A Fast Algorithm for Estimating Two-Dimensional Sample Entropy Based on an Upper Confidence Bound and Monte Carlo Sampling

. 2024 Feb 10;26(2):155. doi: 10.3390/e26020155

Algorithm 3 Monte Carlo sample entropy based on UCB strategy

Require: Sequence $U : = {u_{i, j} : 1 \leq i \leq w, 1 \leq j \leq h}$ , template length m, threshold r,

Sample numbers $N_{0}$ and epoch numbers $N_{1}$ .

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procedure UCBMCSampEn( $U, m, r, N_{0}, N_{1}$ )
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Set ${\bar{A}}_{\tilde{U}} = 0$ and ${\bar{B}}_{\tilde{U}} = 0$ ,
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for $k = 1$ to $N_{1}$ do
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Set $Cor = {(h_{s}, w_{s}) : 1 \leq s \leq N_{0}}$ where $h_{s}$ and $w_{s}$ are selected on $U$ pixel coordinates with uniform distribution,
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Compute ${\tilde{A}}_{k}$ by calling SampEn2D( $U, Cor, m, r$ ),
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Compute ${\tilde{B}}_{k}$ by calling SampEn2D( $U, Cor, m + 1, r$ ),
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Compute $e_{k} = - log \frac{{\tilde{B}}_{k}}{{\tilde{A}}_{k}}$ , $e_{m} = \frac{1}{k} \sum_{1}^{k} e_{k}$ ,
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Compute $e r_{k} = \frac{e_{m} - e_{k}}{e_{m}}$ ,
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Compute ${ucb}_{k} = a \times R (b \times e r_{k}) + c \sqrt{2 ln (i)}$ ,
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Set $\tilde{U} = {{ucb}_{k} : k \in (1, 2, \dots, N_{0})}$ ,
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Set $S = softmax (\tilde{U})$ ,
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for $k = 1$ to $N_{1}$ do
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${\bar{A}}_{\tilde{U}} = {\bar{A}}_{\tilde{U}} + {\tilde{A}}_{k} \times S_{k}$ ,
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${\bar{B}}_{\tilde{U}} = {\bar{B}}_{\tilde{U}} + {\tilde{B}}_{k} \times S_{k}$ ,

$e n t r o p y = - log \frac{{\bar{B}}_{\tilde{U}}}{{\bar{A}}_{\tilde{U}}}$