Related Experiment Video
Updated: Feb 15, 2026
11:18
Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat
Published on: September 12, 2014
15.8K
Decomposition of conditional probability for high-order symbolic Markov chains
1A. Ya. Usikov Institute for Radiophysics and Electronics Ukrainian Academy of Science, 12 Proskura Street, 61805 Kharkov, Ukraine.
Physical Review. E
|January 20, 2018
Summary
This study develops a method to estimate conditional probabilities for symbolic sequences, modeling them as high-order Markov chains. This approach aids in constructing artificial sequences and has potential applications in neural network training.
Area of Science:
- Probability Theory
- Information Theory
- Machine Learning
Background:
- Estimating conditional probabilities is crucial for analyzing symbolic sequences.
- High-order Markov chains offer a powerful framework for sequence modeling.
Purpose of the Study:
- To develop an estimation method for the conditional probability function of random stationary ergodic symbolic sequences.
- To model these sequences as high-order Markov chains.
Main Methods:
- Decomposition procedure for the conditional probability function.
- Representation as a sum of multilinear memory function monomials.
- Construction of artificial sequences via successive iterations.
Main Results:
- A novel family of Markov chain models is introduced.
- Memory functions are uniquely expressed in terms of high-order symbolic correlation functions under weak correlations.
- The method bridges likelihood estimation and additive Markov chains.
Conclusions:
- The proposed method provides a robust way to estimate conditional probabilities for symbolic sequences.
- The findings have potential applications in sequential approximation for artificial neural network training.
More Related Videos
Related Concept Videos
02:36Lewis Symbols and the Octet Rule
82.7K
Chemical bonds are complex interactions between two or more atoms or ions, which reduce the potential energy of the molecule. Gilbert N. Lewis developed a model called the Lewis model that simplified the depiction of chemical bond formation and provided straightforward explanations for the chemical bonds seen in most common compounds.
82.7K
02:31Elements: Chemical Symbols and Isotopes
127.9K
A chemical symbol is an abbreviation used to indicate an element or an atom of an element. For example, the symbol for mercury is Hg. The same symbol is used to indicate one atom of mercury (microscopic domain) or to label a container of many atoms of the element mercury (macroscopic domain).
Some symbols are derived from the common English name of the element; others are abbreviations of the name in another language — Latin, Greek or German. For example, the symbol for aluminum (common name)...
Some symbols are derived from the common English name of the element; others are abbreviations of the name in another language — Latin, Greek or German. For example, the symbol for aluminum (common name)...
127.9K
01:49Probability Laws
44.5K
Overview
44.5K
02:17Synthesis and Decomposition Reactions
38.4K
Synthesis and decomposition are two types of redox reactions. Synthesis means to make something, whereas decomposition means to break something. The reactions are accompanied by chemical and energy changes.
38.4K
01:09Chemical Symbols
122.7K
A chemical symbol is an abbreviation that is used to indicate an element or an atom of an element. For example, the symbol for mercury is Hg. We use the same symbol to indicate one atom of mercury (microscopic domain) or to label a container of many atoms of the element mercury (macroscopic domain).
Some symbols are derived from the common name of the element; others are abbreviations of the name in another language. Most symbols have one or two letters, but three-letter symbols have been used...
Some symbols are derived from the common name of the element; others are abbreviations of the name in another language. Most symbols have one or two letters, but three-letter symbols have been used...
122.7K
01:32Probability Distributions
12.2K
The probability of a random variable x is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
12.2K