Corso di laurea magistrale Interateneo in Fisica dei sistemi complessi

Provide an overview of the most recent tools in the context of Data Analysis
- Discuss a few topical applications both in the context of Human and of Natural Sciences
- Introduce a few of the most recent computational tools for data analysis and inference

At the end of course the student will reach a good knowledge of the most advanced results in Data Analysis and Statistical Inference

Interactive lessons with hands-on in-class analysis of data sets

 The course evaluation will be based on a final  project  and an oral examination, during which the student has to develop ab initio two or three  of the topics explained during the lectures. In case the exam fails, it cannot be repeated earlier than two weeks after the first attempt.

 The course is composed by two set of lectures.  The first is given by  L. Martignetti and the second by M. Chertkov

First part:

    1. Introduction, big data, examples, job orientation

    2. Data acquisition, experimental design, cleaning, pre-processing - types of data: binary, category, discrete, continous - sequence data analysis: sequence entropy, motif discovery, repeats - Normalization - Outliers - Batch effects - Missing values (imputation, not at random missing values)

    3. Exploratory data analysis - descriptive statistics - data distribution: gaussian, Poisson, binomial - two variables: regression - correlation - many variables - Dim reduction: PCA - outliers - clustering - NMF - ICA

    4. Unsupervised/Supervised inference - statistical tests (parametric, non parametric)

    5. Networks - casual networks - bayesian networks - similarity networks - Network component analysis - bipartite networks - modularity - community detection - what to do with these networks (graph analysis) => minimal cut sets => hubs, connectivity....

    6. From networks to a formal models - visualisation of data - use of data for construction of networks / models (ROMA, GSEA) - mathematical modelling (method and motivation) - different types of formalisms - ode - logical modelling - applications - pipeline of modelling applications - data to models - precision medicine - systems pharmacology

    7. Multi-level Data integration - multiplex - SNFIntroduction to Data Gathering and Analysis

Second part:

1) Graphical Models (Language) and Structured Statistical Inference and Learning (problem formulations) in Computer Science, Information Theory and Physics (intro).

2) Computational Complexity & Algorithms (Deterministic & Stochastic).

3) Statistical Inference as an Optimization -- from Partition Function and Marginal Probabilities to Free Energy (Kublack-Leibler Functional).

4) Mean-Field, Belief Propagation, Linear Programming -- Variational Approaches, Relaxations, Lower and Upper Bounds. Exact & Heuristic approaches. Iterative Algorithms.

5) Modern Analysis and Algorithmic Tools. Review of Loop Series, Cummulant Expansions, Computational Trees & Graph Cover Approaches.

6) Sample and Algorithmic Complexity of Learning. Graphical Model Learning. From Graphical Models to Neural Networks and Deep Learning.

Lecture notes and references provided therein.