- Minimal background in mathematics and statistic
- analysis and calculus (integral, derivatives, study of functions, … )
- basic statisticx concepts
- Minimal knowledge on statistical modeling
- Basic expertise with Python and Jupyter Notebook
- installing new packages
- writing basic code and running pipelines
- knowledge of standard libraries (numpy, pandas, scikit-learn)

Assignments: 3 in total, 10 points.

The completed assignments should be sent within 2 weeks from the release date. The notebook must be renamed as <candidate name>_<candidate surname>_<assignment_number>.ipynb and sent to my email address.

Final exam: 10 points

Support slides | Notebook | Assignments | References | |
---|---|---|---|---|

Day 1 | Introduction | Basic Probability Theory | / | / |

Day 2 | / | Probability Distributions | / | [BDA]:Ch1 |

Day 3 | / | Inference in Bayesian models: theory and practice | Assignments 1 | [BDA]:Ch1, [McE]:Ch3 |

Day 4 | / | Practical Exercises 1 , , Data | / | [BDA]:Ch1, [McE]:Ch3 |

Day 5 | / | Laplace approximation , tools.py , Data (from [McE]) | / | [McE]:Ch4 |

Day 6 | / | Bayesian linear regression | / | [McE]:Ch4 |

Day 7 | / | Practical exercises 2 | Assignments 2 , data | [McE]:Ch8, Ch10 |

Day 8 | / | MCMC | / | [McE]:Ch8, [Bet2018], [Stan] |

Day 9 | / | Model Comparison and Logistic Regression | Assignments 3 , data | [McE]:Ch8, Ch10, [Stan] |

Day 9 | / | WAIC and Bayesian classification , Pystan3.0 version | / |

[BDA] * Bayesian Data Analysis*. A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari, D.B. Rubin; Chapman and Hall/CRC, 2014, 3rd Edition.

[McE] * Statistical Rethinking*. R. McElreath; Chapman and Hall/CRC, 2016, 3rd Edition.

[Bet2018] * A Conceptual Introduction to Hamiltonian Monte Carlo*. M. Betancourt; ArXiv

[Stan] * Stan Documentation* . Stan Development Team.

- Minimal background in mathematics and statistic
- analysis and calculus (integral, derivatives, study of functions, … )
- basic statistical concepts (expectation, median, covariance, distributions, … )
- Minimal knowledge on statistical modeling
- regression
- expectation, variance/covariance, statistical descriptors
- Basic expertise with Python and Jupyter Notebook
- installing new packages
- writing basic code and running pipelines
- knowledge of standard libraries (numpy, pandas, scikit-learn)

Three sessions of assignments: 10 points.

The completed assignments should be sent within 2 weeks from the release date. The notebook must be renamed as <candidate name>_<candidate surname>_<assignment_number>.ipynb and sent to my email address.

Final exam: 10 points

Support slides | Notebook | Assignments | References | |
---|---|---|---|---|

Day 1 | Introduction | Basic Probability Models and Sampling in Python | / | / |

Day 2 | / | Data Generation - Regression & Classification | / | [Gu2003], [Gu2007] |

Day 3 | / | Bias and Variance | assignments 1 | [HTF2001]:Ch7, [Bis2006]:Ch1,Ch3, [Gem1992] |

Day 4 | / | Bootstrap and bagging | / | [Brei1996], [Efr1986], [HTF2001]:Ch7 |

Day 5 | / | Cross-validation I | assignments 2 | [HTF2001]:Ch7 |

Day 6 | / | Cross-validation II | / | [HTF2001]:Ch7, [Koh1995], [Rao2008] |

Day 7 | / | Information Criteria I | Assignment 3 | [McE2016]:Ch6 |

Day 8 | / | Information Criteria II | [McE2016]:Ch6, [Wag2004], [Sym2011] | |

Day 9 | / | Class exercises | / | / |

[Gu2003] * Design of experiments for the NIPS 2003 variable selection benchmark*. I. Guyon, 2003. link

[Gu2007] * Competitive baseline methods set new standards for the NIPS 2003 feature selection benchmark*. I. Guyon, J. Li, T. Mader, P.A. Pletscher, G. Schneider, M. Uhr. Pattern Recognition Letters, 28, 1438-1444, 2007.

