LEARNING OUTCOMES

L'insegnamento fornisce gli strumenti essenziali e le competenze operative per l’analisi quantitativa di dati e segnali di interesse per la medicina e la biologia, in una prospettiva probabilistica

AIMS AND LEARNING OUTCOMES

The aim of this course is to provide students with the essential tools for quantitative analysis of data and signals of interest for medicine and biology.

By the end of the course the students will be able to:

1. Design and apply methods of analysis and modelling of data - including temporal data (signals) - of interest for medicine and biology

2. Identify the correct approach (model selection, model identification, data visualization) for a specific data analysis problem

3. Use MATLAB to correctly and effectively visualizing biomedical data and signals and to implement models of them

PREREQUISITES

There are no formal prerequisites, but  the course requires solid foundations in mathematical analysis and linear algebra.

TEACHING METHODS

The course is organised as a combination of lectures and lab activities. 

Lectures will focus on theory and methods for data analysis. 

Lab activities will focus on application to real data analysis problems in the context of bioengineering.

In AY 2021-2022 the course will be taught in presence but all lectures and lab activities will be also offered at a distance, both online and offline.

SYLLABUS/CONTENT

A. Data Analysis and Data Display (wk 1-2)
Data types. Descriptive statistics. Analysis as modeling. Statistical data analysis. Regressione. Visual display of information.

B.Probability density estimates (wk 3-4)
Unsupervised learning. Gaussian model. Principal Component Analysis, FactorAnalysis, Independent Component Analysis, Cluster analysis and the EM algorithm. Graphical models. Regression, decision theory, factor analysis as graphical models. 

C. Pattern analysis and decision theory (wk 5-6)
Bayesian decision theory. Bayes classifiers. Logistic classifiers. Performance of a classifier: ROC curve. Generalized linear models. Introduction to neural networks. 

D. Model selection (wk 7-8). Statistical Inference. Hypothesis testing. General Linear models and the analysis of variance. Mixed-effects models. Bayesian modelselection.

E. Dynamic Models (wk 9-10). Temporal data (signals). Discrete vs continuoussignals. Hidden Markov Models, Linear dynamical systems. Kalman filter.

F. System identification (wk 11-12). Parametric vs nonparametric models. Black-box vs grey-box models. Least square estimators. Prediction error methods. Compartmental models. Application to pharmakinetics and epidemiology .

RECOMMENDED READING/BIBLIOGRAPHY

Murphy, KP. Machine Learning: A Probabilistic Perspective.  MIT Press, 2012.