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Related Experiment Video

Updated: Jun 16, 2026

Measuring Light-Switching Behavior Using an Occupancy and Light Data Logger
05:50

Measuring Light-Switching Behavior Using an Occupancy and Light Data Logger

Published on: January 16, 2020

Norm-observable operator models.

Ming-Jie Zhao1, Herbert Jaeger

  • 1Institute for Theoretical Computer Science, Graz University of Technology, Graz 8010, Austria. mingjie.zhao@gmail.com

Neural Computation
|February 10, 2010
PubMed
Summary
This summary is machine-generated.

Norm-observable operator models (NOOMs) introduce a novel solution to the negative probability problem in observable operator models (OOMs). This new framework ensures non-negative probabilities, retaining OOM advantages for time series analysis.

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Area of Science:

  • Statistics
  • Machine Learning
  • Time Series Analysis

Background:

  • Hidden Markov Models (HMMs) are widely used for time series but have limitations.
  • Observable Operator Models (OOMs) generalize HMMs, offering efficient learning algorithms.
  • OOMs suffer from the negative probability problem (NPP), where models can predict negative probabilities, which is undecidable.

Purpose of the Study:

  • Introduce Norm-Observable Operator Models (NOOMs) as a solution to the NPP in OOMs.
  • Demonstrate that NOOMs avoid negative probabilities by design.
  • Explore the mathematical foundations, expressiveness, and learnability of NOOMs.

Main Methods:

  • NOOMs utilize linear operators to update system states, similar to OOMs.
  • Probabilities in NOOMs are represented by the square of the norm of system states.
  • Mathematical proofs establish the properties and capabilities of NOOMs.

Main Results:

  • NOOMs inherently prevent negative probability predictions, resolving the NPP.
  • NOOMs retain the advantages of OOMs, including modeling capabilities beyond HMMs.
  • NOOMs can be learned constructively from data with asymptotic correctness.

Conclusions:

  • NOOMs offer a robust alternative to OOMs by eliminating the NPP.
  • NOOMs are proven to capture all Markov chain (MC) describable processes.
  • The proposed framework provides a constructive method for estimating NOOMs from data.