Uncertainty Modelling in Data Science 1st ediiton by Sebastien Destercke, Thierry Denoeux, Maria Angeles Gil, Przemyslaw Grzegorzewski, Olgierd Hryniewicz ISBN 3319975471 9783319975474

Introduction to Uncertainty in Data Science

• Definition of uncertainty in data science and machine learning
• Sources of uncertainty: measurement, model, and computational
• Types of uncertainty: epistemic vs. aleatoric
• Role of uncertainty in decision-making and risk analysis

Mathematical Foundations of Uncertainty

• Basic probability theory and statistics
• Probability distributions and their applications
• Bayesian inference and uncertainty propagation
• Fuzzy sets and fuzzy logic

Uncertainty Representation Models

• Probability theory-based models
• Fuzzy sets and possibility theory
• Evidence theory and Dempster-Shafer theory
• Imprecise probability and imprecise credal sets

Uncertainty Propagation and Inference

• Methods for propagating uncertainty in data models
• Monte Carlo methods and their use in uncertainty propagation
• Sensitivity analysis and uncertainty quantification
• Approximation techniques (e.g., polynomial chaos, Gaussian processes)

Uncertainty in Machine Learning

• Incorporating uncertainty into supervised learning
• Bayesian machine learning models (e.g., Bayesian networks, Gaussian processes)
• Uncertainty in deep learning (e.g., Bayesian deep learning, dropout as a form of uncertainty)
• Model uncertainty and uncertainty calibration

Multimodal Uncertainty and Fusion Techniques

• Combining different sources of uncertainty
• Data fusion techniques and decision support systems
• Multi-sensor data fusion and uncertainty management
• Consensus and decision-making under uncertainty

Applications of Uncertainty Modeling

• Uncertainty in classification and regression tasks
• Applications in data-driven decision support
• Uncertainty in time-series forecasting
• Uncertainty in anomaly detection and outlier analysis
• Risk assessment and management in industrial applications

Handling Large-Scale Uncertainty in Big Data

• Challenges in uncertainty modeling with big data
• Scalable techniques for uncertainty propagation in large datasets
• Parallel and distributed uncertainty analysis
• High-dimensional uncertainty and feature selection

Advanced Topics in Uncertainty Modelling

• Handling epistemic uncertainty in complex models
• Dynamic uncertainty models for evolving data
• Uncertainty in optimization and decision-making under uncertainty
• Use of artificial intelligence for managing uncertainty

Uncertainty Visualization and Communication

• Techniques for visualizing uncertainty
• Communicating uncertainty to stakeholders and decision-makers
• Uncertainty in scientific communication and public understanding

Case Studies and Practical Applications

• Uncertainty modeling in medical diagnostics
• Environmental modeling and climate prediction
• Autonomous systems and robotics
• Finance and economic modeling under uncertainty

Conclusion and Future Directions

• Summary of key concepts
• Open problems in uncertainty modeling
• Emerging trends and technologies in uncertainty analysis
• The future of uncertainty in data science and AI