ML Foundations Notes

Personal notes on probability, optimization, statistical inference, classical machine learning, deep learning, and reinforcement learning.

Overview

This repository contains my self-organized study notes built to strengthen the mathematical and conceptual foundations behind machine learning and AI systems.

The notes were compiled as part of a broader effort to develop a more rigorous understanding of:

• probability and statistics
• optimization and operations research
• decision analysis and stochastic processes
• likelihood-based inference
• classical machine learning
• Monte Carlo methods
• deep learning
• reinforcement learning

Rather than serving as a collection of isolated class notes, this repository is intended to form a coherent technical foundation that supports later work in forecasting, predictive maintenance, uncertainty-aware modeling, and AI for real-world systems.

These notes help connect mathematical principles with practical modeling tasks, especially in areas such as:

• time-series prediction
• predictive maintenance
• reliability engineering
• decision-making under uncertainty
• AI-driven engineering systems

Topics Covered

1. Probability and Statistics

• probability rules and conditional probability
• random variables and common distributions
• expectation, variance, covariance
• sampling and estimation basics

2. Optimization and Operations Research

• linear programming
• integer programming
• optimization thinking in engineering systems
• links between mathematical optimization and decision modeling

3. Decision Analysis and Stochastic Processes

• decision structures under uncertainty
• stochastic modeling intuition
• Markov-related concepts and process-based reasoning

4. Statistical Inference

• likelihood
• maximum likelihood estimation
• MAP estimation
• probabilistic interpretation of parameter estimation

5. Classical Machine Learning

• linear and logistic regression
• generative and discriminative methods
• regularization
• dimensionality reduction
• ensemble methods
• model evaluation concepts

6. Monte Carlo and MCMC

• Monte Carlo estimation
• sampling-based approximation
• variance intuition
• effective sample size and related concepts

7. Deep Learning

• neural network fundamentals
• gradient-based learning
• backpropagation intuition
• optimization issues in deep models

8. Reinforcement Learning

• value-based reasoning
• policy-related concepts
• sequential decision-making perspective

Repository Structure