Educational objectives Educational goals
The aim of the course is to introduce students to the application of optimization techniques to training problems arising in supervised machine learning.
Knowledge and understanding
Students are expected to gain insight into the fundamental models used in supervised machine learning (Deep Networks and Support Vector Machines), as well as the most recent optimization algorithms for determining the parameters (training) of such models and the techniques for selecting the hyperparameters that best fit the available data.
Applying knowledge and understanding
By the end of the course, students should be able to select the most appropriate machine learning model for the problem at hand, use standard software to develop suitable models, and develop new optimization algorithms for training.
Making judgements
Lectures, practical exercises, and project sessions will provide students with the ability to assess the main strengths and weaknesses of different machine learning models applied to case studies and to select the models that best fit the application.
Communication skills
By the end of the course, students will be able to identify the main features of a machine learning problem and explain the techniques for its solution to both specialized and non-specialized audiences. These abilities are tested and evaluated through projects developed in small groups, thereby encouraging teamwork and fostering a proactive and collaborative learning process. These abilities may also be assessed during the final oral examination.
Lifelong learning skills
Students are expected to develop the learning skills necessary to undertake further studies on the relevant topics with a high degree of autonomy. During the classes, students are encouraged to work on projects in small groups, thereby stimulating active participation and engagement. They are encouraged to consult supplementary research publications and Internet resources to identify the techniques and detailed choices needed to accomplish the assigned tasks effectively. These skills are tested and evaluated through the final project reports, in which students discuss the main issues related to the problems addressed and justify the choices made to overcome the encountered difficulties, based on the topics and materials covered in class.
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Educational objectives The goal of this course is to understand stochastic processes. However, as I am required to "translate" this objective into "Dublin Descriptors" and sub-objectives, I have added the following with the help of the School Office.
General Objectives
The goal of the course is to provide an overview of stochastic processes, with a focus on their applications in data science and machine learning. Regrettably for those who do not enjoy mathematics, probability theory and stochastic processes are essential for understanding how many algorithms work and for designing new ones. Knowledge of programming languages such as R, Matlab, or Python is useful but not strictly necessary. Programs developed in R will be used throughout the course.
Specific Objectives (Dublin Descriptors)
a) Knowledge and understanding
Understand the foundations of combinatorial stochastic processes, of Markov chains, and of Gaussian processes, as well as their applications in data science. Understand the principles of probabilistic causality and be able to apply these concepts to data science problems.
b) Applying knowledge and understanding
Simulate stochastic processes using Monte Carlo simulations and programming languages such as R, Matlab, or Python.
c) Making judgments
Analyze the advantages and limitations of different stochastic processes as models for real-world phenomena and identify the most appropriate model for a specific dataset.
d) Communication skills
Communicate effectively aspects of stochastic processes, including the solutions chosen and their potential applications.
e) Learning skills
Develop those skills that are necessary to continue studies in the field of stochastic processes, including the ability to undertake research activities in this area.
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Educational objectives Learning goals
Statistical Machine Learning provides a rigorous introduction to the statistical and probabilistic principles that underpin modern artificial intelligence, including predictive and generative AI, and data-driven decision making. The course presents machine learning as a statistical discipline, where learning algorithms are viewed as methods for inference from data under uncertainty.
The course combines theoretical foundations with methodological and computational aspects. Students will develop an understanding of probabilistic modelling, statistical inference, optimization and generalization theory, together with the practical skills required to implement, evaluate and compare modern learning algorithms.
Representative methodologies include kernel methods, deep neural networks, probabilistic generative models such as denoising diffusion probabilistic models (DDPMs), and modern uncertainty quantification techniques including conformal prediction. Throughout the course, particular emphasis is placed on principled model assessment, uncertainty quantification, and the interpretation of predictive models.
Theoretical results are complemented by programming assignments and a substantial project based on real datasets, allowing students to connect statistical principles with computational implementation using modern open-source scientific computing environments.
Knowledge and understanding
Upon successful completion of the course, students will understand the statistical principles underlying modern machine learning and their role in predictive and generative artificial intelligence. They will be able to interpret learning algorithms within a unified probabilistic framework, understanding how statistical modelling, inference, optimization and regularization jointly determine predictive performance and generalization.
Students will understand the assumptions, mathematical foundations and computational characteristics of the principal supervised and unsupervised learning methodologies, including kernel methods, (deep) neural networks and probabilistic generative models.
They will also understand the theoretical principles governing model selection, validation, complexity control/regularization, and uncertainty quantification, together with the statistical tools used to assess and compare learning algorithms.
Finally, students will acquire familiarity with modern scientific computing environments for implementing, analysing and experimentally evaluating statistical machine learning methods.
Applying knowledge and understanding
Upon successful completion of the course, students will be able to formulate complex data analysis problems within an appropriate statistical learning framework and identify suitable modelling strategies based on the characteristics of the data and the objectives of the analysis.
They will acquire the practical skills required to implement, train and compare modern machine learning methods, integrating statistical modelling with computational techniques to build complete data analysis pipelines.
Students will learn to assess predictive performance using principled statistical methodologies, quantify predictive uncertainty, and interpret the results in light of the assumptions and limitations of the adopted models.
Programming assignments and a final project will provide hands-on experience with real-world datasets, enabling students to bridge theoretical concepts with practical implementation and to develop reproducible machine learning solutions.
Making judgements
Upon successful completion of the course, students will have developed the ability to critically evaluate statistical learning methodologies from both theoretical and empirical perspectives.
They will be able to assess whether the assumptions underlying a learning model are appropriate for a given application, compare competing modelling approaches, and interpret empirical results in light of statistical evidence.
Particular emphasis is placed on understanding the role of uncertainty in statistical learning, enabling students to distinguish between predictive performance, statistical significance, and confidence in model outputs.
Students will develop the ability to critically assess the reliability, robustness and limitations of learning algorithms when applied to complex real-world data.
Communication skills
Students will develop the ability to communicate statistical and machine learning methodologies effectively through written reports and oral presentations.
They will learn to present methodological choices, experimental results, and quantitative evidence in a clear, rigorous and reproducible manner, adapting the level of technical detail to both specialist and non-specialist audiences.
The final project will also foster the ability to discuss modelling decisions, interpret experimental findings, and provide constructive scientific feedback on the work of peers.
Learning Skill
The course aims to develop the independent learning skills required for continued study and research in statistical machine learning and artificial intelligence.
By combining theoretical analysis with computational practice, students will acquire the ability to understand new methodologies from the scientific literature, critically evaluate their statistical foundations, and adapt them to novel application domains.
Particular emphasis is placed on developing a probabilistic mindset for reasoning under uncertainty, enabling students to understand emerging machine learning methodologies, integrate advances from the rapidly evolving AI landscape, and pursue lifelong learning with methodological rigour and intellectual independence.
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