[HTF2001] * The Elements of Statistical Learning*. T. Hastie, R. Tibshirani, and J. Friedman. Springer Series in Statistics Springer New York Inc., New York, NY, USA, 2001.

[Bis2006] * Pattern Recognition and Machine Learning*. C.M. Bishop. Springer-Verlag Berlin, Heidelberg, DE, 2006.

[Gem1992] * Neural networks and the bias/variance dilemma*. S. Geman, E. Bienenstock, R Doursat. Neural Computation, 4:2, 1-58, 1992.

[Brei1996] * Bagging predictors *. L. Breiman. Machine learning, 24(2), 123-140, 1996

[Efr1986] * Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy*. B. Efron, R. Tibshirani, Statistical science, 54-75. 1986.

[Koh1995] * A study of cross-validation and bootstrap for accuracy estimation and model selection*. R. Kohavi. IJCAI, 14:2, 1995.

[Rao2008] * On the dangers of cross-validation. An experimental evaluation. * R. Barat Rao, G. Fung, and R. Rosales. Proceedings of the 2008 SIAM International Conference on Data Mining. Society for Industrial and Applied Mathematics, 2008.

[McE2016] * Statistical Rethinking. A Bayesian Course with Examples in R and Stan. * R. McElreath. T&F Crc Press, 2016.

[Wag2004] * AIC model selection using Akaike weights.* E.J. Wagenmakers , S. Farrell. Psychon Bull Rev. 11(1):192-6, 2004.

[Sym2011] * A brief guide to model selection, multimodel inference and model averaging in behavioural ecology using Akaike’s information criterion.* M.R. Symonds, A. Moussalli, A. Behavioral Ecology and Sociobiology, 65(1), 13-21, 2011.

P. Geladi and B. Kowalski.* Partial least-squares regression: a tutorial*, Analytica Chimica Acta, 1985.

S. Szymczak, J.M. Biernacka, H.J. Cordell, O. González-Recio, I.R. König, H. Zhang, Y.V. Sun. *Machine learning in genome‐wide association studies*, Genetic Epidemiology 2009.

M. Silver, E. Janousova, X. Hua, P.M. Thompson, G. Montana. *Identification of gene pathways implicated in Alzheimer's disease using longitudinal imaging phenotypes with sparse regression*, NeuroImage 2012.

E. Le Floch, V. Guillemot, V. Frouin, P. Pinel, C. Lalanne, L. Trinchera, A. Tenenhaus, A. Moreno, M. Zilbovicius, T. Bourgeron, S. Dehaene, B. Thirion, J.B. Poline, E. Duchesnay. *Significant correlation between a set of genetic polymorphisms and a functional brain network revealed by feature selection and sparse Partial Least Squares*. Neuroimage. 2012 Oct 15;63(1):11-24.

J. Liu and V. Calhoun. *A review of multivariate analyses in imaging genetics*, Frontiers in Neuroinformatics, 2014.

M. Lorenzi, A. Altmann, B. Gutman, S. Wray, C. Arber, D.P. Hibar, N. Jahanshad, J.M. Schott, D.C. Alexander, P.M. Thompson, S. Ourselin. *Susceptibility of brain atrophy to TRIB3 in Alzheimer’s disease, evidence from functional prioritization in imaging genetics*. PNAS March 20, 2018 115 (12) 3162-3167.

L. Antelmi, N. Ayache, P. Robert, M. Lorenzi. *Sparse Multi-Channel Variational Autoencoder for the Joint Analysis of Heterogeneous Data*. 36th International Conference on Machine Learning (ICML), 2019.

L. Shen and P.M. Thompson. *Brain Imaging Genomics: Integrated Analysis and Machine Learning*. Proceedings of the IEEE, 2019.