Moving to the era of explainable AI, a comprehensive comparison of the performance of stochastic optimization algorithms has become increasingly important task. One of the most common ways to do this is to apply statistical analyses, which require good knowledge from the user to apply them properly. This tutorial will provide an overview of statistical approaches that can be used for analyzing algorithms performance with special emphasis on issues that are often overlooked. We will show how these issues can be easily avoided by applying simple principles that leads to Deep Statistical Comparison. The tutorial will not be based on equations, but mainly examples through which a deeper understanding of statistics will be achieved. Examples will be based on various comparisons scenarios including single- and multi-objective optimization algorithms. The tutorial will end with a demonstration of a web-service-based framework for statistical comparison of stochastic optimization algorithms.

Pareto optimization is a general optimization framework for solving single-objective optimization problems, based on multi-objective evolutionary optimization. The main idea is to transform a single-objective optimization problem into a bi-objective one, then employ a multi-objective evolutionary algorithm to solve it, and finally return the best feasible solution w.r.t. the original single-objective optimization problem from the generated non-dominated solution set. Pareto optimization has been shown a promising method for the subset selection problem, which has applications in diverse areas, including machine learning, data mining, natural language processing, computer vision, information retrieval, etc. The theoretical understanding of Pareto optimization has recently been significantly developed, showing its irreplaceability for subset selection. This tutorial will introduce Pareto optimization from scratch. We will show that it achieves the best-so-far theoretical and practical performances in several applications of subset selection. We will also introduce advanced variants of Pareto optimization for large-scale, noisy and dynamic subset selection.

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