48
Mathematics for Economics, Actuarial Studies and Finance
REGGIO DI CALABRIA
Overview
Date/time interval
Syllabus
Course Objectives
In recent years, the convergence of Artificial Intelligence (AI) and Decision-Making processes has become a transformative force across a wide range of industries. The integration of AI technologies is reshaping entrepreneurship and management landscapes in sectors such as healthcare, finance, manufacturing, and retail in Supply Chain issues. Machine learning models and advanced neural networks, including Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and Generative Adversarial Networks (GANs), have achieved significant breakthroughs in fields like computer vision, natural language processing, and predictive analytics. Their capabilities extend to practical applications in healthcare, business, and autonomous vehicles, where they excel in analyzing and leveraging complex data. However, the intricate architectures and inherent opacity of deep learning neural networks and supervised machine learning pose challenges to their comprehensive understanding, limiting their application in critical areas, particularly in interdisciplinary domains. To tackle this issue and expand the scope of research, through this course, we are broadening the focus of our mission to encompass successful applications of Machine Learning and Deep Learning Neural Networks. This expansion aims to showcase their effectiveness in extracting valuable insights from complex datasets, thereby enhancing understanding and application across various contexts
Course Prerequisites
Mathematical Tools: Structures on Vector Spaces, Linear Algebra, Statistics, and Informatics.
Teaching Methods
Teaching Methods: Lectures, Laboratory activities at the Decision LAB, Seminars and Workshops
Assessment Methods
Assessment Methods: Written and oral examination
Evaluation Criteria:
- 30 cum laude: complete, in-depth, and critical knowledge of the topics, excellent language skills, complete and original interpretative ability, full ability to independently apply knowledge to solve the proposed problems;
- 28 - 30: complete and in-depth knowledge of the topics, excellent language skills, complete and effective interpretative skills, able to independently apply the knowledge to solve the proposed problems;
- 24 - 27: knowledge of the topics with a good degree of mastery, good command of the language, correct and sure interpretative ability, good ability to correctly apply most of the knowledge to solve the proposed problems;
- 20 - 23: adequate knowledge of the topics but limited mastery of the same, satisfactory language skills, correct interpretative ability, more than sufficient ability to independently apply the knowledge to solve the proposed problems;
- 18 - 19: basic knowledge of the main topics, basic knowledge of the technical language, sufficient interpretative ability, and sufficient ability to apply the acquired basic knowledge.
Texts
Massimiliano Ferrara: "Intelligenza Artificiale Affidabile: una nuova frontiera della Conoscenza - Dalla teoria matematica alle applicazioni nel Decision-Making - ". EGEA BOCCONI, Milan, 2025
Contents
Contents
- Mathematical Foundations of Explainable Artificial Intelligence
- Introduction to XAI and historical motivation
- Linear algebra and matrix decompositions
- Information theory and optimization
- Shapley values and SHAP applications
- Interpretability techniques (LIME, gradient-based methods)
- Evaluation metrics for XAI
- Security and Robustness in AI Systems
- Data Poisoning: taxonomy and mechanisms
- Mathematical framework for poisoning attacks
- Defensive strategies and robust algorithms
- Dataset Core approach to preserve informational value
- Deep Learning: Architectures and Functions
- Activation functions: mathematical properties and applications
- ReLU, Sigmoid, TanH: comparative analysis
- Multi-temporal dynamics in deep learning
- Optimization and convergence
- Game Theory for AI Security
- Game-theoretic formulation of AI security
- Nash equilibria and Stackelberg games
- Evolutionary game theory applied to AI
- Multi-agent reinforcement learning
- Topological Data Analysis (TDA)
- Foundations of algebraic topology
- Simplicial complexes and filtrations
- Persistent homology
- Applications to algorithmic robustness
- Adversarial attack detection through TDA
- Unified Framework: XAI and Robustness
- Theoretical integration of explainability and robustness
- Unified framework architecture
- Robust SHAP values and stable counterfactuals
- Multi-objective optimization
- Practical Applications in Decision-Making
- Robust and interpretable computer vision
- Natural language processing with XAI
- Secure recommendation systems
- Healthcare and AI diagnostics
- Machine Learning Models for Applications
- Linear and logistic regression
- Support Vector Machines
- Random Forest and ensemble methods
- Neural networks and backpropagation
- Evaluation and validation techniques
- Case Studies and Implementations
- Credit scoring with ML
- Algorithmic trading
- Supply chain optimization
- Fraud detection systems
- Complete Python implementations
- Ethical Considerations and Future Perspectives
- Algorithmic bias and fairness
- Privacy and transparency
- AI sustainability
- Regulatory compliance
- Future trends and AutoML
More information
None