The Traveling Salesperson Problem (TSP), a quintessential NP-hard combinatorial optimisation challenge, is vital for logistics and network design but limited by exponential complexity in large instances. We propose a hybrid quantum-classical framework integrating variational quantum eigensolver (VQE) optimisation with classical machine learning, using K-means clustering for problem decomposition and a RandomForestRegressor for path refinement. Evaluated on 80 European cities (from 4 to 80 cities, 38,500 samples in total) via Qiskit's AerSimulator and ibm_kyiv 127-qubit backend, the hybrid approach outperforms quantum-only methods, achieving an approximation ratio of 1.0287 at 80 cities, a 47.5% improvement over quantum-only's 1.9614, nearing the classical baseline. Machine learning reduces variability in tour distances (interquartile range, IQR - the spread of the middle 50% of results relative to the median - from 0.06 to 0.04), enhancing stability despite noisy intermediate-scale quantum (NISQ) noise. This framework underscores hybrid strategies' potential for scalable TSP optimisation, with future hardware advancements promising practical quantum advantages.

Binary classification, multilabel classification, and regression prediction constitute fundamental paradigms in machine learning, addressing distinct types of predictive modeling tasks. Binary classification involves categorizing instances into one of two classes, typically denoted as positive and negative [1][2][3]. This modeling framework is particularly applicable to scenarios where outcomes are binary in nature, as observed in domains such as spam detection and medical diagnosis. In multilabel classification, the scope extends to situations where instances can be associated with multiple classes simultaneously, a common occurrence in applications like image tagging and document categorization [1][4]. Conversely, regression prediction is concerned with forecasting continuous outcomes, aiming to predict numeric values [3].

In most sports, especially football, most coaches and analysts search for key performance indicators using notational analysis. This method utilizes a statistical summary of events based on video footage and numerical records of goal scores. Unfortunately, this approach is now obsolete owing to the continuous evolutionary increase in technology that simplifies the analysis of more complex process variables through machine learning (ML). Machine learning, a form of artificial intelligence (AI), uses algorithms to detect meaningful patterns and define a structure based on positional data. This research investigates a new method to evaluate the value of current football players, based on establishing the machine learning models to investigate the relations among the various features of players, the salary of players, and the market value of players. The data of the football players used for this project is from several football websites. The data on the salary of football players will be the proxy for evaluating the value of players, and other features will be used to establish and train the ML model for predicting the suitable salary for the players. The motivation is to explore what are the relations between different features of football players and their salaries - how each feature affects their salaries, or which are the most important features to affect the salary? Although many standards can reflect the value of football players, the salary of the players is one of the most intuitive and crucial indexes, so this study will use the salary of players as the proxy to evaluate their value. Moreover, many features of players can affect the valuation of the football players, but the value of players is mainly decided by three types of factors: basic characteristics, performance on the court, and achievements at the club.

It is interesting to decipher the working of Machine Learning through a web-based dashboard. Imagine gaining access to the interactive plots displaying information on model performance, feature importance as well as What-if analysis. What is exciting is that one does not need any web development expertise to build such an informative dashboard but simple few lines of python code are sufficient to generate a stunningly interactive Machine Learning Dashboard. This is possible by using a library called'Explainer Dashboard'. The ExplainerDashboard is a python package which generates interactive dashboards which allow users to understand as well as explain how the model works and how it is deciding the outcome.

I chose the Bay Area housing price dataset that was sourced from Bay Area Home Sales Database and Zillow. This dataset was based on the homes sold between January 2013 and December 2015. It has many characteristics of learning. The dataset can be downloaded from here. There are several features that we do not need, such as "info", "z_address", "zipcode"(We have "neighborhood" as a location variable), "zipid" and "zestimate"(This is the price estimated by Zillow, we don't want our model to be affected by this).