Stochastics and Machine Learning

Abstract

This is an introduction to probability, statistics, and machine learning for students of mechanical engineering. We cover the fundamental concepts from probability theory, statistics and machine learning, with a focus on applications for mechanical engineering.

Objective

Basic notions of probability theory and statistics such as probability space, probability measure, random variables, expected value, variance, covariance, standard deviation, correlation, quantiles, conditional distributions, parameter estimation, statistical tests, linear regression Learn the fundamentals of machine learning: training, testing, validation, model selection. Learn essential Python libraries for machine learning: scikit-learn, pytorch, gym. Understand the mathematical foundations of diverse ML algorithms: empirical risk minimization, bias-variance tradeoff, stochastic gradient descent, back propagation, Bellman equations. Learn how to preprocess data for machine learning. Acquire an overview of the trending applications of machine learning for mechanical engineering.

Content

Part I: Stochastics Probability space, probability measure, independence, conditional probabilities, Bayes’ theorem, random variables, probability mass functions, densities, distributions, expected value, variance, covariance, standard deviation, correlation, random vectors, multivariate distributions, law of large numbers, central limit theorem, descriptive statistics, histograms, box plots, empirical distributions, parameter estimation, statistical tests Part II: Machine learning Linear and logistic regression. Basic regression and classification with machine learning Regularization and bias-variance tradeoff Ensembles and unsupervised learning Deep learning, neural networks, convolutional neural networks, and transformers Autoencoders, GANs Reinforcement learning, Markov decision processes, Q learning

Resources