Data Sciences Summer Institute
University of Illinois at Urbana-Champaign
The Mathematics, Algorithms and Tools for Data Analytics
Core Course: Foundations of Data Sciences
Probability Review – Conditional Probability, Bayes’ Theorem, Independence, Random Variables, Distribution Functions, Expectation, Variance, Joint Distributions, Central Limit Theorem, Strong Law of Large Numbers.
Stochastic Processes – definitions, Markov Chains, state classification, stationary distribution.
Statistics – Hypothesis testing, Analysis of Variance, Maximum Likelihood Estimators, Bayes’ Estimators, Regression.
Entropy, Mutual Information, KL divergence.
Optimization – Linear Programming, Least Mean Squares, Steepest Descent, Lagrange multipliers.
Clustering – Gaussian Mixture Models, k-Means.
Data Reduction – Singular Value Decomposition, Principal Component Analysis, Wavelets.
Hidden Markov Models.