What is the state-of-the-art in unsupervised learning on temporal data?

Question

I'm looking for an overview of the state-of-the-art methods that

• find temporal patterns (of arbitrary length) in temporal data

• and are unsupervised (no labels).

In other words, given a steam/sequence of (potentially high-dimensional) data, how do you find those common subsequences that best capture the structure in the data.

1. Any pointers to recent developments or papers (that go beyond HMMs, hopefully) are welcome!

2. Is this problem maybe well-understood in a more specific application domain, like

   • motion capture
   • speech processing
   • natural language processing
   • game action sequences
   • stock market prediction?

3. In addition, are some of these methods general enough to deal with
   • highly noisy data
   • hierarchical structure
   • irregularly spacing on time axis

Answer 1

There are many available resources on non-parametric HMMs, extensions to infinite state spaces, as well as factorial models, explaining an observation using a set of factors rather than a single mixture component.

Here are some interesting papers to start with:

• 'Beam Sampling for the Infinite Hidden Markov Model'
• 'The Infinite Factorial Hidden Markov Model'
• 'Bayesian Non-parametric Inference of Switching Dynamic Linear Models'
• 'Sharing features among dynamical systems with beta processes'

There are some applications in text modeling, speaker diarization, and motion capture, among other things. 

For more details on this, study Types of Machine Learning, which is a part of Machine Learning Tutorial.

Hope this answer helps.