Time Series Class - Part 2 - Professor Chris Williams, University of Edinburgh

Explore advanced concepts in time series analysis through this comprehensive lecture by Professor Chris Williams from the University of Edinburgh. Delve into state-space models, including hidden Markov models and Kalman filters, and their practical applications. Learn about parameter estimation, likelihood-based inference, and forecasting techniques for time series data. Discover the intricacies of recurrent neural network models and their applications in sequential data processing. Gain insights into advanced topics such as Switching Linear Dynamical Systems, Control Theory, and Conditional Random Fields. Examine the challenges of vanishing and exploding gradients in recurrent networks and explore solutions through LSTM architectures. Investigate the applications of recurrent networks in speech recognition and language modeling, and understand the principles behind encoder-decoder networks for sequence-to-sequence tasks.

Intro
Time Series
Overview
Inference Problems
Recursion formula
Viterbl alignment
Training a HMM
Aside: learning a Markov model
EM parameter updates
Outline
Linear-Gaussian HMMS
Inference Problem - filtering
Simple example
Applications
Extensions
Switching Linear Dynamical System (SLDS)
Factorial Switching Linear Dynamical System (FSLDS)
Control Theory
Conditional Random Fields (CRFS)
Recurrent Neural Networks
Sequential Data
Simplest recurrent network
Recurrent network unfolded in time
Vanishing and exploding gradients
speech recognition with recurrent networks
speech recognition with stacked LSTMs
recurrent network language models
recurrent encoder-decoder
Encoder-Recurrent-Decoder Networks
Summary