An empirical study of the complexity and randomness of prediction error sequences

Ratsaby, Joel

doi:10.1016/j.cnsns.2010.10.015

Cited by 3 publications

(3 citation statements)

References 23 publications

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“…In the former case, if we take the upper bound (7.2) on the deviation to be a measure of non-randomness of the system's output sequence and view the number of states 2 k as the complexity of the FSM (which is based on model M k ), then it follows that the larger the complexity the less random the output. This is evident in numerical simulations [17] (Section 6.3). Also, the output becomes less random if the mismatch k − k * between the system's model order and the environment's Markov order grows or if the environment's Markov order k * increases.…”

Section: Resultsmentioning

confidence: 64%

“…In order to measure how nonrandom the output sequence may be, we compare the deviation between the average number of 1 bit in the output versus the probability of a symbol 1. Empirical investigations of such matching systems [17,18] show that subsequences that are selected by them have empirical frequencies that deviate from the probabilities in proportion to the complexity of the system's FSM. The current paper confirms this.…”

Section: Introductionmentioning

confidence: 99%

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On Deterministic Finite State Machines in Random Environments

Ratsaby

2018

Prob. Eng. Inf. Sci.

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The general problem under investigation is to understand how the complexity of a system which has been adapted to its random environment affects the level of randomness of its output (which is a function of its random input). In this paper, we consider a specific instance of this problem in which a deterministic finite-state decision system operates in a random environment that is modeled by a binary Markov chain. The system interacts with it by trying to match states of inactivity (represented by 0). Matching means that the system selects the (t + 1)th bit from the Markov chain whenever it predicts at time t that the environment will take a 0 value. The actual value at time t + 1 may be 0 or 1 thus the selected sequence of bits (which forms the system's output) may have both binary values. To try to predict well, the system's decision function is inferred based on a sample of the random environment.We are interested in assessing how non-random the output sequence may be. To do that, we apply the adapted system on a second random sample of the environment and derive an upper bound on the deviation between the average number of 1 bit in the output sequence and the probability of a 1. The bound shows that the complexity of the system has a direct effect on this deviation and hence on how non-random the output sequence may be. The bound takes the form of $O(\sqrt {(2^k/n} ))$ where 2k is the complexity of the system and n is the length of the second sample.

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Section: Resultsmentioning

confidence: 64%

Section: Introductionmentioning

confidence: 99%

On Deterministic Finite State Machines in Random Environments

Ratsaby

2018

Prob. Eng. Inf. Sci.

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“…This measure of complexity was shown to directly effect the algorithmic complexity and level of randomness of the learner's mistake sequence. Ratsaby [9] investigated a population of binary mistake sequences that result from such a learning process. Estimates of the algorithmic complexity and stochastic divergence of the mistake sequences were obtained.…”

Section: Introductionmentioning

confidence: 99%

On the algorithmic complexity of static structures

Chaskalovic

2010

J Syst Sci Complex

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This paper provides a first indication that this is true for a system comprised of a static structure described by hyperbolic partial differential equations and is subjected to an external random input force. The system deforms the randomness of an input force sequence in proportion to its algorithmic complexity. The authors demonstrate this by numerical analysis of a one-dimensional vibrating elastic solid (the system) on which we apply a maximally-random force sequence (input). The level of complexity of the system is controlled via external parameters. The output response is the field of displacements observed at several positions on the body. The algorithmic complexity and stochasticity of the resulting output displacement sequence is measured and compared against the complexity of the system. The results show that the higher the system complexity, the more random-deficient the output sequence.

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Recurrence quantity analysis based on singular value decomposition

Bian

Shang

2017

Communications in Nonlinear Science and Numerical Simulation

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An empirical study of the complexity and randomness of prediction error sequences

Cited by 3 publications

References 23 publications

On Deterministic Finite State Machines in Random Environments

On Deterministic Finite State Machines in Random Environments

On the algorithmic complexity of static structures

Recurrence quantity analysis based on singular value decomposition

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