Efficiently learning linear-linear exponential family predictive representations of state

ABSTRACT

Exponential Family PSR (EFPSR) models capture stochastic dynamical systems by representing state as the parameters of an exponential family distribution over a shortterm window of future observations. They are appealing from a learning perspective because they are fully observed (meaning expressions for maximum likelihood do not involve hidden quantities), but are still expressive enough to both capture existing models and predict new models. While maximum-likelihood learning algorithms for EFPSRs exist, they are not computationally feasible. We present a new, computationally efficient, learning algorithm based on an approximate likelihood function. The algorithm can be interpreted as attempting to induce stationary distributions of observations, features and states which match their empirically observed counterparts. The approximate likelihood, and the idea of matching stationary distributions, may apply to other models.

REFERENCES

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.6 Learning

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
          Subjects: Linear approximation
      G.1.3 Numerical Linear Algebra
          Subjects: Linear systems (direct and iterative methods)

  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.4 Model Validation and Analysis
      I.6.5 Model Development
          Subjects: Modeling methodologies

General Terms:
Algorithms, Design, Performance, Theory