Development and Assessment of SPM: A Sigmoid-Based Model for Probability Estimation in Non-Repetitive Unit Selection With Replacement

Abstract

Probability estimation plays a pivotal role across diverse domains, particularly in scenarios where the objective is to select non-repetitive units one at a time, with the option of replacement, from a predefined set of units. Traditional probability calculations in this scenario pose three challenges: the number of floating-point operations to be executed is directly proportional to the chosen set size, susceptibility to floating-point precision errors, and exponential growth in storage needs with increasing number of chosen units. In this scenario, the presented work aims to develop SPM: a sigmoid function-based model that estimates probabilities for such problems with a fixed number of calculations (independent of the input parameter), achieving a constant time complexity algorithm. The research methodology involves generating probability data points, selecting the optimal sigmoid function, augmenting additional data to enhance parameter estimation, identifying parameter estimation equations, and evaluating the model. Moreover, the study’s second objective includes training and comparing six established machine learning-based models (including Decision Tree, Random Forest, Support Vector, Linear Regression, Nearest Neighbour, and Artificial Neural Network) against the proposed SPM. The rigorous assessment of the model’s performance, utilising metrics including RMSE, MAE and $r^{2}$ across a wide range of scenarios involving varying values of the total units, affirms the model’s accuracy and resilience. The study findings can improve decision-making processes in various domains, including statistics, cryptography, machine learning and optimisation, by offering a faster, more adaptable solution for probability estimation in units’ selection with replacement.

Keywords

• Probability estimation
• sigmoid function
• modeling
• non-repetitive units selection
• optimization