Application of Mutual Information QUBO for Feature Selection

Project Purpose & Goal

The research aims to investigate the utilization of mutual information combined with Quadratic Unconstrained Binary Optimization (QUBO) on the D-wave quantum computer. The ultimate goal is to accurately predict the top-performing sectors in the S&P 500, with a focus on the sharpe ratio, thereby enhancing the efficiency and performance of machine learning models in financial predictions.

Explanation

The project commences by emphasizing the significance of feature selection in machine learning, where mutual information stands out as a crucial technique for handling high-dimensional data. By examining the relationship between features and the sharpe ratio, the study identifies the most relevant features using mutual information.

QUBO, a binary optimization problem traditionally used in computer science, is then applied, formulated based on mutual information to maximize it. Using data from the S&P 500 (from 2020 to 2022), the Mutual Information QUBO (MIQUBO) application pinpoints features with the highest mutual information to the sharpe ratio.

The top 8 of these features undergo processing on the D-Wave quantum computer's QPU. The results showcase the capability of the MIQUBO method in predicting sector performance and emphasize its scalability for broader applications.

Problems

Optimizing Computation with Quantum Computing: Classical computing methods might not be efficient for such large-scale optimization problems and quantum computing offer potential solutions. However, it's worth noting that current quantum technology hasn't reached its full potential yet.

Feature Selection in Machine Learning: After retrieving S&P 500 data from Yahoo Finance, there was a need to streamline the feature set. Large datasets typically present a multitude of features, not all of which contribute value. Optimal feature selection is crucial to avoid the inclusion of irrelevant or redundant elements that can introduce noise, thereby impacting the performance of machine learning models.

Thought Process

This was part of my final project for a class in applications of quantum computing. I drew inspiration from another course I was taking on information theory. This led me to blend various academic techniques and employ financial analysis to practically validate and assess the effectiveness of my research conclusions.

Here's what I learned:

1. QUBO has potential advantages in computer science, particularly for binary challenges. By merging it with mutual information, termed MIQUBO, enhancing the utilization of mutual information.

2. I got hands-on experience with D-Wave's quantum annealer, recognizing its ability to derive solutions more efficiently compared to traditional techniques for such challenges.

3. This project gave me the opportunity to refine my analytical skills. I mapped selected features to the Quantum Processing Unit (QPU) and meticulously analyzed the output to ensure the precision of the devised method.