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Course Information

**Lecturer:**

Dr Ivan Guo, Monash University

Dr Tiangang Cui, Monash University

**Synopsis:**

Statistical machine learning merges statistics with the computational sciences—computer science, systems science and optimization. Much of the work in statistical machine learning is driven by applied problems in science and technology, where data streams are increasingly large-scale, dynamic and heterogeneous, and where mathematical and algorithmic creativity is required to bring statistical methodology to bear.

In this course we will study how to use probability models to analyze data, focusing on the mathematical details of the models and the algorithms for computing them. We will study both foundations and advanced methods. The goal of the course is to understand modern probabilistic modelling, and develop good practices for specifying and applying probabilistic models to analyze real-world data. The applications include financial modelling, pattern recognition and remote sensing.

**Course Overview:**

- Bayesian inference and parameter estimation
- Priors, Posteriors and likelihood
- Expectation maximisation algorithm

- Regression and classification
- Linear and nonlinear regressions
- Discriminant analysis
- Neural Networks

- Sampling methods
- Importance sampling
- Markov chain Monte Carlo

- Time series filtering
- Kalman filters
- Particle filters

**3 Contact hours**

28 hours

**Prerequisites:**

- Multivariable calculus.
- Second year probability and statistics.
- Familiarity with a programming language for statistics, such as MATLAB, R or Python.

**Assessment:**

- Mid-school assignment: 40%
- Final examination: 60%

**Resources:**

- Trevor J.. Hastie, Tibshirani, R. J., & Friedman, J. H. (2011). The elements of statistical learning: data mining, inference, and prediction. Springer.
- Brockwell, P. J., & Davis, R. A. (2016). Introduction to time series and forecasting. Springer.

## Lecturer Biography

**Dr Ivan Guo, Monash University
**

Ivan is a Lecturer in the School of Mathematical Sciences at Monash University. He has previously held research positions at the University of Sydney and the University of Wollongong. Ivan has also worked in the Market Risk Quantitative Support division at National Australian Bank. His research interests include financial mathematics, stochastic control, backward stochastic differential equations, computational finance and stochastic game theory.

** Dr Tiangang Cui, Monash University**

Tiangang is a Lecturer in the School of Mathematical Sciences at Monash University. He has previously held positions at the Massachusetts Institute of Technology and the ExxonMobil Corporation. He has been worked on a wide range of topics on the intersection of data analytics and computational mathematics. His research interests include Bayesian inference, inverse problems, model reduction, stochastic computation, and statistical learning.