Data Science & Machine Learning¶

Comprehensive reference covering statistics, machine learning, deep learning, computer vision, NLP, and applied data science. From mathematical foundations through production deployment.

Foundations¶

• math precalculus - number systems, equations, functions, sets, combinatorics
• math logic - propositional logic, first-order logic, proof techniques, computability
• math for ml - calculus, optimization, gradient descent, backpropagation
• math linear algebra - vectors, matrices, eigenvalues, SVD
• math probability statistics - probability theory, estimation, MLE, confidence intervals

Statistics & Probability¶

• descriptive statistics - central tendency, spread, shape, correlation, z-scores
• probability distributions - Bernoulli, binomial, Poisson, normal, exponential, CLT
• hypothesis testing - A/B testing, statistical tests, CUPED, experiment design
• causal inference - DiD, propensity score matching, synthetic control, DAGs
• bias variance tradeoff - overfitting, underfitting, regularization, ensemble tradeoffs

Tools & Languages¶

• python for ds - Python fundamentals for data science, Jupyter/Colab
• numpy fundamentals - array operations, linear algebra, random generation
• pandas eda - DataFrame manipulation, groupby, filtering, EDA workflow
• data visualization - matplotlib, seaborn, plotly, chart selection
• sql for data science - queries, window functions, CTEs, analytics patterns

Classical Machine Learning¶

• linear models - linear/logistic regression, gradient descent, regularization
• gradient boosting - CatBoost, XGBoost, LightGBM, Random Forest, hyperparameters
• knn and classical ml - KNN, SVM, decision trees, algorithm selection guide
• unsupervised learning - K-Means, DBSCAN, PCA, t-SNE, UMAP, SVD
• bayesian methods - Bayes' theorem, Naive Bayes, Bayesian inference

Deep Learning¶

• neural networks - architecture, training, activation functions, optimizers, regularization
• cnn computer vision - convolutions, architectures (ResNet, YOLO), detection, segmentation
• nlp text processing - tokenization, TF-IDF, embeddings, transformers, BERT
• rnn sequences - LSTM, GRU, bidirectional, sequence-to-sequence
• generative models - GANs, VAEs, diffusion models, CycleGAN
• transfer learning - pre-trained models, fine-tuning strategies, domain adaptation
• data augmentation - image/text/tabular augmentation, SMOTE

Techniques & Evaluation¶

• feature engineering - scaling, encoding, imputation, selection, pipelines
• model evaluation - metrics (MAE, ROC AUC, F1), cross-validation, confusion matrix
• time series analysis - stationarity, ARIMA, seasonality, feature engineering for time
• monte carlo simulation - simulation, portfolio optimization, risk metrics
• recommender systems - collaborative filtering, content-based, evaluation
• knowledge tracing - learner modeling, BKT->DKT->SAKT->AKT->simpleKT, adaptive learning, FSRS

Applied & Production¶

• ds workflow - end-to-end project methodology, pitfalls, reproducibility
• bi dashboards - BI systems, dashboard design, KPIs, analytics SQL
• ml production - model serialization, serving, monitoring, drift detection
• financial data science - portfolio theory, derivatives, risk metrics, financial ratios
• ai video production - AI video pipeline, tool chain, prompt engineering for video

Cross-Topic Links¶

• python for ds - Python setup for data science workflows
• sql for data science - SQL for analytical queries
• complexity analysis - computational complexity
• etl elt pipelines - data pipeline infrastructure
• prompt engineering - prompt engineering for LLMs