Machine learning

Machine learning Instead of being explicitly programmed, ML models improve their performance through experience (training on data).

Key Concepts in Machine Learning

Types of Machine Learning

Supervised Learning: Models learn from labeled data (input-output pairs).
Examples: Classification (spam detection), Regression (house price prediction).
Unsupervised Learning: Models find patterns in unlabeled data.
Examples: Clustering (customer segmentation), Dimensionality reduction (PCA).
Examples: Game-playing AI (AlphaGo), robotics.

Common Algorithms

Regression: Linear Regression, Decision Trees.
Classification: Logistic Regression, SVM, Random Forest, Neural Networks.
Clustering: K-Means, DBSCAN.
Deep Learning: A subset of ML using neural networks (e.g., CNNs for images, RNNs for text).

Model Evaluation

Metrics: Accuracy, Precision, Recall, F1-Score (for classification); MSE, RMSE (for regression).
Techniques: Train-Test Split, Cross-Validation.

Bias-Variance Tradeoff

Underfitting (High Bias): Model is too simple.
Overfitting (High Variance): Model memorizes training data but fails on new data.

Feature Engineering

Process of selecting and transforming raw data into meaningful features to improve model performance.

Applications of Machine Learning

Healthcare: Disease prediction, medical imaging analysis.
Finance: Fraud detection, stock market prediction.
E-commerce: Recommendation systems (Amazon, Netflix).
Autonomous Vehicles: Self-driving cars (Tesla, Waymo).
Natural Language Processing (NLP): Chatbots, translation (GPT, BERT).

Popular Tools & Libraries

Python: Scikit-learn, Tensor Flow, PY Torch, KERAS.
Interpretability: Black-box models (e.g., deep learning) can be hard to explain.
Ethics: Bias in AI, privacy concerns (e.g., facial recognition).

Core Mathematical Foundations

Machine learning relies heavily on these mathematical concepts:
Linear Algebra: Matrices, vectors, eigenvalues (used in PCA, neural networks).
Calculus: Gradients, derivatives (optimization via gradient descent).
Probability & Statistics: Bayes’ theorem (Naïve Bayes), distributions, variance.

Advanced Algorithms

Neural Networks & Deep Learning
Activation Functions: RELU, Sigmoid, Soft max.
Backpropagation: Adjusts weights using gradient descent.

Architectures:

CNNs: For images (convolutional layers).
RNNs/LSTMs: For sequential data (time series, NLP).
Transformers: Attention mechanisms (e.g., BERT, GPT).

Ensemble Methods

Random Forest: Combines multiple decision trees.
Gradient Boosting (XG Boost, Light GBM): Sequentially corrects errors.

Dimensionality Reduction

PCA: Projects data into lower dimensions.
t-SNE: Visualizes high-dimensional data.

Model Training & Optimization

Loss Functions: Cross-entropy (classification), MSE (regression).
Optimizers: SGD, Adam, RMS prop.
Hyperparameter Tuning: Grid search, Bayesian optimization.
Regularization: L1/L2 regularization, dropout (in neural networks).

Practical Workflow

Data Collection: Scraping, APIs, datasets (Kaggle, UCI).

Preprocessing:

Handling missing values (imputation).
Encoding categorical variables (one-hot encoding).
Scaling (Standard Scaler, Min Max Scaler).
Feature Selection: Correlation analysis, recursive feature elimination.
Model Deployment: Flask/Django APIs, Docker, cloud (AWS Lambda).

Cutting-Edge Topics

Generative AI: GANs (image generation), Diffusion models.
Self-Supervised Learning: Training on unlabeled data (e.g., contrastive learning).
Quantum ML: Quantum algorithms for optimization.

Ethical Considerations

Bias/Fairness: Models can amplify societal biases (e.g., racial bias in facial recognition).
Privacy: Federated learning helps train models without raw data sharing.
Explain ability: SHAP values, LIME for model interpretability.

Learning Resources

Books:

Pattern Recognition and Machine Learning (Bishop).
Hands-On Machine Learning with Sci kit-Learn & Tensor Flow (Géron).

Courses:

Coursera: Andrew Ng’s ML course.
Fast.ai: Practical deep learning.

