Update method/Readme.md

method/Readme.md

@@ -19,28 +19,5 @@ Our analysis indicates that among the four machine learning models evaluated, DN
 #### Off-chain data
 
 ### Monotonicity
-    <p>In this context, we propose a novel method for predicting gas usage in blockchain transactions, inspired by the concept of pairwise monotonicity as detailed by Chen <a href="#chen2023address">[1]</a>. Unlike traditional methods like EMA, which emphasizes the forgetting of older information, our approach employs a monotonicity representation to attribute varying levels of importance to data over time. Monotonicity has demonstrated its interdisciplinary applicability, as evidenced by works such as Liu et al. <a href="#liu2020certified">[2]</a> and Milani <a href="#milani2016fast">[3]</a>, which focused on individual monotonicity for single variables. Our method is inspired by Chen's work <a href="#chen2023address">[1]</a> for introducing pairwise monotonicity in the financial domain. For instance, past due amounts over a longer period in credit scoring should more significantly impact the scoring of new debt risk. Similarly, older data points are less influential in blockchain transactions, whereas recent data points are more critical for prediction.</p>
-
-    <p>We apply monotonicity to the α feature, where changes in α for recent blocks result in greater prediction variance than changes in distant previous data points. In the case of k=2, where the prediction uses data from the two previous blocks, the α values are α<sub>1</sub> and α<sub>2</sub> with values (α<sub>1</sub>=a, α<sub>2</sub>=a). Given the higher importance assigned to α<sub>2</sub>, increasing or decreasing α<sub>2</sub> by a certain amount t compared with altering α<sub>1</sub> by the same amount will lead to a higher variation of results. The mathematical equation can be denoted as:</p>
-
-    <pre>
-        |f(α<sub>1</sub>=a, α<sub>2</sub>=a) - f(α<sub>1</sub>=a+t, α<sub>2</sub>=a)| ≤ |f(α<sub>1</sub>=a, α<sub>2</sub>=a) - f(α<sub>1</sub>=a, α<sub>2</sub>=a+t)|
-    </pre>
-
-    <p>The formal definition of pairwise monotonicity is modified from Chen's work <a href="#chen2023address">[1]</a>. The output changing can be positively correlated and negatively correlated with variables. Thereby, given f, the model, we conclude f is weakly monotonic concerning x<sub>β</sub> over x<sub>γ</sub> if:</p>
-
-    <pre>
-        |f(x<sub>β</sub>, x<sub>γ</sub>+c, 𝔁<sub>¬</sub>) - f(x<sub>β</sub>, x<sub>γ</sub>, 𝔁<sub>¬</sub>)| ≤ |f(x<sub>β</sub>+c, x<sub>γ</sub>, 𝔁<sub>¬</sub>) - f(x<sub>β</sub>, x<sub>γ</sub>, 𝔁<sub>¬</sub>)|
-        ∀ x<sub>β</sub>, x<sub>γ</sub> such that x<sub>β</sub>=x<sub>γ</sub>, ∀ 𝔁<sub>¬</sub>, ∀ c ∈ ℝ.
-    </pre>
-
-    <p>Under this weak monotonicity definition, we ensure more information is addressed on the nearer data point, enhancing its transparency and explainability.</p>
-
-    <hr>
-
-    <h3>References</h3>
-    <ol>
-        <li id="chen2023address">Chen, Y. (2023). Addressing Pairwise Monotonicity in Financial Predictions.</li>
-        <li id="liu2020certified">Liu, X., et al. (2020). Certified Individual Monotonicity in Single Variable Systems.</li>
-        <li id="milani2016fast">Milani, A. (2016). Fast Monotonicity Checks in Variable Data.</li>
-    </ol>
+we propose a novel method for predicting gas usage in blockchain transactions, inspired by the concept of pairwise monotonicity as detailed by Chen \cite{chen2023address}. Unlike traditional methods like EMA, which emphasizes the forgetting of older information, our approach employs a monotonicity representation to attribute varying levels of importance to data over time. Monotonicity has demonstrated its interdisciplinary applicability, as evidenced by works such as Liu et al. \cite{liu2020certified} and Milani \cite{milani2016fast}, which focused on individual monotonicity for single variables. Our method is inspired by Chen's work \cite{chen2023address} for introducing pairwise monotonicity in the financial domain. For instance, past due amounts over a longer period in credit scoring should more significantly impact the scoring of new debt risk. Similarly, older data points are less influential in blockchain transactions, whereas recent data points are more critical for prediction.
+