Part I: The Mathematical & Statistical Bedrock
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- Scalars, Vectors, Matrices, and Tensors
- Vector Operations
- Matrix Algebra
- Linear Systems
- Matrix Decomposition (SVD, LU, Cholesky, PCA)
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- Differential Calculus
- Multivariable Calculus
- The Chain Rule
- High-Order Derivatives
- Taylor Series Expansion
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- Core Theory (Bayes' Theorem, Independence)
- Probability Distributions (Discrete & Continuous)
- Statistical Inference ( P-Value, Confidence Intervals, Hypothesis Testing )
- Estimation Theory (MLE, MAP)
Part II: Supervised Learning
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4. Linear & Non-Linear Regression
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- Logistic Regression
- Multiclass Classification (OvR, OvO, Softmax)
- Discriminant Analysis (LDA, QDA)
- Support Vector Machines (SVM)
- The Kernel Trick (RBF, Polynomial)
- Instance-Based (KNN)
- Naive Bayes
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- Decision Tree Mechanics
- Information Metrics (Entropy, Gini Impurity)
- Ensemble Methods (Bagging, Random Forests, Boosting: AdaBoost, GBM, XGBoost)
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- Filter Methods (Correlation, Chi-Square, Mutual Information)
- Wrapper Methods (Forward/Backward Selection, RFE)
- Embedded Methods (Lasso, Tree Importance)
- Advanced (Permutation Importance, Boruta)
Part III: Unsupervised Learning & Geometry
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- Partitioning (K-Means, K-Means++)
- Hyperparameter Tuning (Elbow Method, Silhouette Scores)
- Hierarchical Clustering
- Density-Based (DBSCAN, OPTICS)
- Association (Apriori)
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- Linear (PCA, Factor Analysis)
- Non-Linear (t-SNE, UMAP, Isomap, Kernel PCA)
Part IV: Neural Networks & Deep Learning
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- Architecture (Perceptrons, MLP)
- Activation Functions (ReLU, Sigmoid, Tanh)
- The Optimization Loop (Backpropagation)
- Neural Optimizers (Adam, RMSProp, SGD)
- Neural Regularization (Dropout, Batch Norm)
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- Computer Vision (CNNs)
- Sequence Models (RNNs, LSTMs, GRUs)
- The Transformer (Self-Attention)
Part V: The Frontier (2024-2026)
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- Large Language Models (GPT, BERT, T5)
- Fine-Tuning (PEFT, LoRA)
- Generation Models (GANs, VAEs, Diffusion)
- RAG (Vector Databases)
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- Foundations (MDP, Rewards)
- Algorithms (Q-Learning, DQN, PPO)
Part VI: Engineering & Metrics
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- Classification Metrics (Precision, Recall, F1, ROC-AUC)
- Validation (K-Fold Cross-Validation)
- Analysis (Bias-Variance Trade-off)
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- XAI (SHAP, LIME)
- Production (Containerization, Model/Data Drift)