Challenges & Open Problems

Catastrophic Forgetting: Neural networks forget old tasks when learning new ones.
Adversarial Attacks: Small input perturbations fool models (e.g., misclassified images).
Energy Efficiency: Training large models (e.g., GPT-3) has a high carbon footprint.

Theoretical Foundations of Machine Learning

Statistical Learning Theory

VC Dimension: Measures model complexity (capacity to fit data).

Bias-Variance Decomposition:

Optimization in ML

Gradient Descent (and variants):
Batch GD, Stochastic GD (SGD), Mini-batch GD.
Momentum, Nesterov Accelerated Gradient (NAG).
Second-Order Methods: Newton’s method, Quasi-Newton (L-BFGS).

Probabilistic Graphical Models

Bayesian Networks: Directed graphs representing dependencies.
Transformer Blocks: Multi-head attention, residual connections.
Applications: BERT (NLP), Vision Transformers (ViT).

Generative Models

GANs (Generative Adversarial Networks):
Generator vs. Discriminator (minimax game).

Loss:

Diffusion Models: Gradually denoise data (e.g., DALL-E, Stable Diffusion).
Normalizing Flows: Learn invertible transformations.

Meta-Learning & Few-Shot Learning

MAML (Model-Agnostic Meta-Learning): Adapts to new tasks quickly.
Siamese Networks: Learn similarity metrics (e.g., face recognition).

Adversarial Machine Learning

Attack Types

Evasion Attacks: Perturb inputs to fool models (e.g., adversarial images).
Poisoning Attacks: Corrupt training data.

Defense Strategies

Adversarial Training: Train on perturbed examples.
Defensive Distillation: Train a secondary model to smooth predictions.

Open Research Problems

Neural Scaling Laws: How does performance improve with model size?
Causal Inference in ML: Moving beyond correlation to causation.
Energy-Efficient AI: Training models with lower carbon footprints.

Foundational Mathematics Revisited

Measure-Theoretic Probability for ML

σ-algebras and Radon-Nikodym derivatives in Bayesian nonparametrics
Martingale Theory in online learning algorithms

Differential Geometry in ML

Information Geometry: Fisher-Rao metric on statistical manifolds
Manifold Learning: Riemannian optimization for SPD matrices (used in brain-computer interfaces)

Functional Analysis

Spectral Theory: Eigen analysis of graph Laplacians (key for GNNs)

Advanced Optimization Landscapes

Non-Convex Optimization

Kurdyka-Łojasiewicz Inequality: Convergence analysis of SGD in deep learning
Neural Tangent Kernel (NTK): Infinite-width network dynamics

Model Serving at Scale

Batching Strategies: Dynamic batching with NVIDIA Triton
Hardware-Aware Quantization: INT8 quantization with TensoRT

Data-Centric AI

Label Error Detection: Confident learning (cleanlab)
Data Versioning: DVC pipelines with differential data loading

Theoretical Frontiers

Algorithmic Alignment Theory

Neural Networks as Parallel SGD: Relation to boosting algorithms

Category Theory for ML

Functorial Learning: Universal properties of neural architectures

Open Challenges

Grokkking Phenomenon: Sudden generalization after prolonged training
Neural Collapse: Last-layer geometry in classification tasks
Scalarization Bottleneck: Why transformers struggle with compositional generalization

Research Methodology

Gradient Science

Mechanistic Interpretability: Circuits analysis (Anthropic ‘s Toy Models of Superposition)

Experimental Rigor

Power Scaling Laws: Determining compute-optimal model sizes
Counterfactual Evaluation: Causal ablation studies

Checkpointing Strategies:

Delta Checkpoints: Only save parameter deltas
Erasure Coding: For fault-tolerant distributed FS

Real-Time Serving Constraints

Bounded-Time Inference:

Monte Carlo Tree Search with early truncation

Latency Budget Partitioning:

Open Problems

The Scaling Paradox: Why do loss curves obey power laws across modalities?
Manifold Topology Hypothesis: Intrinsic dimensionality of learned representations
Algorithmic Phase Transitions: Sudden emergence of reasoning in LLMs