1. Summary of This Course Huanhuan Chen

2. Outline  Basics about Signal & Systems  Bayesian inference  PCVM  Hidden Markov Model  Kalman filter  Extended Kalman filter  Particle filter  Bayesian Networks  Nonlinear Dynamic Systems  Echo State Networks

3. Signal & System  Time Domain  Signal properties  Frequency Domain  Fourier transform  Z-transform  Laplace transform  System  State space model

4. Machine learning & Bayesians

5. Sparse Bayesian Learning  What’s Bayesian?  Why Bayesian?  How to use Bayesian?

6. Kalman filtering : Recursive update of state  Kalman filtering algorithm: repeat…  Time update: from X t|t, compute a priori distrubution X t+1|t  Measurement update: from X t+1|t (and given y t+1 ), compute a posteriori distribution X t+1|t+1 X0X0 X1X1 X2X2 X3X3 X4X4 X5X5 Y1Y1 Y2Y2 Y3Y3 Y4Y4 Y5Y5 …

7. Particle filter 7

8. Bayesian Networks  Inference  Structure Learning

9. Echo State Networks