Statistical Inference on Memory Structure of Processes and Its Applications to Information Theory

Abstract

The research considered the application of context set models in information theory, and focused on constructing a universal code for this model class. Three areas were investigated. First, new memory models of discrete-time and finitely-valued information sources are introduced and a universal code for the new model class is presented. An algorithm is developed to compute the code, and its practical (polynomial) computational and storage complexities are proved. Second, a statistical method is developed to estimate the memory depth of discrete-time and continuously-valued times series from a sample. (A practical algorithm to compute the estimator is a work in progress.) Third, finitely-valued spatial processes on a d-dimensional integer lattice were considered, which are natural models of images. The open problem of statistical estimation of the spatial memory structure from a single observation of the process in a finite window has been solved.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 12, 2016
Accession Number
AD1014759

Entities

People

  • Zsolt Talata

Organizations

  • University of Kansas

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Computational Complexity
  • Computations
  • Department Of Defense
  • Engineering
  • Ergodic Processes
  • Estimators
  • Information Theory
  • Instructors
  • Markov Chains
  • Mathematics
  • Probability
  • Statistical Analysis
  • Statistical Estimation
  • Statistical Inference
  • Statistics
  • Students

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Graph Algorithms and Convex Optimization.
  • Parallel and Distributed Computing.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms