85302 - DATA SCIENCE

Learning outcomes

At the end of the course, the student has an understanding of fundamental methods for the analysis of complex data. They are familiar with the main and most modern algorithms for data analysis and can implement them in a programming language. Laboratory activities enable the student to implement and perform data analysis on a computer and apply the studied methodologies to test cases.

Course contents

Summary Syllabus:

• Part I: Introduction to Fundamental Methods of Scientific Computing (linear algebra, optimization)
  
• Part II: Machine Learning
  

Detailed Syllabus:

Part I: Introduction to Fundamental Methods of Scientific Computing

1. Introduction: General and administrative information.

2. Linear Algebra:

   • Vector spaces, matrix operations
   • Eigenvalue problems
   • SVD decomposition
   • Other types of decomposition (LU, QR, Cholesky)
   • Systems of linear equations

3. Optimization:

   • Derivatives, gradients, Jacobian, Hessian
   • Different types of optimization (local, global, convex, non-convex)
   • Optimization methods (first-order, second-order)
   • Stochastic Gradient Descent (SGD) 

Part II: Machine Learning

1. Linear Models:

   • Binary regression (logistic)
   • Least squares linear regression
   • Regularization (l1 and sparsity)
   • Splines
   • Generalized linear models

1. Structuring Data Without Neural Networks:

   • Dimensionality reduction
   • Principal Component Analysis (PCA)
   • Kernel PCA
   • Clustering algorithms (k-means)

2. Supervised Learning:

   • Neural networks
   • Training and regularization
   • Convolutional Neural Networks (CNN)
   • Recurrent Neural Networks

3. Unsupervised Learning:

   • Maximum Likelihood Estimation (MLE)
   • Restricted Boltzmann Machine
   • (Variational) Autoencoders (VAE)
   • Generative Adversarial Networks (GANs)

Readings/Bibliography

Necessary Readings:

Lecture notes.

Suggested Readings:

1. Calcolo scientifico. Esercizi e problemi risolti con MATLAB e Octave, A. Quarteroni et al., Springer Verlag (2017)
2. Data-driven modeling & scientific computation: methods for complex systems & big data, J. N. Kutz, Oxford University Press (2013)
3. Probabilistic Machine Learning: An Introduction, K. P. Murphy, The MIT Press (2022)
4. Lecture Notes: Machine Learning for the Sciences, T. Neupert et al., arXiv:2102.04883v2 (2022)
5. Modern applications of machine learning in quantum sciences, A. Dawid et al., arXiv:2204.04198 (2022)

Teaching methods

Lectures at the blackboard and attendance in computer labs.

Given the type of activities and teaching methods adopted, participation in this educational activity requires all students to have previously completed modules 1 and 2 of the safety training for study environments, in e-learning mode.

Assessment methods

The assessment of learning in the Data Science course is aimed at verifying the achievement of the learning objectives, defined in terms of knowledge ("knowing") and skills ("knowing how to do"), as outlined in the “Learning outcomes” framework. The evaluation consists of two components, which contribute equally to the final grade:

Assessment of Laboratory Reports (50%)

Participation in laboratory activities is an integral part of the learning process and provides a fundamental opportunity to acquire practical skills ("knowing how to do") in data analysis, programming, and the use of tools and techniques specific to Data Science.

Throughout the course, guided lab activities will be proposed. At the end of each activity, students must submit individual reports (according to the instructions provided by the instructor), which must include a description of the tasks performed, the results obtained, and a critical commentary.

Reports must be submitted by the deadlines communicated by the instructor, generally before the exam session. Failure to meet the deadlines may negatively affect the evaluation.

The reports will be assessed based on:

• completeness and accuracy in carrying out the assigned tasks;

• correctness of data analysis and interpretation;

• ability to communicate results clearly, in a structured and relevant manner;

• command of the tools used.

The score obtained in this component contributes 50% to the final grade.

Oral Exam on Course Content (50%)

The oral exam is designed to assess the acquisition of theoretical knowledge and the ability to connect it with the practical activities carried out during the course. In particular, the following will be evaluated:

• understanding of the fundamental concepts of Data Science (e.g., statistics, machine learning, data cleaning, visualization);

• ability to provide critical arguments;

• ability to synthesize and present ideas clearly;

• any individual in-depth exploration.

The oral exam may only be taken after the successful submission and positive evaluation of the laboratory reports, as the practical-theoretical component is a prerequisite for the theoretical assessment.

The score obtained in the oral exam contributes 50% to the final grade.
The use of notes, books, or electronic devices is not allowed during the oral exam.

Evaluation Criteria and Final Grade Assignment

The final grade (out of 30) is calculated as a weighted average (50%+50%) of the laboratory report evaluation and the oral exam. Honors (“cum laude”) may be awarded in cases of demonstrated excellence in both components.

The following grading scale is used as a guideline:

• <18: insufficient knowledge and/or skills; failure to meet minimum objectives

• 18–21: minimum knowledge and skills acquired; basic presentation

• 22–24: satisfactory competence; correct and reasoned presentation

• 25–27: good command of the material; autonomy and application ability

• 28–30: thorough understanding; clear and well-structured presentation; strong critical skills

• 30 cum laude: excellence, active participation, and demonstrated ability for independent in-depth analysis

Class Attendance

Attendance is not mandatory, but strongly recommended, especially for laboratory sessions, as practical activities are essential for acquiring the required operational skills.

Type of Exam and Nature of the Evaluation

The course includes a graded evaluation (out of 30 points).
The assessments cover both theoretical knowledge ("knowing") and practical skills ("knowing how to do"), in line with the learning outcomes of the course.

Exam Registration

To take the oral exam, registration through the university’s official platform (AlmaEsami) is mandatory within the specified deadlines. Students who fail to submit the required reports within the established time frame will not be allowed to take the oral exam.

Teaching tools

Blackboard, Projector, Informatic laboratory.

Office hours

See the website of Domenico Di Sante