Joint-Embedding Predictive Architecture formulations and explorations (research notes).

Published at learnaiinminutes.com. Source code: Data-and-AI-Concepts.