Data Sciences Summer Institute

University of Illinois at Urbana-Champaign
The Mathematics, Algorithms and Tools for Data Analytics

Core Course: Foundations of Data Sciences

Course Topics:

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.

Decision Trees.

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.