Beyond hidden Markov models: new techreports

[Herbert Jaeger]

BEYOND HIDDEN MARKOV MODELS

Two technical reports on stochastic time series modeling available

ABSTRACT. 

Hidden Markov models (HMMs) provide widely used techniques for analysing 
discrete stochastic sequences.  HMMs are induced from empirical data by 
gradient descent methods, which are computationally expensive, involve 
heuristic pre-estimation of model structure, and can get trapped in
local 
optima.  Furthermore, HMMs are mathematically not well understood.  In 
particular, model equivalence cannot be characterised.

A new class of stochastic models, "observable operator models" (OOMs), 
presents an advance over HMMs in the following respects:

- OOMs are more general than HMMs, i.e. processes modeled by OOMs
  are a proper superclass of those modeled by HMMs.  
- Equivalence of OOMs can be characterized algebraically.  
- A *constructive* algorithm allows to reconstruct OOMs from empirical
  time series. This algorithm is extremely fast and transparent
  (boiling down essentially to a single matrix inversion).  
- OOMs reveal fundamental connections of stochastic processes with
  information theory and dynamical systems theory. 
  
The basic mathematical theory of OOMs, and their relation to HMMs, 
is described in:

	Herbert Jaeger: Observable Operator Models and Conditioned 
	Continuation Representations. Arbeitspapiere der GMD 1043, 
	GMD, St.  Augustin 1997 (38 pp). 
	
The induction algorithm, and a standardized graphical representation
of OOM-generated processes, is described in:

    Herbert Jaeger: Observable Operator Models II: Interpretable models 
    and model induction. Arbeitspapiere der GMD 1083, GMD, 
    St. Augustin 1997 (33 pp)
	
Both papers can be fetched electronically from the author's webpage
(see below) or directly from the following ftp-site: 

ftp://ftp.gmd.de/GMD/ai-research/Publications/1997/
(files jaeger.97.{oom,oom2}.{ps.gz,pdf})


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Dr. Herbert Jaeger                  Phone  +49-2241-14-2253
German National Research Center		Fax    +49-2241-14-2384
for Information Technology (GMD)	   email  herbert.jaeger at gmd.de
FIT.KI 
Schloss Birlinghoven                
D-53754 Sankt Augustin, Germany


http://www.gmd.de/People/Herbert.Jaeger/
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